tag:blogger.com,1999:blog-59500747944658318982024-02-21T09:18:03.748-08:00Nested ToriA blog dedicated to finding AWESOME visualizations in mathematics and other scientific disciplines. Even if you're not a mathematician or scientist, enjoy the view!Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.comBlogger45125tag:blogger.com,1999:blog-5950074794465831898.post-88180110002123581162023-03-05T13:25:00.003-08:002023-03-05T13:25:00.151-08:00Interstellar Lily Pads<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEi9no1K1IFhi0CnMZ7qMNWgEvi-k-sESPCuTZR7picNN2PirbNTpz0cRHGzXEoXrWz8RcxoC_OCfVKh2UVJSbGOsJK60axbx6Vl1xrbeN-yCllafFLWzTb6UvSXy4p9QF7emhkt92GyysetRW7qegk3L0vq__aIhYX3CwG5qHct-Lrk6YDgIdSVh3zI" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1320" data-original-width="1634" height="517" src="https://blogger.googleusercontent.com/img/a/AVvXsEi9no1K1IFhi0CnMZ7qMNWgEvi-k-sESPCuTZR7picNN2PirbNTpz0cRHGzXEoXrWz8RcxoC_OCfVKh2UVJSbGOsJK60axbx6Vl1xrbeN-yCllafFLWzTb6UvSXy4p9QF7emhkt92GyysetRW7qegk3L0vq__aIhYX3CwG5qHct-Lrk6YDgIdSVh3zI=w640-h517" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">I'll someday explain what this is, but for now just enjoy! (Well, this is ultimately a visualization blog. The math explanations are bonus.)</div><p></p>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-62954315714742236642020-12-10T12:49:00.008-08:002020-12-10T12:52:00.652-08:00Some Loxodromes<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_34eO2qOhD7B1bCobpiRbbHF5UQhjj8Z4xy0c2fsH22DPVwF63QAwefBygvVwX8XKZWAPAU9I0QLl4UR3ByWOMt-9vr5R-YMHCRX4knJ49eSCUiD7SMz5zY6SJGYz8JMqyKfFVOCSlUQ/s1227/loxodromes.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1203" data-original-width="1227" height="628" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_34eO2qOhD7B1bCobpiRbbHF5UQhjj8Z4xy0c2fsH22DPVwF63QAwefBygvVwX8XKZWAPAU9I0QLl4UR3ByWOMt-9vr5R-YMHCRX4knJ49eSCUiD7SMz5zY6SJGYz8JMqyKfFVOCSlUQ/w640-h628/loxodromes.png" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>Loxodromes are generated by curves of constant bearing on a sphere (always making a constant angle with circles of latitude). If you go in a direction and proceed forever in something that's NOT one of the 4 cardinal directions, you'll get something very interesting. It's not really obvious that you actually will spiral forever around a pole. These have the simplest expression in <a href="http://www.nestedtori.com/2020/11/the-uniform-distribution-on-spheres.html">isothermal coordinates</a> we talked about in the last post: they can be represented simply as straight lines in the $uv$ plane (well, if you allow $v$ to range over all of $\mathbb R$ and wrap around; if you insist on $v$ only being in an interval of length $2\pi$, then after the line goes off the top edge, you make it jump back to the bottom edge so you get something that looks like this: $/////$. So the full parametrization would be: $(\operatorname{sech}u \cos(au+b), \operatorname{sech}u \sin(au+b), \tanh u)$. It is easy to intuitively see why the angle between these curves and the $\theta$ curves are constant: the $uv$-plane is first mapped (conformally) to the whole $z$-plane by $(e^u\cos v, e^u\sin v)$, and then the (conformal) stereographic projection wraps it all up. The same cannot be said of the $\varphi\theta$ plane (to confirm, of course, you need to mess with metric coefficients in that last post).Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com2tag:blogger.com,1999:blog-5950074794465831898.post-26678080764866624932020-11-28T00:42:00.001-08:002020-11-28T00:42:24.434-08:00The Uniform-Distribution-on-the-Sphere's Nemesis: Isothermal Coordinates<div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiIkJT2U958-w7-KnkOyLTRP0bQkZbAZ2w7q9FPvr5_WBA5ZNidh37E96iW0ewR8LXXV0cVTBsjjfqTbUEPUqbAWNoYow61vsMGz5f3s9U-WQK7qV6ZpGWHYgYEfh0-8L1jp6boBuw8Hc/s1264/Untitled+2.jpg" style="display: block; padding: 1em 0px; text-align: center;"><img alt="" border="0" data-original-height="1264" data-original-width="1264" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiIkJT2U958-w7-KnkOyLTRP0bQkZbAZ2w7q9FPvr5_WBA5ZNidh37E96iW0ewR8LXXV0cVTBsjjfqTbUEPUqbAWNoYow61vsMGz5f3s9U-WQK7qV6ZpGWHYgYEfh0-8L1jp6boBuw8Hc/s600/Untitled+2.jpg" width="600" /></a>Inspired by the last post where the conformal version of the polar grid is $(x,y) = (e^u \cos v, e^u \sin v)$ i.e. the radius is now exponentiated (namely what looks like a grid of squares in the domain gets mapped to what looks like squares in the range: the concentric circles bunch up much more densely close to the origin, to correspond to radial lines converging at the origin), I set out to do it on the sphere as well (that conformal polar grid is simply the image of the complex plane under the complex exponential $e^z$). This is in some sense the polar (hah) opposite of something that would produce a <a href="http://www.nestedtori.com/2015/09/distributing-points-on-spheres-and.html">uniform distribution of points on a sphere</a>, because this map would assign each square an equal chance (so of course, the closer you get to the poles, the squares are smaller and more of them encompass the same space in the image, so they'll be much more densely packed).</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">The quickest way to see this is to note the <a href="http://www.nestedtori.com/2015/09/clifford-tori.html#stereo">stereographic projection</a> is a conformal map, and has the formula</div><div class="separator" style="clear: both;">\[(x,y) \mapsto \left(\frac{2x}{x^2+y^2+1}, \frac{2y}{x^2+y^2+1}, \frac{x^2+y^2-1}{x^2+y^2+1}\right)\]</div><div class="separator" style="clear: both;">and with a substitution of the complex exponential, you get \[(u,v) \mapsto \left(\frac{2e^u \cos v}{e^{2u}+1}, \frac{2e^u \sin v}{e^{2u}+1}, \frac{e^{2u}-1}{e^{2u}+1}\right) = \left(\frac{2}{e^u+e^{-u}}\cos v, \frac{2}{e^u+e^{-u}}\sin v, \frac{e^u-e^{-u}}{e^u+e^{-u}}\right)\]</div><div class="separator" style="clear: both;">I rewrote that in that form for fans of hyperbolic functions, which gives the map </div><div class="separator" style="clear: both;">\[
(u,v) \mapsto(\operatorname{sech} u \cos v, \operatorname{sech} u \sin v, \tanh u)\] (hyperbolic secant seems to be one of the least used ones; $\LaTeX$ doesn't recognize it!). But the upshot is, this formula looks very similar to the usual geographic coordinate system (just swapping out some transcendental functions).</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGhhNSPSrt5oYmvyRbMUv8gxQpzBj2wWk_WARoR14LlLpqspQnv8t_gO1ykTSXJEVThjR4TS08tIW0zwsRJcbez4IFZ7V5hnZt6sqW8iLtyes6UB6fOmdq8YL62bt6v1NPoeFEF-lX0dc/s2048/isotherm.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="2048" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGhhNSPSrt5oYmvyRbMUv8gxQpzBj2wWk_WARoR14LlLpqspQnv8t_gO1ykTSXJEVThjR4TS08tIW0zwsRJcbez4IFZ7V5hnZt6sqW8iLtyes6UB6fOmdq8YL62bt6v1NPoeFEF-lX0dc/w640-h640/isotherm.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Another version with finer grid lines. Notice how they cluster at the top.</div><div><br /></div></div><div class="separator" style="clear: both;">Another way of looking at this is via manipulation of the metric coefficients directly, which raises some interesting points on the nature of the Laplace equation. If we consider the standard geographic parametrization$(x,y,z) = (\sin\varphi\cos\theta, \sin\varphi\sin\theta, \cos\varphi)$ with Euclidean metric $g = ds^2 = d\varphi^2 + \sin^2 \varphi\; d\theta^2$. To say that the parametrization is conformal (grid squares to grid squares) is to say that there are some parameters $u$ and $v$ and a function $\sigma$ such that $g = \sigma^2(du^2 + dv^2)$ (forcing the matrix to not only be diagonal, but a multiple of the identity). If we set things up so that $du = -\csc\varphi d\varphi$ and $dv = d\theta$, then $\sin^2\varphi (du^2 + dv^2) = d\varphi^2 + \sin^2\varphi\; d\theta^2)$. Consulting trusty integral tables, Wolfram Alpha'ing it, or whatever, we find that this differential equation gives $u = \ln(\csc \varphi + \cot \varphi) + C$. One can make it this derivation a little less "out of the blue" situation in a very interesting derivation of Laplace's equation using certain complex analysis hackery (George Springer's <i>Introduction to Riemann Surfaces</i>, section 1-3). We'll derive this another day, but the summary is, we end up deriving that $u$ has to satisfy the spherical Laplace equation \[\frac{1}{\sin\varphi} \frac{\partial}{\partial \varphi}\left(\sin \varphi \frac{\partial u}{\partial \varphi}\right) + \frac{1}{\sin \varphi} \frac{\partial^2 u}{\partial \theta^2} = 0,\] or really, it only has to satisfy this on an open subset of the sphere, in this case, a sphere with two points deleted. This fact often gets glossed over by people talking about geometry; we know that on a sphere, the only harmonic functions that are actually defined on the sphere everywhere are constant functions—so we can only find "interesting" harmonic functions on a sphere if they blow up at certain points. Using the very reasonable assumption that such a function $u$ should be independent of $\theta$, we derive $\frac{d}{d \varphi} \left(\sin\varphi \frac{d u}{d \varphi}\right) = 0$, making $\sin\varphi \frac{d u}{d \varphi} = C_1$ a constant, and $\frac{du}{d\varphi} = C_1 \csc \varphi$ to finally get $u = C_1 \ln(\csc \varphi + \cot \varphi) + C_2$, as before (just with two degrees of freedom, namely $C_1$ controls what the initial spacing of the grid lines, and $C_2$ controls what the value is at the equator). This function blows up at the poles, a fact which manifests itself visually by the grid curves $u =$ constant become more closely spaced together at the poles (and become infinitely dense there, meaning, this is only a valid coordinate system in the sphere outside the poles). We just set $C_1 = 1$ and $C_2 = 0$, which assigns the equator to $u=0$.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Finally, we have to do some algebra, though, to get to where we want: trying to find the inverse of $u = \ln(\csc \varphi + \cot \varphi)$. This says $e^u = \csc\varphi+\cot\varphi = \frac{1+\cos\varphi}{\sin\varphi}$. This is just $\frac{1+z}{r}$ where $r$ is the cylindrical coordinate $\sqrt{x^2+y^2}$. But if we're on the sphere, $z^2 + r^2 =1$, so this gives us \[e^{2u} = \frac{(1+z)^2}{1-z^2} = \frac{1+z}{1-z}.\] Rearranging we get $e^{2u}-e^{2u}z = 1+z$, or $z(1+e^{2u}) = e^{2u}-1$. This gives \[z=\frac{e^{2u}-1}{e^{2u}+1} = \frac{e^{u}-e^{-u}}{e^{u}+e^{-u}} = \tanh u.\]. To get the $x$ and $y$, we note that $\sin\varphi = r = e^{-u}(1+z) = e^{-u}(1+\tanh u)$. Finally,</div>\[
1+ \tanh u = \frac{\cosh u + \sinh u}{\cosh u} = \frac{e^u}{\cosh u}, \] which, multiplying by the $e^{-u}$ gives $\frac{1}{\cosh u}$ or $\operatorname{sech} u$. <div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">The coordinates we derived are called <i>isothermal coordinates</i>, and knowing what a big fan I am of <a href="http://www.nestedtori.com/2016/05/a-calculation-in-statistical-mechanics.html">stat mech</a>, I'd like to fully understand the origin of the term someday. Finally, one might ask if there are coordinate systems (conformal or otherwise) that will cover up all the sphere without weird coordinate singularities like that. The answer is <i>no, </i>and the short explanation of why is because a smooth vector field on the sphere must vanish somewhere (the <i>hairy ball theorem</i>), and since coordinates always set up vector fields (take the vector in the direction of a coordinate curve) and aren't supposed to collapse at good points. This is a long topic for another day (we'll show some pretty cool coordinate systems on the sphere, though!)</div>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com1tag:blogger.com,1999:blog-5950074794465831898.post-91939118087217022232020-10-31T23:56:00.009-07:002020-11-28T00:36:09.869-08:00Happy Halloween from Nested Tori!<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_Jwzl6icGAdq5sB-RwfDNWX7k0OJCIB_AQAyEfayx9Yez7D43yjYmmEQ6H5D_GWeBDY_4e-PFoXJmMtig39KCRcDSaW7l0iTeqNz8WuMnfIrE70P8hEjFk3M0JhpsWVF-phE-wKARNSE/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1365" data-original-width="2048" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_Jwzl6icGAdq5sB-RwfDNWX7k0OJCIB_AQAyEfayx9Yez7D43yjYmmEQ6H5D_GWeBDY_4e-PFoXJmMtig39KCRcDSaW7l0iTeqNz8WuMnfIrE70P8hEjFk3M0JhpsWVF-phE-wKARNSE/w640-h426/desmos-graph.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Spooky greetings. A quick post with more complex analysis for you. Though maybe not as visually interesting as fractals, but getting back to some basics and/or nuance regarding complex functions. For one thing, I just never had a chance to really fit in a good study of Riemann surfaces (interest in them was partially stirred on by all that recent cubic hackery). Also, a lot of stuff involving branch cuts and branch points are something quickly gone over in standard complex analysis and never really explored in depth, other than to say "we take the <i>principal branch</i> of the logarithm/root/power" function to be... and you don't get into the nuance with the details of differences between different branches of functions. This example here is exploring the mapping $z \mapsto \sqrt{z^2 + 1}$. This is already interesting from the Riemann surface point of view, because neither the function nor its inverse is definable in its most interesting form by mapping (subsets of) the complex plane alone. <i>Formally</i>, to work on $\mathbb{C}$, we have to define things by taking a continuous choice of square root on $\mathbb{C}$ minus some ray from $0$ to $\infty$. The choice here is between a square root and its opposite (which is also a square root of the same complex number!) is not natural in the complex plane (unlike in the real numbers where you can always take the positive square root of a positive number, which is in some sense, a defining characteristic of real numbers, cementing why it is the unique complete ordered field), and being forced to choose forces a discontinuity somewhere. Riemann surface theory is, in some sense, about never having to make the choice. To quote Sir Roger Penrose (congrats on that Nobel Prize!): </div><div class="separator" style="clear: both; text-align: left;">
<div class="page" title="Page 165">
<div class="section">
<div class="layoutArea">
<div class="column">
<p><i><span style="font-family: 'AdvP40418'; font-size: 10pt;">In particular, the domain of
the logarithm function would be ‘cut’ in some arbitrary way, by a line out
from the origin to in</span><span style="font-size: 10pt;"><span style="font-family: AdvP40669;">fi</span></span></i><span style="font-family: 'AdvP40418'; font-size: 10pt;"><i>nity. To my way of thinking, this was a brutal
mutilation of a sublime mathematical structure</i>. <i>(</i>The Road to Reality<i>, p. 136)</i></span></p>
</div>
</div>
</div>
</div></div><div class="separator" style="clear: both; text-align: left;"></div><p></p><div class="separator" style="clear: both; text-align: left;">A couple of references (e.g. Penrose's student Tristan Needham, in his otherwise fantastic <i>Visual Complex Analysis</i>) suggest the most common branch cut for this is function is two horizontal lines to the left of $\mathsf{i}$ and $-\mathsf{i}$. I wrangled with this a bit, but I believe a subtlety is left out. To study $\sqrt{z^2 + 1}$ as truly the composition of a square root function, and the mapping $z^2 + 1$, your branch cuts will have to be the corresponding inverse image of the branch cut of the square root, under $z^2 + 1$. Using the negative real axis, this is the ray above $\mathsf{i}$ and the ray below $-\mathsf{i}$. Two rays to the left of $\pm \mathsf{i}$ cannot be realized as such an inverse image, for any ray to infinity (the image under $z^2 + 1$ is a whole parabola to infinity). Of course, the essential definition for complex analysis is that you define the function in this set by taking paths from an origin point and <i>analytically continuing,</i> and entrusting your result to algebraic topology. But this is not very effective, computationally. This is basically saying that for some selections of branch cuts, the function composition $\sqrt{z^2 + 1}$ is a lie: you cannot get it by assembling square root, squaring, and plus one. What turns out to work, in terms of assembling functions rather than continuing along curves, is not $\sqrt{z^2 + 1}$, but $\sqrt{z+\mathsf{i}} \sqrt{z-\mathsf{i}}$, that is, if you take the branch of square root, along the negative axis, subtract and add $\mathsf{i}$, take the square root of each, and then multiply, you <i>do</i> get something that reproduces what you theoretically get by paths. One might wonder what is the difference between $\sqrt{z^2 + 1} = \sqrt{(z+\mathsf{i})(z-\mathsf{i})}$ and $\sqrt{z+\mathsf{i}}\sqrt{z- \mathsf{i}}$; these are not the same because $\sqrt{ab} \neq \sqrt{a}\sqrt{b}$ in the complex plane unless you regard it as a multivalued set equality.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The best rendering of this function is, I've discovered, is taking the branch $-\mathsf{i}$ to $\mathsf{i}$ along the imaginary axis—something that doesn't even go out to infinity. To his credit, Needham does mention that connecting the two branch points in a finite part of the plane is possible, and it just has to be done in a manner that disables you from being able to complete a turn around the two branch points $\pm \mathsf{i}$. But there's no explicit computation that develops a visceral understanding of this fact (and so I made this post).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The title picture is the image of a large disk (parametrized by the usual polar coordinates) under the mapping $\sqrt{z-\mathsf{i}} \sqrt{z+ \mathsf{i}}$. The cut (deleted out of the disk) is taken on the interval $-\mathsf{i}$ to $\mathsf{i}$ ($y=-1$ to $y=1$ in the picture). Computationally this means the square roots were taken with the angles in the interval $-\pi/2$ to $3\pi/2$, which required me to define the square root using some hackery of the arctan function. I leave you with the conformal version of this (where the concentric ring radii increase exponentially rather than linearly; the linear increase looks better for looking like a cobweb, but this version looks better in preserving the proportions of the grid rectangles formed by the intersecting lines).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0hMhahKMHgOEir5DKqIkMLNq00G-JPYCvu3BdsnAo0YiiYxRm93jroZb2H1yO7ERHTYiaxKzUp-nd7luERir-3ToJp2PFyCzXuxT2VCGX4k9BdvZbRc_H705Y0BgYi4AUyWJPdGpnRS4/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="2000" data-original-width="2000" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0hMhahKMHgOEir5DKqIkMLNq00G-JPYCvu3BdsnAo0YiiYxRm93jroZb2H1yO7ERHTYiaxKzUp-nd7luERir-3ToJp2PFyCzXuxT2VCGX4k9BdvZbRc_H705Y0BgYi4AUyWJPdGpnRS4/w640-h640/desmos-graph+%25281%2529.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Or, take a look at it in Desmos:</div><div class="separator" style="clear: both; text-align: center;"><iframe frameborder="0" height="500px" src="https://www.desmos.com/calculator/equbckuayl?embed" style="border: 1px solid #ccc;" width="550px"></iframe><br /></div>
<div class="separator" style="clear: both; text-align: left;"><br /></div></div>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-46424505525236887442020-10-11T14:00:00.228-07:002020-11-28T00:32:07.627-08:00Chaos Still Reigns!!A quick follow-on to <a href="http://www.nestedtori.com/">last week's post</a>. It would be blasphemous to talk about chaos without at least mentioning the most iconic fractal since fractals became a thing via <i><a href="https://en.wikipedia.org/wiki/The_Fractal_Geometry_of_Nature" target="_blank">The Fractal Geometry of Nature</a>,</i> the set of complex numbers named after its author, Benoit Mandelbrot. I've spent a lot of time exploring the Mandelbrot set since I've been able to use computers, so you'd think I'd have plenty to say about it. And I do, but not this week. Indeed it is this, more than anything else, that started me on the visualization track. Instead, I'll leave you with the real reason why the thing is so damn captivating in the first place, with, what else, a visualization.<div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMyCvyAr9n5OihZA1IKTt8Y3pcnS5IPWmZTGnvHMSl9zXqcpxX4COq6ZtgIB2lOFHUcvxjJ7643JT2PEzc8D4w_FfnVIsR_bR4BsPgXsU3gx4i_QK5O-tzpLWOePBUIAF6td-8QF2X-N4/s2048/mandel_mod50_xxxxl.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="2048" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMyCvyAr9n5OihZA1IKTt8Y3pcnS5IPWmZTGnvHMSl9zXqcpxX4COq6ZtgIB2lOFHUcvxjJ7643JT2PEzc8D4w_FfnVIsR_bR4BsPgXsU3gx4i_QK5O-tzpLWOePBUIAF6td-8QF2X-N4/w640-h640/mandel_mod50_xxxxl.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">The Mandelbrot Set with $-1.01 \leq\operatorname{Re}(z) \leq -1.006$ and $0.309 \leq \operatorname{Im}(z) \leq 0.313$.</div><div> </div><div>The Mandelbrot set is in fact relevant to strongest theme of this blog, that of parameter spaces. Namely, it is the set of all parameters $c$ such that the iteration $z \mapsto z^2 + c$, starting at $z=0$, remains bounded. It in fact is a catalogue of another bunch of fractals (just like having a <a href="http://www.nestedtori.com/2015/09/the-configuration-space-of-all-lines-in.html">catalogue of all lines in the plane</a>), Julia sets, which describe for each fixed $c$, what starting values of the iteration $z \mapsto z^2 + c$ stay bounded. In other words, Julia sets describe a collection involving the $z$ values of the iteration, and the Mandelbrot set describes a collection involving $c$ values. The main dark blobby part of the image is the actual set; the fancy colors are just colorings according to how long it takes for a point there to escape outside a certain disk in the plane ($|z|\leq 2$). Here the colors are assigned to the <a href="https://cran.r-project.org/web/packages/viridis/vignettes/intro-to-viridis.html">Viridis</a> palette, and the iteration is done up to 1000 times (at 1000, it's just considered to be in the set). It cycles through the Viridis palette by the number of iterations modulo 50 (every 50 times, the color repeats), which is why you see interesting discontinuous jumps in color. Enjoy. (The next post will probably include some examples of Julia sets, showing precisely how the Mandelbrot set is a catalogue of them). I leave you with my all-time favorite from the 90s, the "Jewel Box" as coined by Rollo Silver in a fractal newsletter <i>Amygdala</i> back in the '90s. Unfortunately, I don't know where he is now and what the state of the newsletter is!</div></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8KjFbuCgla68gK_Cghw4KBlOQvPskf8irtcwtdcu_FO1WqLWccUU1tKup5gWVFKps77GASU_jfwpV-WYA3AHYXK8doiTTFQhZ_svR4NpZ3Abj1RP_8cSJye8JdmdCpSeYW9eD3cBgz1w/s2048/mandel_jewel_box.xxxxl.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1638" data-original-width="2048" height="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8KjFbuCgla68gK_Cghw4KBlOQvPskf8irtcwtdcu_FO1WqLWccUU1tKup5gWVFKps77GASU_jfwpV-WYA3AHYXK8doiTTFQhZ_svR4NpZ3Abj1RP_8cSJye8JdmdCpSeYW9eD3cBgz1w/w640-h512/mandel_jewel_box.xxxxl.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Centered at $-0.74542846 + 0.11300888\mathsf{i}$ and going about $10^{-5}$ on either side in the $x$-direction</div><br /><div><br /></div>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-80966994230689099302020-10-03T10:30:00.012-07:002020-10-05T16:59:44.039-07:00Chaos Reigns!!!<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY5WsnLFHLIf-naZEXoQ3B0H_DNZmmY2Hju9CsVUUir1xRPlcy28eayWPIAWyBXsvI2YH_v0dhgLqd0SBntXIu9qJPnSu1slQwaMXNbn3gbFCLfkJ_oQhuchzrTXeg9i5MLYm6wAk1z28/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1180" data-original-width="1966" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY5WsnLFHLIf-naZEXoQ3B0H_DNZmmY2Hju9CsVUUir1xRPlcy28eayWPIAWyBXsvI2YH_v0dhgLqd0SBntXIu9qJPnSu1slQwaMXNbn3gbFCLfkJ_oQhuchzrTXeg9i5MLYm6wAk1z28/w640-h384/image.png" width="640" /></a></div><p></p><p>Chaos and fractals were all the rage when I was growing up, and was probably one of the major factors in getting me interested in math, programming, and differential equations, since much of this is ultimately about how systems evolve over time. Oh, and getting me into TOTALLY AWESOME visualizations. This is a graph of the various possible final states of the quadratic iterator: $x_{n+1} = ax_n (1-x_n)$. What this means is, for a given parameter $a$, and some start value in the range $(0, 1)$, we consider iterating the map $F(a, x) = ax(1-x)$, namely, the sequence $F(a, x)$, $F(a, F(a, x))$, $F(a, F(a, F(a, x)))\dots$. For some ridiculous history here, one of my favorite things to do as a child was to repeatedly press buttons on a calculator over and over again to see what happens. Little did I know that this is basically, in math, <i>the only thing that actually exists</i>: everything is built on the foundation of recursion. Of course, I don't actually believe recursion is the only thing that exists, rather, there is interesting conceptual structure that is built up upon fundamental components, and it is damn amazing how something so simple can ultimately create something so complex. And here is one example in which this is true.</p><p>Anyway, to get back to it: if we keep iterating $F$ in the variable $x$, we will eventually fall into some stable pattern. For small $a$, iterating $F$ in the variable $x$ eventually gives convergence to a fixed point, namely $1-\frac{1}{a}$. How did we find this? If we have a fixed point $x = F(a, x)$, then $x = ax(1-x)$ or $-ax^2 + (a-1)x = 0$. This gives two solutions $x = 0$, and $-ax + (a-1) = 0$, or $x = (a-1)/a$. </p><p>Now, for each such $a$ (which we take to be the horizontal axis), we plot this fixed point (on the vertical axis). And as you move up to $a=3$, all is peaceful, as all iterations eventually settle on one and only one point. But at $a = 3$, something strange happens. You stop getting a single fixed point, but rather, you start bouncing between two values. We can actually solve for what these two values are using none other than ... the cubic equation (that's the small extent of continuity here with the <a href="http://www.nestedtori.com/2020/09/more-cubic-fun.html">previous posts</a>!). The way to see this: if there's a period-2 sequence, $x = F(a, y)$ and $y = F(a, x)$ for the two values, which means $x = F(a, F(a, x))$ and therefore $x = aF(a, x)(1-F(a, x)) = a(ax(1-x))(1- ax(1-x))$. This is a priori a quartic equation, since the number of $x$'s eventually multiply out to degree $4$, but once you realize there's a trivial solution $x = 0$ here (because there's a factor of $x$ multiplying on both side), it's a cubic equation $a^2(1-x)(1-ax(1-x)) -1 = 0$. I'm not going to try solving this, despite having had much fun wrangling with Cardano's formula in the past few weeks, because that distracts from the ultimate insight (and indeed, as fun as that formula is, and the beautiful theory that eventually comes from trying to solve polynomial equations, Galois theory), you quickly enter territory in which you stop being able to solve for things in terms of roots. To visualize we instead proceed numerically, directly iterating from a start value and waiting for things to stabilize around a set of values. One sees that as $a$ grows higher and higher, the number of final points starts doubling and doubling, faster and faster (in fact, a factor of the <a href="https://en.wikipedia.org/wiki/Feigenbaum_constants#The_first_constant">Feigenbaum constant</a> faster), until all chaos breaks loose and the iterator never settles on any fixed point. It's very weird how just varying the parameter $a$, one can go from very nice fixed point behavior to wild chaos.</p><p>Ok, you can't go very far analytically, but we can still try anyway:</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwvjTZJeLR4xwNAUOTnZLMB-QGoVyb9INgmxrLtZXT0SbdDcN-nM-k_4GAMT0Ql47IZ1H6whv_nKUHMlue8CeZ2SaATWgroMiECjhq1guD_GmslM3TTCKAi81KupsedHS0XI9irYRoGYo/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1169" data-original-width="2048" height="365" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwvjTZJeLR4xwNAUOTnZLMB-QGoVyb9INgmxrLtZXT0SbdDcN-nM-k_4GAMT0Ql47IZ1H6whv_nKUHMlue8CeZ2SaATWgroMiECjhq1guD_GmslM3TTCKAi81KupsedHS0XI9irYRoGYo/w640-h365/image.png" width="640" /></a></div><br /><p></p><p>To explain it, we'll have to back up a little. Note that I said the $2$-periodic solution involves the solution to a <i>cubic</i> equation. Where is the third one? (actually, as previously mentioned, it's really quartic, and $x=0$ is a solution). Is the cubic always one that has a zero discriminant? Probably not. We mentioned that these "fixed" points come about from iterating the mappings, i.e., there is dynamics involved. Solving the cubic, you will actually get $1 - 1/a$, the original fixed point, as one of the solutions (in fact, here is again where numerical analysis helps: you can get around using Cardano's formula if you realize from the picture that the original fixed point continues; then you guess the solution $1-1/a$, factor it out with synthetic division, and solve the remaining <i>quadratic</i> equation — this is exactly how I taught college algebra students to solve cubics). Of course, this has to satisfy $x = F(a, F(a, x)) = G(a, x)$, and the two solutions to this equation fixed points of $G$, and thus when $F$ is evaluated on it, it alternates between the two values. What goes wrong here is that this point (as well as the point $x=0$) is <i>unstable</i>, namely, if you start iterating from some point even slightly away from this fixed point, iterating the map will run away from that point $1 - 1/a$. What is significant about the value $a = 3$ is that the discriminant of the cubic forces two of the roots to become complex conjugates, so there is only one real solution, and the discriminant <i>also</i> is the switchover point from when the iteration is stable there versus anywhere else. A fixed point $x$ is stable whenever $|\partial G/\partial x| < 1$ at that point. This can be roughly seen by linearizing about the fixed point, a standard technique:</p><p>\[G(a, x+h) \approx G(a, x) + (\partial G/\partial x(a, x))h + O(h^2) = x + (\partial G/\partial x) h + O(h^2).\]</p><p>In other words, $G(a, x+h)$ is closer to $x$ than $x + h$ is, because $h$ is being multiplied by something of magnitude $< 1$. So iterating brings things close to the fixed point even closer. It can be seen that at least for a little bit after $a = 3$, the central $1-1/a$ continues, but the other two solutions are the stable fixed points. So if you plot the curves $x = G(a, x))$, you'll get something that divides into $3$ branches at $a = 3$ (referred to as a <a href="https://en.wikipedia.org/wiki/Pitchfork_bifurcation">pitchfork bifurcation</a>). Similarly, if you plot $x = F(a, F(a, F(a, F(a, x)))) = H(a, x)$, the 4th order iterate, it will divide into pitchforks twice. This is given in the above plot. However, to figure out which fixed points will actually happen if you iterate from a random starting point, you can figure out where $|\partial H/\partial x| < 1$. This gives the regions in the plane where solutions are stable. You can alternatively plot the complement, where it is $\geq 1$, which can be made to cover up the parts of the pitchforks that are not stable solutions. The weird gloopy visualization of these regions is just cool to look at, even where there aren't any stable points. The curves you see inside there are still the correct initial ones before it branches out into a complete mess. It of course quickly becomes ferociously hard to compute for higher degrees, so a numerical study is still the way to go. But this is conceptually fun, though!</p><p>I leave you with a similar implicit function graph, but now color-coded:</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaOv-16GjGCmfCs5JQhBya5CEESaz8Ad5ro7GsbG6gI2jAIrjLCWEYEsCqxCypazV86APd6Q9JGnYpVadf4MJI98u-oElpdvjGVOxHenv2KBsrwqe7p446le1T2CJEkayRPxT4eNmU-Ag/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1149" data-original-width="2048" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaOv-16GjGCmfCs5JQhBya5CEESaz8Ad5ro7GsbG6gI2jAIrjLCWEYEsCqxCypazV86APd6Q9JGnYpVadf4MJI98u-oElpdvjGVOxHenv2KBsrwqe7p446le1T2CJEkayRPxT4eNmU-Ag/w640-h360/image.png" width="640" /></a></div><br />The red and blue correspond to $|\partial G/\partial x| \geq 1$ and the greens are where it is $< 1$.<p></p><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXlkpKatfAdwy482m3TIIVIZvXzgbQSyfDlzVphti98ylSNruVgAKnV1L7b3QIOqqwETfml3I03S4_Z98y_STrwlTyvdWoyUKyHIZZnAWEtH7-9OEZsxQqwZu_8m07UYHP8n8WHF3cRtU/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1200" data-original-width="2400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXlkpKatfAdwy482m3TIIVIZvXzgbQSyfDlzVphti98ylSNruVgAKnV1L7b3QIOqqwETfml3I03S4_Z98y_STrwlTyvdWoyUKyHIZZnAWEtH7-9OEZsxQqwZu_8m07UYHP8n8WHF3cRtU/w640-h320/bifurcation.png" width="640" /></a></div></div><div class="separator" style="clear: both; text-align: center;">Another version, executed much faster using TensorFlow (yes, it can be used for non-machine learning applications!)</div><br /><br /></div>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com1tag:blogger.com,1999:blog-5950074794465831898.post-67054672104164784312020-09-05T17:52:00.011-07:002020-09-17T21:54:51.913-07:00More Cubic Fun<div>As sort of a quick follow-up to the <a href="http://www.nestedtori.com/2020/08/i-need-half-tablespoon-so-i-have.html">last post</a>, I decided that it was high time to start exploring (of course) the <i>configuration space</i> of cubics. More explorations on this forthcoming, but I'm testing out a new graphing calculator interface called Desmos. Let's see how well it can be shared.</div><div><br /></div><iframe frameborder="0" height="500px" src="https://www.desmos.com/calculator/kmyqlurshe?embed" style="border: 1px solid #ccc;" width="500px"></iframe><div><div style="text-align: left;">(click the lower right to go to an interactive graph. What may be fun is playing around with the sliders. If I can figure out how to save it to a movie, I'll update it here)</div><div><br /></div><div>Basically what's going on here is I'm trying to visualize the phase space of depressed cubics $x^3 + px + q$ (In our <a href="http://www.nestedtori.com/2020/08/i-need-half-tablespoon-so-i-have.html">half-tablespoon example</a>, $p = -3$ and $q = 1$) by seeing what happens when you map the unit disk in the complex plane. (If $p=0$ it's basically the cubing function which triples angles and makes things wind around the origin 3 times as often). It stands to reason that if $p$ and $q$ pass through certain interesting values, a qualitative change may occur (to relate this to some math that may be familiar, think the duscrumminanmanaent, I mean, <i>discriminant</i> (that word is just so annoyingly hard to say), of the quadratic: $b^2 - 4ac$ in $ax^2 + bx+c$: when it passes through 0, the nature of the solution changes). One day I may make a post detailing the connection between this kind visualization and topological understanding of the concept of solvability by radicals. It might be far in the future, though!</div></div><div><br /></div><div>Here's a 3D rendering of the image of the unit disk as $p$ varies (with a vertical dimension rendered to distinguish distinct domain points that map to the same point (because the mapping is not 1-1. The mapping is not perfect, as the surface still self-intersects in places, but the direction the surface is facing as one traverses an intersection is distinct enough so you stay on the right path). (This is generated using SageMath, not Desmos, which doesn't yet have 3D stuff, oh well)</div><div><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dyuxtogbDqYszsZO3-FmjMK44kw6yLIEEP3bXhi1p5PeIxVP-pkRNx8sJGwJ5SbRHWrBJzfSSrrk2rj0ncr8Q' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;">$r \leq 1, -3 \leq p \leq 3$</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/gsuFBfchI90" width="320" youtube-src-id="gsuFBfchI90"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">$r \leq 2, -6 \leq p \leq 6$, </div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /></div>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-31140991499384417792020-08-22T12:00:00.021-07:002020-09-06T19:22:13.991-07:00I need a half-tablespoon. So I have absolutely no choice but to accept complex numbers.<div><br /></div><div><img height="378" src="data:image/png;base64,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" width="640" /></div><div><br /></div>You never know what math problems will show up in applications. I once had a passing thought to include the following problem on a calculus test, but I sure as heck am glad I didn't (I have included variations which seemed just slightly different from this, but solving for a different variable). Anyway so here's the story. I use measuring spoons (and cups) when I cook (<a href="https://www.youtube.com/watch?v=53me-ICi_f8&fbclid=IwAR3MllmLZoxzK9sQ9gZOJzVRZIKdCQZoqlsFl0A0CxfbjbRvZFbKTm6VtoY">I may already cause offense by doing so,</a> lol). Notably, my measuring spoons are hemispherical. I needed a half tablespoon of something. A bit of soy sauce, being the Real Asian™ that I am. I'm missing a few teaspoon measures, due to a mishap in the garbage disposer (oops). So not having my usual measures for 1½ teaspoons (or 3/2 teaspoons, since mathematicians like improper fractions), involving very easy math, like multiplication by 3, I decided, well, why don't I just fill the hemisphere to the exact height needed to get a volume of half a hemisphere? Easy peasy. Shouldn't be much harder than multiplying by 3, right? Well... turns out to involve the number 3 in something way, way more complicated.<div><br /></div><div>Now the calculus problem that I have definitely put on exams is: if you fill a hemisphere (of radius $R$) to exactly half the height ($\frac{1}{2} R$), what's the volume of such a thing? Now of course, because the curve of the hemisphere changes with the height, filling to the halfway <i>height</i> point is going to give you less than half the <i>volume</i>. Realizing the volume as a stack of disks, the answer is </div><div><br /></div><div>$\int_{R/2}^{R} \pi(R^2 - z^2) \; dz = \frac{2\pi}{3} R^3 - \int_0^{R/2} \pi(R^2 - z^2) \; dz = \frac{2\pi}{3} R^3 - \pi R^2 z + \frac{\pi}{3} z^3 = \frac{2\pi}{3}R^3 - \frac{\pi}{2} R^3 +\frac{\pi}{3\cdot 8} R^3 = \frac{5\pi}{24} R^3.$</div><div><br /></div><div>Oh. I thought it involved $\sqrt{2} - 1$ or something. Oh well. My memory is not what it used to be, I guess. I think that may be the answer to my volume-of-a-Sno-Cone problem, lol, which is the volume of the segment of spherical cap cut off by a cone. I don't feel like busting out the spherical coordinates today, anyway, to do that problem, lol. Some other time!</div><div><br /></div><div>Anyway, this is of course, not half a hemisphere's worth, which is $\frac{1}{3} \pi R^3$. To get that, we have to <i>solve</i> for the height. It is easier to measure from the top of the spoon ($xy$-plane) than from the bottom, so we solve</div><div><br /></div><div>$\frac13 R^3 = \int_0^h \pi(R^2 - z^2) \; dz = hR^3-\frac{1}{3} \pi h^3.$</div><div><br /></div><div>for $h$. Simple, right? Clearing denominators and moving stuff to the other side, and canceling off the pesky $\pi$, we end up with</div><div><br /></div><div>$h^3 - 3R^3 h + R^3 = 0$.</div><div><br /></div><div>A nontrivial cubic polynomial. As it happens, this is the case of the <i>depressed</i> cubic (insert many jokes/puns here and catch flack from the sensitivity police for making light of serious, real mental illnesses). Of course, using Mathematician's Privilege (dimensional consistency is such a ... physicist ... thing), we can just set our units to $1$ and be done with it; this gives us the polynomial </div><div><br /></div><div>$h^3 -3h + 1 = 0$.</div><div><br /></div><div>Now I could have also tried to have my college algebra students solve this one. Rational roots theorem and all that. Nope, not gonna work, throwing $1$ and $-1$ at it. It turns out that this one is a true <i><a href="https://en.wikipedia.org/wiki/Casus_irreducibilis">casus irreducibilis</a></i>. It being a depressed cubic, <a href="https://mathworld.wolfram.com/TschirnhausenTransformation.html">I don't have to deal</a> with the <a href="https://en.wikipedia.org/wiki/Ehrenfried_Walther_von_Tschirnhaus">Germans</a>, and can skip directly to <a href="https://en.wikipedia.org/wiki/Cubic_equation#Cardano's_formula">Italians</a> with <a href="https://en.wikipedia.org/wiki/Quartic_function#Ferrari's_solution">fancy cars</a> (perhaps I'll "retcon" my story and say I was cooking a nice <i><a href="https://youtu.be/bGtR3l_JeUo?t=245">risotto</a></i> and needed to use half a hemispherical teacup), the solution to this is </div><div><br /></div><div>$\sqrt[3]{-\frac{1}{2} + \sqrt{\frac{1}{4} - 1}} + \sqrt[3]{-\frac{1}{2} - \sqrt{\frac{1}{4} - 1}}$,</div><div><br class="Apple-interchange-newline" />$\zeta\sqrt[3]{-\frac{1}{2} + \sqrt{\frac{1}{4} - 1}} + \bar\zeta\sqrt[3]{-\frac{1}{2} - \sqrt{\frac{1}{4} - 1}}$,</div><div><br class="Apple-interchange-newline" />$\bar \zeta\sqrt[3]{-\frac{1}{2} + \sqrt{\frac{1}{4} - 1}} + \zeta \sqrt[3]{-\frac{1}{2} -\sqrt{\frac{1}{4} - 1}}$, where $\zeta$ is a cube root of unity (please print these formulas out onto posters and hold them up to enforce social distancing). It happens that $\zeta = -\frac{1}{2} + \frac{\sqrt{3}}{2}\mathsf i$, which is exactly what is under the cube root, so we're dealing with <i>ninth</i> roots of unity here! (who would have thought??). The way to see that these formulas work, generally from the depressed cubic, is basically to substitute $x = w - \frac{p}{3w}$, which results in a quadratic for $w^3$. That it's quadratic explains the nearly identical features of the stuff under the cube roots, but for a sign, and that it's $w^3$ that gets solved for is responsible for the cube roots outside, as well as mutiplying by roots of unity.</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img height="640" src="data:image/png;base64,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" style="margin-left: auto; margin-right: auto;" width="471" /><br /><br /></td></tr><tr><td class="tr-caption" style="text-align: center;">The cubic $y = x^3 - 3x + 1$. It has three <i>real</i> roots, but they <i>only</i> can be expressed algebraically by the sum of complex numbers!<br /></td></tr></tbody></table><br /><div>So the three solutions are $\sqrt[3]{\zeta} + \sqrt[3]{\bar{\zeta}} = \zeta^{1/3} + \zeta^{-1/3}$, $\zeta^{4/3} + \zeta^{-4/3}$, and $\zeta^{-2/3} + \zeta^{2/3}$. Taking the cube root of a complex number is not a trivial matter. It happens that the imaginary parts all cancel out and you get three real solutions, but this cannot be done without admitting complex numbers in some form (after now consulting with the <a href="https://en.wikipedia.org/wiki/%C3%89variste_Galois">French</a>). Well, almost, anyway. Let's call in trigonometry to save the day (but that's cheating, because trigonometry really is $e^{\mathsf i x}$). We'll take $\zeta = e^{2\pi\mathsf i/3}$ and the "principal" complex cube root to take minimum argument. Actually this is irrelevant, because the extra multiplications of the $\zeta$s give you the other cube roots anyway, but for definiteness... $\zeta^{1/3}$ then is $e^{2\pi\mathsf i / 9}$ and the <i>possible </i>solutions are</div><div><br /></div><div>$e^{2\pi\mathsf i / 9} + e^{-2\pi\mathsf i / 9} = 2\cos(2\pi/9)$</div><div>$e^{8\pi\mathsf i / 9} + e^{-8\pi\mathsf i / 9} = 2\cos(8\pi/9)$, and</div><div>$e^{-4\pi\mathsf i / 9} + e^{4\pi\mathsf i / 9} = 2\cos(4\pi/9)$.</div><div><br /></div><div>Ok, so which one of these solutions is the correct one? The solution has to be between $-1$ and $1$ (in our units; the original units would be between $-R$ and $R$), and as such, only $2 \cos(4\pi/9) \approx 0.3472$ (the middle one in the graph of the full cubic above) works. So to answer the question, you need to fill up the tablespoon measure so that it is 34.72% of the way down <i>from the top</i>. Here's another picture and zoomed in:</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img height="640" src="data:image/png;base64,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" style="margin-left: auto; margin-right: auto;" width="514" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><br />A cross section of the hemisphere in question, together with a zoomed in view of the cubic curve (green). The vertical line (cyan) drawn through the cubic at its root will intersect the circle (red) where it needs to be filled (here you'd fill everything to the right of this line)</td></tr></tbody></table><br /><div>Again the fact that solving a cubic <i>has</i> to go through the complex numbers is why complex numbers were finally accepted. It is not, as commonly believed, due to trying to solve for the quadratic, since in that case, complex numbers <i>only</i> appear when the parabola fails to intersect the $x$-axis, meaning the complex solutions are of the impossible, nonexistent intersection points, so, the various Renaissance mathematicians thought, obviously should not be taken seriously. But the cubic forces it to happen no matter what, because a cubic curve <i>always</i> crosses the $x$-axis. So there it is: half a tablespoon? You'll need complex numbers for that. Some more views (the title image sort of is looking from above, so might obscure the fact you must fill it <i>more</i> than halfway from the bottom):</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img height="464" src="data:image/png;base64,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" style="margin-left: auto; margin-right: auto;" width="640" /></td></tr><tr><td class="tr-caption" style="text-align: center;">View from below the tablespoon. The little extra disk sticking out is the fill line.<br /></td></tr></tbody></table><br /><div>Finally, I'll end with more social distancing formulas: the full cubic formula $ax^3 + bx^2 + cx + d = 0$:</div><div><br /></div><div><img height="191" src="data:image/png;base64,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" width="640" /></div><div><br /></div><div><img height="170" src="data:image/png;base64,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" width="640" /></div><div><br /></div><div><img height="178" src="data:image/png;base64,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" width="640" /></div><div><br /></div><div>For those who are interested, here's a nice video explaining this formula, and why we don't teach it in high school...<br/>
<iframe allowfullscreen="" frameborder="0" height="270" src="https://www.youtube.com/embed/N-KXStupwsc" width="480"></iframe>
<br />
It's not taught because the solutions you get may not be easily reducible to something you can recognize, even in simple cases. Conceptually, however, it is a real adventure, and solving it by breaking it into a 2-step process makes it tractable and interesting. Our tablespoon example already skips step 1 ... all that about Germans and Italians.</div><br class="Apple-interchange-newline" />Enjoy and stay safe! <div><br /></div><div><br /></div>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com6Mountain View, CA, USA37.3860517 -122.08385119.0758178638211575 -157.2401011 65.696285536178848 -86.9276011tag:blogger.com,1999:blog-5950074794465831898.post-85213859735552594882020-07-05T17:04:00.001-07:002020-07-06T16:36:53.080-07:00Fun with Trees<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5JiT_mjxJCy1symrB4AnA1PNiwj2lXwwtexYB01MkH4xagVtnTbqRTC24lWrkupde3QOgQvaozF8tZEBGLmB8E2iZvK5sLhB3nOTuMqgkfoWTKeP65XOM6WPFtnDp-kXjcfMIHRHAk2s/s1600/Screen+Shot+2020-07-05+at+03.47.45.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1066" data-original-width="1098" height="620" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5JiT_mjxJCy1symrB4AnA1PNiwj2lXwwtexYB01MkH4xagVtnTbqRTC24lWrkupde3QOgQvaozF8tZEBGLmB8E2iZvK5sLhB3nOTuMqgkfoWTKeP65XOM6WPFtnDp-kXjcfMIHRHAk2s/s640/Screen+Shot+2020-07-05+at+03.47.45.png" width="640" /></a></div>
<br />
<br />
Greetings. Yes, I know it's been a while. Lots of adjustments and entering the workforce. But when you're cooped up in a pandemic... Oh and by the way, that whole thing about <i>flattening the curve</i>... yes that's right, that was all about <i>geometry</i> and <i>visualization</i>; it it showed that visualization often carries pretty good information. (At least to people willing to listen to science and reason. But that's a rant for a different blog.) Anyway, I haven't really ever stopped reading math, though with a lot of life restructuring after leaving academia (another rant for a different blog), not a lot of time to at least confidently make posts. Lately, I've gotten into a lot of computer science related math reading. One, because, well, I use it in my job daily, and two, I've always had the interest, and developing good visualizations was really a big part of what drove me into CS back in the day (fractals, remember those? It was kind of a fad science, I'll admit, but it really was the start of me getting into the concept of TOTALLY AWESOME visualizations, and imagining spaces beyond, well, space). And also revisiting a lot of that stuff with a firmer mathematical foundation really has cleared out some former stumbling blocks. I'm pretty amazed at how much I've improved at combinatorial arguments. It could be said that avoiding combinatorics and discrete math drove me to research the most continuous of continuous things, the smooth surfaces of differential geometry, but perhaps I did myself a disservice. There really does seem to be an underlying unity, and unexpected weird connections is what made me love math in the first place. And I can't truly say I avoided discrete math forever, for I had to dive into SOME discrete stuff because I wanted to actually, you know, <i>solve</i> some of these equations and, of course, <i>visualize</i>.<br />
<br />
Anyway, so in that spirit, while poking around general algorithms reading, I delved into some CS data structures, <i>binary trees</i>, and got a chance to get some TOTALLY AWESOME visualizations in. It's one of those subjects I thought was completely old hat and elementary. But armed with new analytic tools, I never knew how interesting it could get. My interest, in particular, is in is getting a sense of the variety of tree shapes, and exploring that variety probabilistically (we've done <a href="http://www.nestedtori.com/2016/05/a-calculation-in-statistical-mechanics.html" target="_blank">more</a> than one <a href="http://www.nestedtori.com/2015/09/distributing-points-on-spheres-and.html" target="_blank">probability post</a>). It completely fits into one of the major threads of this blog, namely, exploring <a href="http://www.nestedtori.com/search/label/configuration%20space" target="_blank">state space</a>. So good that they are worthy of a first blog update in 3 years. It is an excellent example of a space that has a couple of distinct, natural probability distributions (in particular, it can be seen as explorations of two different <a href="http://www.nestedtori.com/search/label/parametrization" target="_blank">parametrizations</a> of the space). Plus, throw in a bit about realizing trees as monomials in noncommutative polynomial rings in infinitely many variables... and only after thinking about it that way, I managed to come up with a sensible encoding of the possible shapes of trees that I could use as dictionary keys to verify subsequent calculations with simulation... I hope y'all get my drift about the essential unity of math. Anyway, one shout-out; I got on this thread by poking around the algorithms literature, and I have to say, Prof. Robert Sedgewick's <a href="https://www.coursera.org/learn/analysis-of-algorithms/home/welcome" target="_blank">course</a> on <a href="https://ac.cs.princeton.edu/home/" target="_blank">analytic combinatorics</a> (and generally, the approach of <a href="https://aofa.cs.princeton.edu/home/" target="_blank">analyzing algorithms</a> by way of real/complex-analytic asymptotics) kicks super ass (or as the young whippersnappers these days say: it is <i>totally sick</i>, but in the time of The Rona, probably not the best terminology...)<br />
<br />
So we begin with binary trees. What they are, how to count them, one of its most common uses in CS, and how the theory of permutations that surrounds this common use causes a nontrivial difference in probability distributions, from which we may obtain different definitions for what it means to be "a random tree". So what's a binary tree? Actually, surprisingly, this is also not a 100% transparent and straightforward answer, because different texts define things differently, and there are subtle variations. Sometimes it's not apparent what the difference in definitions can be. At its most basic, and the canonical introductory CS book definition, is that a binary tree is either empty, or a root node together with a left subtree and a right subtree (recursively defined). This distinction between left and right is what forces it to be different from a <i>rooted acyclic graph</i>, or algebraic topologists' <i>simply connected graph, </i>or, perhaps surprisingly, even an <i>ordered tree with at most 2 children per node</i>. Here's a couple of examples describing such subtleties:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvb2CI_-eqj_2hjWpaZQKLmsGgXEMPtga5QIhd3AJwcw6SqncOFYiqasDXMPzMqx3pDer90Um-3h8vDVCdEbb8TXBSAWC6Bhq97gZO4Gr_dTvaU9prH-6Aks-KDQywKF32HLPCUwlkfZA/s1600/Screen+Shot+2020-07-05+at+14.59.18.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="451" data-original-width="981" height="147" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvb2CI_-eqj_2hjWpaZQKLmsGgXEMPtga5QIhd3AJwcw6SqncOFYiqasDXMPzMqx3pDer90Um-3h8vDVCdEbb8TXBSAWC6Bhq97gZO4Gr_dTvaU9prH-6Aks-KDQywKF32HLPCUwlkfZA/s320/Screen+Shot+2020-07-05+at+14.59.18.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">These two rooted trees are the same (isomorphic) as rooted trees, but are different as <i>ordered</i> rooted trees, because the left-right order matters in that case.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5cB50gzTha0StsW02rE1bRQem8LZCnGE03Bv3_BeaiIbEf956fD0MmszrhAHnMSvahgucrQE7-PfRdr34C7_pSv2JtwSiQuVtCZiZO1RKkL7Rv6Y6ELcTQ0XP75H84pw_7O9O1Et44-s/s1600/Screen+Shot+2020-07-05+at+15.04.05.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="398" data-original-width="903" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5cB50gzTha0StsW02rE1bRQem8LZCnGE03Bv3_BeaiIbEf956fD0MmszrhAHnMSvahgucrQE7-PfRdr34C7_pSv2JtwSiQuVtCZiZO1RKkL7Rv6Y6ELcTQ0XP75H84pw_7O9O1Et44-s/s320/Screen+Shot+2020-07-05+at+15.04.05.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">These trees are isomorphic as ordered rooted trees, because there are no other nodes in each level, but not isomorphic as binary trees.</td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
The reason for the last one is that a tree with two lefts is distinct from a tree with two rights, whereas, they'd be identical as ordered trees. <i>But</i>, if one designates that all nodes <i>must</i> have either two or zero children, and we call the ones with zero children "external", and the others "internal", then the tree that we care about is contained in the internal nodes, and it is sufficient to say they are ordered trees (because the left-right distinction is now realized as which node is getting the two terminal children). This actually is close to what is implemented in practice, because external nodes can be considered to be the null pointers that signify the lack of a child in that direction. Here's a picture of what we mean, adding external nodes to the two above distinct trees (the unfilled circles correspond to external nodes):<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGnZ8luU9tjwSNqAest-c8eQpN7OywB3dFCoQ_mpCN_PJCiwTpnl2UqGZvwqdza6MSdIwgv_bx1-NwFuyBGVezOehzU3IJRKGeoc9KWvMN8GMdAEpp1I_iaAiB6o5Hb87jgkk1wXF60Wg/s1600/Screen+Shot+2020-07-05+at+15.17.52.png" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGnZ8luU9tjwSNqAest-c8eQpN7OywB3dFCoQ_mpCN_PJCiwTpnl2UqGZvwqdza6MSdIwgv_bx1-NwFuyBGVezOehzU3IJRKGeoc9KWvMN8GMdAEpp1I_iaAiB6o5Hb87jgkk1wXF60Wg/s400/Screen+Shot+2020-07-05+at+15.17.52.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">After adding the external nodes (in cyan with empty holes) to the two binary trees above, they are no longer isomorphic as ordered rooted trees, because now there's more than one node on a given level, so there's now a choice of where to attach subtrees. The external nodes are attached differently for the left-leaning vs. right-leaning trees. Again, in CS terms, you should think of the cyan nodes being null.</td></tr>
</tbody></table>
How do we get a sense of what varieties of binary trees exist? First on the todo-list is to count them. Actually, it may be because of trees that one of the most famous sequences of numbers in combinatorics, the <i><a href="https://en.wikipedia.org/wiki/Catalan_number" target="_blank">Catalan numbers</a></i>, is so famous—many things can be modeled using binary trees, so that naturally leads to those things <a href="https://www.google.com/books/edition/Catalan_Numbers/IRIHBwAAQBAJ?hl=en&gbpv=0&kptab=getbook" target="_blank">being counted using Catalan numbers</a> $c_n = 1, 1, 2, 5, 14, 42, 132,...$. They are defined by the recurrence relation $c_{n+1} = \sum_{k=0}^n c_k c_{n-k}$ with $c_0=1$. Using the "internal node" definition, there are $c_n$ binary trees that have $n$ internal nodes. This can be seen by showing that it satisfied that recurrence relation with the same initial conditions. Let's temporarily write $T_n$ for the number of trees of size $n$. A single external node (root node being null, in the CS terminology) corresponds to $n=0$, and it is obviously only one tree; similarly, a single internal node (root node having no children) is $n=1$, also only one tree, so $T_0=1$ and $T_1=1$. For the general case, we use the recursive definition: a tree is a root node plus two subtrees. Given a tree of size $n+1$, the root counts as one, and for each $k$, $0 \leq k \leq n$, we can consider a left subtree of size $k$, and the right subtree has to be of size $n-k$. Since there are $T_k$ possibilities for the left subtree, and $T_{n-k}$ possibilities for the right subtree, the total number of possibilities of trees with left subtree of size $k$ is $T_k T_{n-k}$. Adding up over all possible $k$ makes $T_{n+1} = \sum_{k=0}^{n} T_k T_{n-k}$, exactly the Catalan recurrence relation. Using a lot of algebraic trickery (or generating functions, which are also totally awesome, even though they really are not a visual thing), we can derive an explicit formula and asymptotic expansion<br />
\[<br />
c_n = \frac{1}{n+1} {2n \choose n} \sim \frac{4^{n}}{\sqrt{\pi n^3}}<br />
\] (yes, that $\pi$, another completely random connection; who knew you'd find $\pi$ studying trees??). As $n\to\infty$, the asymptotic formula comes closer and closer to approximating the number of nodes in a tree (it's related to Stirling's formula, which we've encountered in our <a href="http://www.nestedtori.com/2016/05/a-calculation-in-statistical-mechanics.html" target="_blank">Stat Mech</a> post).<br />
<br />
Ok, now that we got that count, the next natural thing to do is to explore the variety of trees that exist. One natural way of constructing trees is to consider binary search trees, often the first example of a tree given in elementary CS. Every node stores a key, keys are comparable, and smaller keys go into the left subtree and larger keys go into the right subtree. Keys are inserted by recursively traversing until a suitable null node is found and creating a new node there. Random input is modeled by considering random permutations. Say, an input of size $n$ is a random permutation of $0, 1, \dots, n-1$. Inserting in that order creates some tree. Now, there are $n!$ random permutations of $0, 1, \dots, n -1$, but $c_n$ trees, and $n!$ grows much faster than $c_n$ ($c_n$ is bounded above by an exponential $4^n$, whereas $n!$ grows like $\sqrt{2\pi n}(n/e)^n$, Stirling's approximation), so clearly, there must be distinct permutations that create the same tree, and they don't do so uniformly. In fact, as it turns out, random permutations heavily bias towards forming balanced trees, trees with roughly equal-sized left and right subtrees for a given root. This is, in practice, a very good thing, because balanced trees also exhibit very good performance for actual searching, and it's nice to know that typical cases that occur in practice in fact are also the best performing. Visualizing trees after a random permutation (here, $n=800$) is what created this post's title image (the tree nodes on each level are centered). Here's a couple more:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnyQCHrDGSeFBUXjTpBXj8yXYtXeueP1cDVVvviuOA7XGEoJRpY3C7HXjKjpRzXDx6t9JKq7eWh5xv6bEq2lx8YICxww80bQ754IZvI_-yqKIbQCTq1N7DloZEqLPvxkQf8rU4fq7MUvM/s1600/Screen+Shot+2020-07-05+at+14.49.43.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1082" data-original-width="1110" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnyQCHrDGSeFBUXjTpBXj8yXYtXeueP1cDVVvviuOA7XGEoJRpY3C7HXjKjpRzXDx6t9JKq7eWh5xv6bEq2lx8YICxww80bQ754IZvI_-yqKIbQCTq1N7DloZEqLPvxkQf8rU4fq7MUvM/s320/Screen+Shot+2020-07-05+at+14.49.43.png" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-XPXJjpbcTlEUjbiUj_CPbwo2ilfmATd_tsFhO322nkkS5WWxe1DFeJrxdpcFgEhkbim7_Jb3Wdaw6IEVRyEHK9GHi__GySFrOrZI5e3DnHA-TybQlSzc6jfi3lNlduNBxax6m2IFSmM/s1600/Screen+Shot+2020-07-05+at+14.50.47.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1082" data-original-width="1108" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-XPXJjpbcTlEUjbiUj_CPbwo2ilfmATd_tsFhO322nkkS5WWxe1DFeJrxdpcFgEhkbim7_Jb3Wdaw6IEVRyEHK9GHi__GySFrOrZI5e3DnHA-TybQlSzc6jfi3lNlduNBxax6m2IFSmM/s320/Screen+Shot+2020-07-05+at+14.50.47.png" width="320" /></a></div>
<br />
The wide middle seems to be characteristic of what balanced trees look like. They look like nice lanterns, or maybe acorns. It turns out that we can precisely quantify (using again, a recurrence relation) how many permutations will correspond to a given tree shape. It is also a very interesting decomposition. The first element of a permutation (represented as a scrambled array of $0, 1, 2, \dots. n-1$) corresponds to the root node, and all the elements less than it are in the left subtree, and all the elements greater than it are in the right subtree. Now the key observation here is: if you <i>shuffle</i> the permutation corresponding two subtrees (now, perhaps, visualizing the root node as the top card in a deck of cards and the two subtrees as two piles of the remaining cards), namely, interleave them with one another in an arbitrary way, but <i>keep the same ordering within each group</i>, this will lead to the <i>same tree</i>. This is because each insertion of a node greater than the root affects only the right subtree and completely ignores the left subtree, and vice versa. For an example, the permutation $[3, 1, 4, 6, 0, 2, 5]$, the root is $3$, and the left subtree consists of nodes $[1, 0, 2]$, and the right subtree corresponds to $[4, 6, 5]$. Then a shuffle is scanning both those lists from left to right and picking from one or the other in an arbitrary way, so long as the order for the left remains $1$, then possibly a bunch of things from the other tree, then $0$, then stuff, then $2$, and similarly for the right, $4$ then stuff then $6$ then stuff then $5$. So $[3, 4, 6, 1, 5, 0, 2]$, $[3, 4, 1, 6, 5, 0, 2]$, $[3, 1, 0, 4, 2, 6, 5]$ are examples of shuffles that lead to the same tree, but $[3, 4, 0, 6, 5, 1, 2]$ does not (because the $1$ and $0$ are no longer in the same order). It's possible to count the replications; namely a shuffle of $k$ elements is choosing $k$ positions among the $n-1$ leftover spots (since the root is always going to take the first spot). So the total number of replications is ${n-1 \choose k}$. This and we have to multiply by the replications of the left and right subtrees as well.<br />
<br />
Anyway, given this, what does this mean for random trees? The more balanced the trees are, the larger the number of shuffles; for an exact split, $n-1 = 2k$, and thus the number of shuffles is ${2k \choose k}$. The middle binomial coefficient (or the middle of two, if odd) is always the biggest one. So most random permutations, on average, will probably land in this huge space of possibilities. Ok, but what if we want to sample trees randomly so that every tree of size $n$ has equal probability? We can do this if we skew the probabilities involved in a random permutation. Basically, the key is to weight extreme values more, to purposely make it more likely to form unbalanced trees. What weight to choose? Since the number of $(n+1)$-node trees with a left subtree of size $k$ is $c_k c_{n-k}$, to get an even representation of that tree, such a tree should appear with probability $c_k c_{n-k}/c_{n+1}$. In other words, we should choose our root node to have value $k$ with probability $c_k c_{n-k}/c_{n+1}$, rather than the ordinary $1/(n+1)$. Once the root node is chosen, we can <i>recursively</i> get a random subtree for the left and right (both skewed in the same way). Finally, we shuffle the remaining. Now let's see what trees we get with this algorithm (using the same technique of generating a permutation, but according to this skewed way, and inserting it into a tree):<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdfVyi-oWrFL55dC3QEDjJfT-SOLaKOo2Cd9c2fJwFsSbdkuDN94AJcZK3yhvRTjK_Os-ekN3RBkn_ajqDMI7xJ59MNpjhAX3s7g63m4hjVaX9nevhiUhTIeNvPtevnTEh3WvtaMpupyM/s1600/Screen+Shot+2020-07-05+at+16.12.48.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1082" data-original-width="1110" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdfVyi-oWrFL55dC3QEDjJfT-SOLaKOo2Cd9c2fJwFsSbdkuDN94AJcZK3yhvRTjK_Os-ekN3RBkn_ajqDMI7xJ59MNpjhAX3s7g63m4hjVaX9nevhiUhTIeNvPtevnTEh3WvtaMpupyM/s320/Screen+Shot+2020-07-05+at+16.12.48.png" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibQ9wBSBImbk_aY1hXH2AuMXu1rHejqxH2r3zvV22IARKLRDgGldLZ5BpYyXSSguMWU1CY1Q8xcEvs54TNGHR0pXXSyxVyVajL7_PkP_A0VayH08lNecA35a53y3fw_zdIl4IUVV0qKJA/s1600/Screen+Shot+2020-07-05+at+16.13.08.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1082" data-original-width="1112" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibQ9wBSBImbk_aY1hXH2AuMXu1rHejqxH2r3zvV22IARKLRDgGldLZ5BpYyXSSguMWU1CY1Q8xcEvs54TNGHR0pXXSyxVyVajL7_PkP_A0VayH08lNecA35a53y3fw_zdIl4IUVV0qKJA/s320/Screen+Shot+2020-07-05+at+16.13.08.png" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAVL0sQfp3mo1FgSgYqnJMwEri5CfKm11ZuLHCYUTDUIFILJHRjP4SLOuYN9Mq6c98G2OeR_yPQ15trRxAmu4zzjZdj4kB2975HwgMOJsR4a2U8ciNalNIp9BIv4yDxRiQuTJJ1Cl2aJs/s1600/Screen+Shot+2020-07-05+at+16.14.07.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1082" data-original-width="1112" height="311" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAVL0sQfp3mo1FgSgYqnJMwEri5CfKm11ZuLHCYUTDUIFILJHRjP4SLOuYN9Mq6c98G2OeR_yPQ15trRxAmu4zzjZdj4kB2975HwgMOJsR4a2U8ciNalNIp9BIv4yDxRiQuTJJ1Cl2aJs/s320/Screen+Shot+2020-07-05+at+16.14.07.png" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Very different! They look a lot more like Christmas trees. 'Tis the season! (Har, it's about as far from the Christmas season as we're gonna get...). Anyway, there's loads of other fun I had with this, playing around in a <a href="https://github.com/ch0ndawg/tree-visualizer/blob/master/python-tree-explorer-sage.ipynb" target="_blank">SageMath notebook</a> (beware, it's not super cleaned up). Also <a href="https://www.sagemath.org/" target="_blank">SageMath</a> has taken the place of <i>Mathematica</i> as my main symbolic math package of choice. I'll leave you with two additional pictures. One of them is an interesting formula that enumerates trees using a polynomial ring with noncommuting variables $x_i$ (the subscript denotes the level the node is in the tree, and distinct occurrences of a variable correspond to distinct nodes; the power of $z$ is how many nodes in the tree, and substituting $1$ for all the $x_i$ gives the generating function of the Catalan numbers). Truly a non geometric visualization, but pretty to look at anyway (or, maybe terrifying; I could print it on a poster to make sure people keep social distancing)!</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfEyuYq84q5ITRprq3wOz8m2j4gsRS4jDQRatTO-NnbFOZkqM_S3NgWh1szK0h9NvNNaf_LsgPMZ_Vq63IgAnpmndXwhMzQG4thEyW2bH6QYe0W2MlTwDQf2G3Ktjo_5IdEl33KZjhGrc/s1600/Screen+Shot+2020-07-05+at+16.23.28.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="304" data-original-width="1600" height="121" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfEyuYq84q5ITRprq3wOz8m2j4gsRS4jDQRatTO-NnbFOZkqM_S3NgWh1szK0h9NvNNaf_LsgPMZ_Vq63IgAnpmndXwhMzQG4thEyW2bH6QYe0W2MlTwDQf2G3Ktjo_5IdEl33KZjhGrc/s640/Screen+Shot+2020-07-05+at+16.23.28.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
and finally trees visualized a different way, with inorder traversal as opposed to just centering each level:</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1Q9kuD-oV6cgO5xHcyLSsQ5EjH5JrDKN9AI3ADRATfqwroXSJIdRhNaAJjIsUhK8ATmvLA32YNmuQzmXIPQ7Gm6UKMqw4UuUFvUTLdHI4v18-YV6fv0_5J6VA2Ed6tcl6slk0eSsfw_g/s1600/Screen+Shot+2020-07-05+at+16.53.01.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="385" data-original-width="1600" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1Q9kuD-oV6cgO5xHcyLSsQ5EjH5JrDKN9AI3ADRATfqwroXSJIdRhNaAJjIsUhK8ATmvLA32YNmuQzmXIPQ7Gm6UKMqw4UuUFvUTLdHI4v18-YV6fv0_5J6VA2Ed6tcl6slk0eSsfw_g/s640/Screen+Shot+2020-07-05+at+16.53.01.png" width="640" /></a></div>
Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com1tag:blogger.com,1999:blog-5950074794465831898.post-43810661061072188232017-02-07T13:12:00.000-08:002017-02-07T15:44:56.119-08:00Finite Element Methods on SurfacesIn this post, we return to one of the roots of Nested Tori, namely, visualization of problems solved using finite element methods. There's quite a few projects that I worked on for that PhD, whose scattered results have not managed to make it on here today, concerning curved domains. For some topics we <i>have </i>covered, see <a href="http://www.nestedtori.com/search/label/finite%20element%20methods">posts with the tag <i>finite element methods</i></a>. These include, e.g., <a href="http://www.nestedtori.com/2012/10/fun-with-fenics.html">basic diffusion in planar domains</a>, <a href="http://www.nestedtori.com/2012/11/hyperbolic-equations-and-symplectic.html">wave equations in planar domains using symplectic methods</a>, and <a href="http://www.nestedtori.com/2012/11/sneak-peek-vector-finite-elements.html">electromagnetic wave simulation using vector finite elements</a>. These posts will be a useful preview of today's post.<br />
<br />
Our first two examples concern heat diffusion on evolving surfaces with two interesting topologies: the sphere and the torus. The evolution is fairly simple: rotation about an axis. The heat source remains fixed in the surrounding 3D space, and focuses on a fixed (in the ambient space) spot on the sphere; the rotation carries the heat away and it spreads throughout the sphere (or torus).<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/yI1QdupBkPc/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/yI1QdupBkPc?feature=player_embedded" width="320"></iframe></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/TQ2Rc-rYi4c/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/TQ2Rc-rYi4c?feature=player_embedded" width="320"></iframe></div>
<br />
<br />
Next, we consider a case where the solution can't be effected by an obvious or simple change of coordinates (i.e. in the terminology of fluids and continuum mechanics, switching from Eulerian to Lagarangian coordinates): heat on a bouncing sphere that stretches and shrinks vertically. Here the heat source builds with time and cuts off midway to just let the heat spread:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/P8ua2oRaDeE/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/P8ua2oRaDeE?feature=player_embedded" width="320"></iframe></div>
<br />
The implementation of all of these cases are via surface finite elements in the Eulerian description: the surface is considered a material that moves through space, but the spatial coordinates are fixed.<br />
<br />
Our last example is a wave equation on a sphere, using surface finite elements and <a href="http://www.nestedtori.com/2012/11/hyperbolic-equations-and-symplectic.html">symplectic methods</a>. The oscillating quantity $u$ is depicted as displacement along the normal direction of a sphere (so that, for example, if $u$ has some small positive value at one point and decreases rapidly to 0 as you move away, it looks like a small lump over that point). The initial condition is a ruffly structure (with speed 0), and we just <a href="https://www.youtube.com/watch?v=moSFlvxnbgk">let it go</a>.<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/4kPT-P_K5dY/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/4kPT-P_K5dY?feature=player_embedded" width="320"></iframe></div>
<div class="separator" style="clear: both; text-align: left;">
Enjoy!</div>
<br />Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-41455994402292648472016-08-27T11:55:00.000-07:002016-09-02T03:21:09.210-07:00The Best CakeOptimization is one of the most useful tools in all of math. Many of the visualizations here based in finding the optimum solution to something (and indeed, it drives many of the solution methods of differential equations). Here's an optimization <a href="http://fivethirtyeight.com/features/can-you-bake-the-optimal-cake/">puzzler</a> brought to you by <a href="http://fivethirtyeight.com/">FiveThirtyEight</a>. What are the optimal thicknesses of a 3-layer cake (each layer is cylindrical) that can fit into a given (right, circular) cone, that maximizes the volume? My <a href="https://ccom.ucsd.edu/~ctiee/538puzzler-0826.pdf">solution</a> is complicated, but here's a picture of the result... (it's red velvet)<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyX8ulHFhyphenhyphent2CWpux2SALZYX-SJUHskZViTNaOFI2TjbInW0IHJ4jWT3yxY0OLCuUuVd5zpm8x4PLLm6B08mEO_WVea92MyAib5Z7gVFPwAqX_Rgk-1gL9r85uxEDO3wOztJ-RUjNWJlQ/s1600/Screen+Shot+2016-08-27+at+11.46.15+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="484" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyX8ulHFhyphenhyphent2CWpux2SALZYX-SJUHskZViTNaOFI2TjbInW0IHJ4jWT3yxY0OLCuUuVd5zpm8x4PLLm6B08mEO_WVea92MyAib5Z7gVFPwAqX_Rgk-1gL9r85uxEDO3wOztJ-RUjNWJlQ/s640/Screen+Shot+2016-08-27+at+11.46.15+AM.png" width="640" /></a></div>
<br />Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-77146309295529261762016-05-18T13:01:00.000-07:002016-05-19T02:48:29.819-07:00A Calculation in Statistical MechanicsWe've been harping about phase and state space for a long while, now, and have mentioned at more than one point that statistical mechanics is a subject dealing with, in some sense, the ultimate state space, of many gazillions of dimensions. It is amazing that we can even calculate anything about such spaces. So we take a break from tori, and return to the (music of the) spheres, today, to give an example. We consider $N$-dimensional spheres, for $N = 0, 1, 2, 3, \dots$ and their "volumes". Note, of course, by $N$-sphere, we always mean the curved surface of points in $(N+1)$-dimensional space with unit distance from the orgin, and not the whole ball. [The $3$-sphere, as we know, is foliated by nested tori. We aren't going TOO far afield].<br />
<br />
To talk about this right, we need a little physics. Most of you probably have heard of the principle of conservation of energy... If you haven't, or even if you have, make sure to read about how <a href="http://www.nestedtori.com/2015/08/hamiltonian-mechanics-is-awesome-double.html">Hamiltonian Mechanics is Awesome</a>. Anyway, so if you imagine little billiard balls of uniform mass $m$ freely zipping about, banging into stuff, each particle having position $\mathbf{q}_i$ and momentum $\mathbf{p}_i$, then since we know <a href="http://www.nestedtori.com/2015/08/hamiltonian-mechanics-is-awesome-double.html">Hamiltonian Mechanics is Awesome</a>, this says that the two quantities evolve in such a way that the energy of the $i$th particle \[<br />
E_i = \frac{|\mathbf{p}_i|^2}{2m}<br />
\]<br />
stays constant. But if you imagine having a very, very large number of such billiard balls (several billiards of such (1 billiard = $10^{15}$ in most dialects of English, or such equivalent cognates) HAR HAR!), and compute the <i>total energy</i>, summing them all up,\[<br />
H = \sum_i E_i = \sum_i \frac{|\mathbf{p}_i|^2}{2m}.<br />
\] To say that the <i>total</i> energy is constant, then, is to say \[<br />
\sum_i \frac{|\mathbf{p}_i|^2}{2m} = E<br />
\] for some fixed number $E$. But what does this say? If we write out each \[<br />
|\mathbf{p}_i|^2 = p_{ix}^2 + p_{iy}^2 + p_{iz}^2,<br />
\] then \[<br />
2mE=\sum_i p_{ix}^2 + p_{iy}^2 + p_{iz}^2,<br />
\] meaning that if we sum over all the particles, say $N$ of them, where $N \approx 10^{24}$ (a milliard billiard of billiard balls), this means <i>we're summing the squares of a $3N$-dimensional vector and equating it to a constant</i>. So if we ask ourselves:<br />
<br />
<i>What is the collection of all possible momenta of $N$ particles that have one constant energy level $E$,</i><br />
<br />
<i></i>this is the <i>same</i> as saying,<br />
<i><br /></i>
<i>What are all the points on the $(3N-1)$-dimensional sphere of radius $\sqrt{2mE}$?</i><br />
<i><br /></i>
(the -1 from the fact that you're expressing the surface as the solution set to one equation: the boundary of the $k$-ball is the $(k-1)$-sphere)<i> Interesting</i>, you might say, but is there any occasion which actually requires you to <i>truly</i> do calculations treating it precisely as a geometrical $(3N-1)$-dimensional object?<br />
<br />
Well, what's one of the first things you think about when talking geometry? Areas and volumes, of course. There are situations in which you need to <i>integrate</i> over such energy "surface", or within the $N$-ball contained within, for $N \sim 10^{24}$. Basically, to find quantities like entropy, one needs to "count some number of cells" inside the $3N$-ball . This yields the total "number" of energy states with level <i>less than or equal to</i> $E$. "Number" in quotations because classically, of course, the actual number of states is the number of points on a sphere, which is of course uncountably infinite. We instead mean, per unit $3N$-dimensional volume, which actually leads to the <i>density</i> of states. The distinction is a little blurry, because, with a little help of quantum mechanics, we can think of each state as a cell of volume $(2\pi \hbar)^{3N}$, and each distinct state of momentum, which must be quantized, ultimately arises from boundary conditions in solving Schrödinger's equation, or eigenstuff.<br />
<br />
Suffice to say, however, let's talk as if calculating the volume of the $3N$-ball does indeed count the total number of momentum states with energy less than or equal to $E$, i.e., let's calculate \[<br />
\frac{1}{(2\pi \hbar)^{3N}}\int_{|\mathbf{p}|^2 \leq 2mE} d\mathbf{q}d\mathbf{p} =\frac{V^N}{(2\pi \hbar)^{3N}}\int_{|\mathbf{p}|^2 \leq 2mE} d\mathbf{p} .<br />
\]<br />
where $V$ is the ordinary 3D volume of the spatial region where all our particles live. For the momentum integral, we need the formula (whose derivation is fodder for another post!) for the <a href="https://en.wikipedia.org/wiki/N-sphere">volume of an $K$-ball</a> \[<br />
V_K(R) = \frac{\pi^{K/2}}{\Gamma\left(1+\frac{K}{2}\right)}R^K<br />
\]<br />
where $\Gamma(1+ K/2)$ is $(K/2)!$, the factorial of $K/2$, if $K$ is even, and $\pi^{1/2} K!!/2^{K/2}$ where $K!!$ is the double factorial $1\cdot 3 \cdot 5 \cdots k$, for $k$ odd.<br />
<br />
Plugging this in with $R = \sqrt{2mE}$ and $K=3N$ we have the total volume of a $3N$-ball in momentum space: \[<br />
V_{3N}(\sqrt{2mE}) = \frac{\pi^{3N/2}}{\Gamma\left(1+\frac{3N}{2}\right)} (2mE)^{3N/2}<br />
\]<br />
To make headway here, we can use <a href="https://en.wikipedia.org/wiki/Stirling%27s_approximation">Stirling's Approximation</a> for the Gamma function:\[<br />
\Gamma\left(1+\frac{3N}{2}\right) \approx \sqrt{3N\pi} \left(\frac{3N}{2e}\right)^{3N/2}<br />
\] This gives \[<br />
V_{3N}(\sqrt{2mE}) \approx \frac{1}{\sqrt{3\pi N}}\left(\frac{4\pi meE}{3N} \right)^{3N/2}<br />
\] or, the total number of states is \[<br />
\#\text{states} = \frac{V^N V_{3N}(\sqrt{2mE})}{(2\pi \hbar)^{3N}} \approx \frac{1}{\sqrt{3\pi N}}\left(\frac{4\pi meEV^{2/3}}{3N (2\pi \hbar)^2} \right)^{3N/2}<br />
\]<br />
Considering the smallness of $\hbar$ ($10^{-34}$ in everyday units) and the exponent $3N/2$ being on the order of $10^{24}$, this could be a staggeringly huge number (but that's what you expect: for lots of particles, they really can occupy even more states. For example, two particles behaving independently is the <i>square</i> the total number of states of for one particle). Thus to measure entropy, we take the natural log of all of this (and add a factor of the Boltzmann constant, $k$ which is on the order of $10^{-23}$ in ordinary units), we get \[<br />
k\ln(\#\text{states}) = \frac{3Nk}{2} \left( \ln \left(\frac{4\pi mEV^{2/3}}{3N(2\pi \hbar)^2}\right) +1\right) -\frac{1}{2}\ln(3\pi N)k.<br />
\]<br />
Since those last terms are small potatoes (not being multiplied by $N$), we usually just drop it to arrive at the <b>entropy</b> of our system of particles as<br />
\[<br />
S = \frac{3Nk}{2} \left( \ln \left(\frac{4\pi mEV^{2/3}}{3N(2\pi \hbar)^2}\right)\right)+\frac{3Nk}{2}.<br />
\] And for you chemists, $Nk = nR$, where $n$ is the number of moles and $R$ is the gas constant:<br />
\[<br />
S = \frac{3nR}{2}\left( \ln \left(\frac{4\pi mEV^{2/3}}{3N(2\pi \hbar)^2}\right)\right)+\frac{3nR}{2}.<br />
\]<br />
That's really nasty. How about we try to plug numbers into this and see what it is? We'll do that more concretely next time. But suffice to say, let's get back to what's interesting: we calculated the volume of some high-dimensional stuff!Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com3tag:blogger.com,1999:blog-5950074794465831898.post-37193832194499826782016-05-13T10:48:00.000-07:002016-05-13T10:48:16.659-07:00The Volume of Intersecting Cylinders<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPELJqLw4XajZT_NMrznmXk86bt-62GztuttmcObX3u-v9saFBmeGDPXhWy3ZWILZQ3_USEnrjzEDJRCS-NeptwPk3ro0oPqUMoYtDYwCtostFkgeD2JjfRq281J7KBtd3Va8kbcJd7Oo/s1600/classic-intersecting-cyls-larger-view.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="466" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPELJqLw4XajZT_NMrznmXk86bt-62GztuttmcObX3u-v9saFBmeGDPXhWy3ZWILZQ3_USEnrjzEDJRCS-NeptwPk3ro0oPqUMoYtDYwCtostFkgeD2JjfRq281J7KBtd3Va8kbcJd7Oo/s640/classic-intersecting-cyls-larger-view.png" width="640" /></a></div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
Now for another classic, although not as "kewel" as the spiral example. This time, it was <i>I</i> who asked for the help: once upon a time in a calculus class, we were asked to compute the volume of the solid that is the intersection of two cylinders at right angles. This is a surprisingly subtle calculation, and one of the more difficult-to-visualize things. Fortunately, I've managed to reproduce it above, with some transparency so the intersection is a little bit more visible. Now, here is the full intersection itself without the extra cylinder parts (called the <a href="http://mathworld.wolfram.com/SteinmetzSolid.html">Steinmetz Solid</a>):</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_0UfmbATtNd5C4EEu9gEDJU9NdYihK8iCJ9bux1OiUveH66x-g7-tSt8pUgIkWkB1V-DXDO0g09201-VDbajBEb7Om3ev6lVxIvM_5lwrA2syUtb7TmDgziDrkwJba_0sJBupfcrNcY4/s1600/classic-intersecting-cylinders.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="554" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_0UfmbATtNd5C4EEu9gEDJU9NdYihK8iCJ9bux1OiUveH66x-g7-tSt8pUgIkWkB1V-DXDO0g09201-VDbajBEb7Om3ev6lVxIvM_5lwrA2syUtb7TmDgziDrkwJba_0sJBupfcrNcY4/s640/classic-intersecting-cylinders.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
It is said that the Chinese mathematician <span style="background-color: #f9f9f9; font-family: sans-serif; font-size: 16px; line-height: 18.48px;">祖沖之</span> (Zu Chongzhi) computed the volume of this solid in the 400s ... I don't know how he did it without calculus, which is the way we're going to do it today. To do this, we write the equations of the two cylinders, say of radius $R$, which we will assume to have their axes in the $xy$-plane: </div>
\[
x^2 + z^2 = R^2
\] \[
y^2 + z^2 = R^2. \]<br />
Let's see what the actual intersection is. We set the two equations equal to each other:<br />
\[<br />
x^2 + z^2 = y^2 +z^2<br />
\]<br />
which means $x^2 = y^2$. This in turn means $y = \pm x$. In the $xy$-plane, this looks like two intersecting lines in an "X" shape, which you can see by looking at the solid above from the very tippy top. Of course, this is not exactly what the intersection actually looks like: we still have that there is a $z$-coordinate, given by $z = \pm \sqrt{R^2-x^2} =\pm \sqrt{R^2-y^2}$, so that the complete parametrization of the curves (four of them corresponding to each choice of $+$ or $-$) are given by, for example<br />
\[<br />
x = t<br />
\]\[<br />
y = \pm t<br />
\]\[<br />
z = \pm\sqrt{R^2-t^2}<br />
\]<br />
for $t$ varying from $-R$ to $R$ (the maximum allowable range given that it has to lie on a cylinder). This gives the "corners" of the solid given above. The solid itself is given by stacking squares with edges running from one curve to another (you can also see that in the solid above). To calculate the volume, we integrate the area of cross-sections perpendicular to the $z$-axis:<br />
\[<br />
V=\int_{-R}^R A(z)\,dz = \int_{-R}^R s^2\,dz.<br />
\]<br />
Therefore, we must find the side length $s$, which requires us to solve things in terms of $z$: $z =\pm\sqrt{R^2-x^2}$ means $z^2 = R^2 - x^2$, or $x^2 = R^2 - z^2$, so finally $x = \pm\sqrt{R^2 - z^2}$. Since the sides of the square are the same on either side, we can choose the positive square root. Then, since one side of the square goes between the two different values of $y$ for a given $x$, we find $s = \sqrt{R^2 - z^2}-(-\sqrt{R^2 - z^2}) = 2\sqrt{R^2 - z^2}$. Finally, we can find the integral:<br />
\[<br />
V = \int_{-R}^R s^2\, dz = \int_{-R}^{R} 4(R^2-z^2)\,dz = \left.4R^2 z - \frac{4}{3}z^3\right|_{-R}^R = \left(8-\frac{8}{3}\right)R^3 = \frac{16}{3}R^3.<br />
\]Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-49691584676816312832016-05-11T13:53:00.002-07:002016-05-12T13:30:17.102-07:00Yitz..'s Kewel SpiralEvery once in a while, I get an "assignment" to calculate some interesting parametrization (because parametrizations are awesome like that). For example, the <a href="http://www.nestedtori.com/2016/04/pasta-parametrization-high-resolution.html">bowtie pasta</a> was originally a request from a student. Today's goes way back, to someone asking a question on a forum in math way back when. He needed a spiral that started out and twisted its way through space as it got larger. In essence, a spiral that <i>doesn't</i> stay in the same plane. Obviously, polar curves are out of the question, since they are, well, in the plane. But what's one dimension up from polar coordinates? <i>Spherical</i> coordinates $(r,\varphi,\theta)$, of course (or if you're a physicist, $(r,\theta,\phi)$).<sup><a href="http:/#footnote_1">1 </a></sup>We fall back on a good ol' tool, <a href="http://www.nestedtori.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">parametrization</a>.<br />
<br />
To discover what its equation might be, we first consider an Archimedean spiral ($r = a\varphi$) in the $r\varphi$-plane (or $yz$-plane), or possibly a logarithmic one, like $e^{\varphi/3}$, which grows as it goes around (like some spirals <a href="http://www.nestedtori.com/2016/04/more-polar-classics-spirals.html">last time</a>) the "pole" which is now the $x$-axis. This ends up growing as you move clockwise, rather than counterclockwise, since $\varphi$ increases as it goes from north toward east.<br />
<br />
This is most efficiently represented in a parametric manner: first, in the $yz$-plane:\[<br />
x=0,<br />
\] \[<br />
y = at \sin t,<br />
\] \[<br />
z = at \cos t.<br />
\]<br />
gives the parametric equation of the Archimedean spiral in the $yz$-plane going clockwise. This gives $\varphi = t$ and $r = at$, which recovers the original polar equation $r = a\varphi$.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi15hUKr5xHUpn7kCEJ5HUXr5boxVyB_hgs8fMcrtEP4QX9TQMWQwNoUQwueks1ecBH3J9bO7zulecDmgbOBo59FRwUfK8rJrkpVXq6uxP9YRFDhFpq12WA8ibBWqEcSJ6O5U9wMrbhk3M/s1600/archim-to-yitz.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi15hUKr5xHUpn7kCEJ5HUXr5boxVyB_hgs8fMcrtEP4QX9TQMWQwNoUQwueks1ecBH3J9bO7zulecDmgbOBo59FRwUfK8rJrkpVXq6uxP9YRFDhFpq12WA8ibBWqEcSJ6O5U9wMrbhk3M/s640/archim-to-yitz.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Archimedean Spiral in the $yz$-plane, with $a = 1/20$.</td></tr>
</tbody></table>
<br />
<br />
How do we give it a twist? We reason that, after each revolution, we want it twisted out of the plane by some small amount (say, rotated about the $z$-axis by $b$ times a full revolution): we apply the rotation to the $x$ and $y$, giving:\[<br />
x=at\sin t \cos (bt),<br />
\] \[<br />
y = at \sin t \sin(bt),<br />
\] \[<br />
z = at \cos t.<br />
\]<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB8O1afhzsyF25GS0Q_E5sAQQGILNgYsHOSGLe0kgdiJQgsIJM7cNcMGzIxdtDkmH7FhoFcfPThE5d2PgCA_6TF6bE9EOhHt2m0c-q8AVRDns0n-DwGMyW_O4UY0byZQB3aYlmjd39MmY/s1600/Screen+Shot+2016-05-11+at+1.51.57+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjB8O1afhzsyF25GS0Q_E5sAQQGILNgYsHOSGLe0kgdiJQgsIJM7cNcMGzIxdtDkmH7FhoFcfPThE5d2PgCA_6TF6bE9EOhHt2m0c-q8AVRDns0n-DwGMyW_O4UY0byZQB3aYlmjd39MmY/s640/Screen+Shot+2016-05-11+at+1.51.57+PM.png" width="604" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Twisting out of the plane with parameter $b = 1/20$, also.</td></tr>
</tbody></table>
<br />
Here's the original one I delivered to Yitz.. (it is actually exponential):<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvYfTlT2xnx9TObfJl2qHED-qOQ8G3k1sYo-rTadRoZtzwLjoC-PTwb58LjKkYvn4Oyu9OlU9pDuOaoUMhvOLgDcgdkZozr-Ejizq6FS9wHUI6Nq3ag5fWOV6DtCPX9IvwxudS27-Dcqg/s1600/yitz-kewel-spiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvYfTlT2xnx9TObfJl2qHED-qOQ8G3k1sYo-rTadRoZtzwLjoC-PTwb58LjKkYvn4Oyu9OlU9pDuOaoUMhvOLgDcgdkZozr-Ejizq6FS9wHUI6Nq3ag5fWOV6DtCPX9IvwxudS27-Dcqg/s640/yitz-kewel-spiral.png" width="532" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="text-align: start;">Pretty </span><i style="text-align: start;">kewel</i><span style="text-align: start;">, right? (that was his exact word to describe it).</span></div>
<br />
<sup>1<span style="font-size: small;"> </span></sup><span style="font-size: x-small;">I always use the convention that if I indeed need to refer to a physics text, do calculations to be consistent... but I always write my $\phi$'s as non-curly in that context... I haven't yet figured how to draw my $\theta$s different though. Yes, I know there is $\vartheta$, but it hasn't caught on in my notation. It just doesn't feel enough like a $\theta$.</span>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com1tag:blogger.com,1999:blog-5950074794465831898.post-86980686316109223802016-04-30T16:43:00.000-07:002016-04-30T16:43:15.797-07:00More Polar Classics: SpiralsSome more from the classic polar curves collection... today we specialize in <i>spirals</i>. The basic concept of what a spiral should be, in polar coordinates, is any plot $r$ varying with $\theta$, $r=f(\theta)$, where $f$ is always increasing, and $\theta$ is allowed to go beyond the usual range of $0\leq \theta < 2\pi$ (or $-\pi < \theta \leq \pi$). The most fundamental one, of course, is $r = \theta$, which says the distance from the origin is proportional to the amount you've wound around the origin:<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitC8YShGbwF8tLlD6b7JBbWjff3Kshrk8mXUyDEYYPr8ZRly1nWr0JZULfNplRNN0Ofzrkj8gipkeoTafKLPEjRPNALfHjVX5-jjONe5S3J5G66d_MVZVwuX0kTtm1r5-vbDiYbY46n0o/s1600/archimedes-spiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="608" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitC8YShGbwF8tLlD6b7JBbWjff3Kshrk8mXUyDEYYPr8ZRly1nWr0JZULfNplRNN0Ofzrkj8gipkeoTafKLPEjRPNALfHjVX5-jjONe5S3J5G66d_MVZVwuX0kTtm1r5-vbDiYbY46n0o/s640/archimedes-spiral.png" width="640" /></a></div>
<br />
(here the angle is in radians and the equation is $r = \theta$). Of course, some people thought this was a bit boring, so Fermat spiced it up and thought what if we make the spirals wind tighter as you go around? Basically, make it a concave-down, increasing function, $r = \sqrt{\theta}$. Actually, it's more fun to also consider $r = -\sqrt{\theta}$:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZTPJSicxFsO94wgCO9aDrSg-rpSBGSjyJYV3Tcduis_zeoCCzJtXUBvH6EpA0S-Bmg75ZsdhzxJcJ7CGluCtJtvVBSSaCPmFs8ZDDDAAzfWyz2yuwERd27K2XB3f7cp8oCiyVqZXnW8U/s1600/fermat-spiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="622" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZTPJSicxFsO94wgCO9aDrSg-rpSBGSjyJYV3Tcduis_zeoCCzJtXUBvH6EpA0S-Bmg75ZsdhzxJcJ7CGluCtJtvVBSSaCPmFs8ZDDDAAzfWyz2yuwERd27K2XB3f7cp8oCiyVqZXnW8U/s640/fermat-spiral.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
($r=\sqrt{\theta}$ is in blue, and $r = -\sqrt{\theta} is in yellow$)</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This of course could more succinctly be written $\theta = r^2$. But perhaps the second-most famous, due to its ubiquity in nature (because stuff tends to grow exponentially) is the famous logarithmic spiral $r = e^{c \theta}$ or $\theta = \frac{1}{c} \log r$, which magnifies every time you spin it.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdgUDCydAKEUFE42PzOgWKQbv6aCvfW9jzAcUEcuofMD_L7V4rd5S12RUPy9L1f8ajWmqYIbcmGx_EGTs4s9x_1WfGhX3EGsCGvbN4J8HQbO0TW6O1GUvhexHmVmGh9wrG6HSdiK-tPFY/s1600/logspiral.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="628" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdgUDCydAKEUFE42PzOgWKQbv6aCvfW9jzAcUEcuofMD_L7V4rd5S12RUPy9L1f8ajWmqYIbcmGx_EGTs4s9x_1WfGhX3EGsCGvbN4J8HQbO0TW6O1GUvhexHmVmGh9wrG6HSdiK-tPFY/s640/logspiral.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
($r=e^{\theta/5}$)</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
And finally, where would we be in polar graphs if we didn't have the analogue of stuff with asymptotes? Consider $r^{-2} = \theta$ (instead of $r^+2$):</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfFUDsZg-8bkeJzYxqyM0auvw4dOAJq7zFH9NtswGLtyYt7ly0HtB3VMFIcgs8FyOTq6LQNhYFSzg-oOjT2FS5YaexuaGzNuuxrxuA1o_GcM7FzAMA0n6Sspoqv-5GxHrWtUWzLRzd4ew/s1600/lituus-of-cotes.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfFUDsZg-8bkeJzYxqyM0auvw4dOAJq7zFH9NtswGLtyYt7ly0HtB3VMFIcgs8FyOTq6LQNhYFSzg-oOjT2FS5YaexuaGzNuuxrxuA1o_GcM7FzAMA0n6Sspoqv-5GxHrWtUWzLRzd4ew/s640/lituus-of-cotes.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
This is called the <i>lituus of Cotes. </i>There's all sorts of curves from back in the day with very funny names; I used to look for a lot of them on the <a href="http://www-history.mcs.st-and.ac.uk/">MacTutor History of Math Page</a> (more specifically, its <a href="http://www-history.mcs.st-and.ac.uk/Curves/Curves.html">Curves Index</a>).</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
There's one other spiral that's my favorite, but (1) it isn't polar, and (2) there's a lot of interesting differential geometry going on in it, so I'm saving it for another post.</div>
Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com3tag:blogger.com,1999:blog-5950074794465831898.post-56928340116156762162016-04-28T10:00:00.000-07:002016-05-10T12:16:35.051-07:00Variance Solids: Volumes and $\mathscr{L}^2$, Part 2<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaFi6jMTNCKDzm7IpBPakuHD9tqVVZJTdqch-gepAYvQYp3Gr7E3_VIQ_8xnSew-5tU7NjuEdIvCsWSkD-BcMRCnKtXXb9d_di5Pyq9ewV0A5_ooqGFkJX4NHAFxLyKzIrShHyY8gWZOA/s1600/var-surf-revolution-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaFi6jMTNCKDzm7IpBPakuHD9tqVVZJTdqch-gepAYvQYp3Gr7E3_VIQ_8xnSew-5tU7NjuEdIvCsWSkD-BcMRCnKtXXb9d_di5Pyq9ewV0A5_ooqGFkJX4NHAFxLyKzIrShHyY8gWZOA/s640/var-surf-revolution-2.png" width="640" /></a></div>
<br />
<a href="http://www.nestedtori.com/2016/04/volumes-of-solids-and-squared-mathscrl2.html">Last time</a>, we talked about how the classical $\mathscr{L}^2$ norm of a (one-variable) function could be visualized as a solid consisting of squares. Of course, there's another formula that is defined by almost the same formula, with an extra factor of $\pi$: the <i>solid of revolution</i> of the function about the $x$-axis: \[<br />
V = \int_a^b \pi f(x)^2\,dx<br />
\]<br />
It looks pretty cool, although not quite as cool as twisted square cross-sections.<br />
<br />
I wanted to mention another common application of $\mathscr{L}^2$ norms that probably is more familiar than any other: the statistical concept of <i>variance</i>. For functions $f$ defined on a continuous domain, we can define an average value:\[<br />
\overline{f} = \frac1{b-a}\int_a^b f(x)\,dx.<br />
\] which basically is the height of a rectangle over the same domain $[a,b]$ <i>that has the same area as the area under </i>$f$. For example, for \[<br />
f(x) = \sin \left( x \right)\sin \left( t \right)+\frac{1}{3}\sin \left( 5x \right)\sin \left( 5t \right)+\frac{1}{3}\sin \left( 10x \right)\sin \left( 10t \right)+\frac{1}{5}\sin \left( 15x \right)\sin \left( 15t \right)<br />
\]<br />
(choosing $t=3.030303$), it looks like:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbG6uYgDnkoIWS1YY_SNeaSVxT8LdUzzIxC1NL9yqQ6SSc0cw4XipwLPZoaRtc_xNeKYJkwmx7gR7Rer3Tj8K3Nq0Mp36tgkpLzs9L3W04R39wJ-y1NQhpiXlch5lb2Fc-JCBQFFNuXtw/s1600/var-surf-generator.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="476" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbG6uYgDnkoIWS1YY_SNeaSVxT8LdUzzIxC1NL9yqQ6SSc0cw4XipwLPZoaRtc_xNeKYJkwmx7gR7Rer3Tj8K3Nq0Mp36tgkpLzs9L3W04R39wJ-y1NQhpiXlch5lb2Fc-JCBQFFNuXtw/s640/var-surf-generator.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
(the blue line in the middle is the mean value). The variance $\sigma^2$ is then a measure of how far $f$ is from its mean:\[
\sigma^2 = \frac{1}{b-a}\int_a^b (f(x) - \overline{f})^2\,dx.
\] This of course can be visualized exactly as <a href="http://www.nestedtori.com/2016/04/volumes-of-solids-and-squared-mathscrl2.html">last time</a>, namely, make a bunch of square cross sections about the line $y=\overline{f}$, and possibly do funny things to such squares, such as rotate it. But ... for kicks, let's add a factor of $\pi(b-a)$:\[
\pi(b-a)\sigma^2 = \int_a^b\pi (f(x) - \overline{f})^2\,dx,
\] <i>which is precisely the same quantity as the solid obtained by revolving $f(x)$ around its mean $y=\overline{f}$.</i> The resulting solid is the title picture.Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-50147011693742093822016-04-24T02:38:00.001-07:002016-04-28T00:50:29.474-07:00Volumes of Solids and (squared) $\mathscr{L}^2$ Norms<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9SmBFQ3vwRh9sguBqNUlgjyREqATUtUKXm_HpMQuxqcRphYSBv2fIXULvo8xuvNzLNoqdufcjmQuUfaQKRlIVy68jx64csbsSCOpPAadKTP2e6fYhZqRrUUs_YeQn0EuqTJgAYaQ7390/s1600/l2norm-swirl.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9SmBFQ3vwRh9sguBqNUlgjyREqATUtUKXm_HpMQuxqcRphYSBv2fIXULvo8xuvNzLNoqdufcjmQuUfaQKRlIVy68jx64csbsSCOpPAadKTP2e6fYhZqRrUUs_YeQn0EuqTJgAYaQ7390/s640/l2norm-swirl.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The volume of this solid is the squared $\mathscr{L}^2$ distance between $y=x^2$ and $y=x^3$ on the interval $[0,\frac{3}{2}]$.</td></tr>
</tbody></table>
<br />
The good ol' $\mathscr{L}^2$ norm has an outsized importance in many applications of math, principally, because Hilbert spaces (spaces with inner product) are useful for, well, just about anything. Much of a fan of Hilbert spaces I might have been for much of my recent life, it is only when teaching how to find the volume of solids (and a little help from Math Homie William) when it hit me what the best visualization for them is, at least for functions defined on $\mathbb{R}$. (For the longest time, I just said "It's sort of like the area between two curves, but, you know, squared, and stuff.") But we learn in integration theory that we can base a solid by putting squares (or semidisks or triangles, or whatever) in a perpendicular, 3rd dimension, over the area between curves; the volume of the solid is \[<br />
V=\int_a^b A(x) \, dx<br />
\] where $A(x)$ is the area of the cross section. But of course there's an obvious candidate: if you choose <i>squares</i> to have side length being the height of your function $f(x)$, then $A(x)$ is just $f(x)^2$. Thus,\[<br />
V = \int_a^b f(x)^2 dx.<br />
\] But that's none other than the squared $\mathscr{L}^2$ norm of $f$! Similarly, for the volume of a solid consisting of squares between two curves $f(x)$ and $g(x)$, this is just \[<br />
V=\int_a^b (f(x) - g(x))^2dx,<br />
\] the (squared) $\mathscr{L}^2$ distance between the two functions. Now if we treat each of these squares like a deck of cards, and rotate them, it shouldn't change the volume. So we apply this to the functions $f(x)=x^2$ and $g(x)=x^3$ on $[0,\frac{3}{2}]$:<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghxaohUxlCYzYNwTRJNmT5PywpcJrY4GqVS-HViGXJyTIVhBxQQhpKruysugt3r88nPZP-MoXldLVPQ6iYNtLzT4cl_yh-7_qiK_Rd0yGfwHW7MqETPGza7TGDYYssd4NoKG6K1Cxbxek/s1600/abetween.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="476" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghxaohUxlCYzYNwTRJNmT5PywpcJrY4GqVS-HViGXJyTIVhBxQQhpKruysugt3r88nPZP-MoXldLVPQ6iYNtLzT4cl_yh-7_qiK_Rd0yGfwHW7MqETPGza7TGDYYssd4NoKG6K1Cxbxek/s640/abetween.png" width="640" /></a><br />
<br />
Now making vertical segments between the curve, and making a square with that side length pop half out of the plane, and half into the plane, gives us a nice solid. Rotating it gives the picture at the top.<br />
<br />Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-91919210525230935752016-04-15T21:02:00.000-07:002016-04-28T00:49:23.760-07:00Polar Coordinate ClassicIn some sense, my first "Nested Tori" was a notebook which contained really cool plots and graphs. There's lots of old gems there worth posting and updating. Today, I bring you a nice polar plot. I was really intrigued by plots in polar coordinates, because it represented the first real departure from simply graphing $y=f(x)$. We instead (most commonly) write $r = f(\theta)$ where $r$ is distance from the origin and $\theta$ is counterclockwise angle, and let things get farther or closer as we go around. Without further ado, here is the famed butterfly (it does have a little post-warping afterward, though), which shows you that you don't need fancy-schmancy 3D stuff to still find great things:<br />
<div>
<br />
<div>
$r = e^{\sin \theta} - 2 \cos(4\theta) +\sin^5\left(\dfrac{\theta-\frac{\pi}{2}}{12}\right), 0 \leq \theta \leq 24\pi$</div>
<div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs9y8shseLUq3ZyGSr4Jcra7IVmtnpxeSpP3GNaqaJMVjhEbVG1UWvUeVLdMPyrkOrvtHTxQt3YBW0TmOFiOsoyMEnW_ljmEIGOUutDLalA-c0xUqGFwyh5UkuXpkMJjgXwMxRQbSRbnA/s1600/butterfly.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs9y8shseLUq3ZyGSr4Jcra7IVmtnpxeSpP3GNaqaJMVjhEbVG1UWvUeVLdMPyrkOrvtHTxQt3YBW0TmOFiOsoyMEnW_ljmEIGOUutDLalA-c0xUqGFwyh5UkuXpkMJjgXwMxRQbSRbnA/s640/butterfly.png" width="494" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div>
<br /></div>
</div>
</div>
Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-78036224843839431422016-04-11T13:45:00.001-07:002016-04-11T18:16:11.421-07:00Pasta Parametrization, High ResolutionIntegrating (ha ha) Nested Tori back into life (of course I'm doing a lot of integrating, if I'm teaching, anyway). Lots of change was (and is) afoot.<br />
<div>
<br /></div>
<div>
Anyway, instead of continually getting peeved with Apple for <i>not</i> ever fixing any bugs in Grapher for over 10 years (a job that I would <i>gladly</i> take the mantle on, by the way: anyone at Apple listening??), I took matters into my own hands and started experimenting with some open source plotting libraries. In particular, I've taken somewhat of a liking for <a href="http://matplotlib.org/">matplotlib</a>, a famous Python package. The boon is, it can generate pdf files properly (unlike Grapher, which basically puts the bitmap into a pdf file and adds the extension .pdf, but when you zoom in, it's blocky and clearly still a bitmap). Honestly, though, it <i>is</i> in fact a lot more work (which was mitigated somewhat by defining some functions).</div>
<div>
<br /></div>
<div>
Here are the results for plotting the <a href="http://www.nestedtori.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">Pasta Parametrization</a> in matplotlib (specifically, the mplot3d toolkit):</div>
<div>
<br /></div>
<div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtzarSz6E_f2wLQZgbeAe51cOzeyb3YDfhaqYIvfxXdq0wp9zehOCKasOxSlS8VTS2URZ0xuajYrkmfdOb8dMRWe9iBlwSgxuJdQDzQC2lgJQ5emmiwsyZsgUSEcchm_O-iqQT_TfciA/s1600/pasta-hi-res-bitmap.png" imageanchor="1"><img border="0" height="526" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtzarSz6E_f2wLQZgbeAe51cOzeyb3YDfhaqYIvfxXdq0wp9zehOCKasOxSlS8VTS2URZ0xuajYrkmfdOb8dMRWe9iBlwSgxuJdQDzQC2lgJQ5emmiwsyZsgUSEcchm_O-iqQT_TfciA/s640/pasta-hi-res-bitmap.png" width="640" /></a></div>
<div>
<br /></div>
<div>
Of course, I should probably figure out how to control the lighting better: it doesn't look as good as Grapher's (at a scale for which the resolution issue is not a problem). And here are the matching formulas (at a larger size than the old version):</div>
<div>
<br /></div>
<div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5jFk-41VFmTFrCNP2FFBtndLOBVAtKq9EGwiIE6Y-f7K_qP8ZVyaUMOUftvr80IwcKWAkDGWHAd5saw98raKK_vPe9qbZFCY2zbQyUzhwy8ldracSoJNGopmmn3BHsMIB3Q_FQ77Hl3k/s1600/latex-image-1.png" imageanchor="1"><img border="0" height="506" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5jFk-41VFmTFrCNP2FFBtndLOBVAtKq9EGwiIE6Y-f7K_qP8ZVyaUMOUftvr80IwcKWAkDGWHAd5saw98raKK_vPe9qbZFCY2zbQyUzhwy8ldracSoJNGopmmn3BHsMIB3Q_FQ77Hl3k/s640/latex-image-1.png" width="640" /></a></div>
<div>
<br /></div>
<div>
Happy parametrizing! (see <a href="http://www.nestedtori.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">here</a> for the answer key, and <a href="https://ccom.ucsd.edu/~ctiee/nt/PastaParam.py">here</a> for the Python source)<br />
(Astute readers may notice that the above images are actually <i>still</i> bitmaps... but that's an artifact of the blogging software, which does not natively display pdf's ... see <a href="https://ccom.ucsd.edu/~ctiee/nt/pasta-param.pdf">here</a> for the pdf for that)</div>
Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com4tag:blogger.com,1999:blog-5950074794465831898.post-25204059094702932302015-09-21T16:03:00.000-07:002015-09-26T00:14:11.914-07:00The Configuration Space of All Lines In the Plane<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn_t6vv6PQpFRvlEUHN2S32hZfEFSs9Qe8biNVRng2WCXi83RdRf0DI1cu6vHH5nLL2wDL7Cq-P0NAHqqXoiqUxTPs2-6WMd3_l8IDuRn0F0X1pL0RP17wAXQtYHqKcz5LPsPZEC2avAw/s1600/Mo%25CC%2588bius+strip.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="522" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn_t6vv6PQpFRvlEUHN2S32hZfEFSs9Qe8biNVRng2WCXi83RdRf0DI1cu6vHH5nLL2wDL7Cq-P0NAHqqXoiqUxTPs2-6WMd3_l8IDuRn0F0X1pL0RP17wAXQtYHqKcz5LPsPZEC2avAw/s640/Mo%25CC%2588bius+strip.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Time for another classic post from the old site, while I'm at it… As we have seen in a bunch of previous posts, the notion of <i>configuration space</i> has held a prominent place in my mathematical explorations, because, I can't emphasize enough, it's not just the geometry of things that you can directly <i>see</i> that are important; it's the use of geometric methods to model many things that is.</div>
<br />
Consider all possible straight lines in the plane (by <em>straight line</em> I mean those that are infinitely long). This collection is a configuration space—a <em>catalogue </em>of these lines. What does that mean? Of course, in short words, it's a manifold, and we've talked about many of those before. But it always helps to examine examples in detail to help develop familiarity. Being a manifold means we can find local <a href="http://www.nestedtori.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">parametrizations</a> of our collection by $n$-tuples of real numbers. How do we do this for lines in the plane?<br />
<br />
<h4>
Finding Some Coordinates: The Slope-Intercept Equation</h4>
First off, almost anyone reading this, regardless of mathematical background, probably was drilled at one time or another on the following famous equation, called the <em>slope-intercept equation</em>:<br />
\[<br />
y = mx + b.<br />
\] The variable <em>m</em> if you recall is the slope of a line, and <em>b</em> is the <em>y-intercept</em> which means where the line crosses the <em>y</em>-axis. However few people realize that what they're doing, really, is <em>indexing</em> every non-vertical line in the plane with some <em>point</em> in <em>another</em> plane (called, say, the <em>mb</em>-plane rather than the old traditional <em>xy</em>-plane). That is, we have a correspondence between points in one abstract <em>mb</em>-plane to the lines in the <em>xy</em>-plane, where <em>m</em> is the slope, and <em>b</em> the <em>y</em>-intercept. It doesn't get all lines, though—vertical lines have infinite slope, and you can't have a coordinate on any plane with an infinite value. That is, you have <em>charted out</em> the space of all possible nonvertical lines with points in a <em>different</em> plane.<br />
<br />
Of course how would we catch the vertical lines? We chart it out using different coordinates. There's the possibility of using <em>inverse slope</em> and <em>x</em>-intercept, which merely means we write the equation using <em>x</em> as a function of <em>y</em>. In other words, all <em>non-horizontal</em> lines are given by:<br />
\[<br />
x=ky + c.<br />
\] It's essentially obtained by reflecting everything about the diagonal line <em>x</em> = <em>y</em> and finding the usual slope and intercept. In other words we can <em>chart out</em> all non-horizontal lines on this new <em>kc</em>-plane. So you could represent the collection of all lines in the plane by having two charts... an <em>atlas</em> or <em>catalogue</em> of all lines, with these two sheets, the <em>mb</em>-plane and the <em>kc</em>-plane.<br />
<br />
<em>However</em>, note that <em>most</em> lines in the plane—ones that are neither vertical nor horizontal, can be represented in both forms. That is, they correspond to points on <em>both</em> sheets. So, we would say in our usual terminology that these two sheets, or charts, determine a manifold of all possible lines; we just need to check that the overlap is smooth. But let's stop to think about what that means. We can think of it as trying to <em>glue together</em> both sheets to form just a single catalogue. The method of gluing is that we glue together the points that represent the same line in the plane. There is a nice, exact formula for the gluing, which is very simply determined: $(m,b)$ and $(k,c)$ represent the same line if and only if $y = mx + b$ and $x = ky + c$ are equations of the same line. All we have to do to convert from one to the other is solve for <em>x</em> in terms of <em>y</em>, that is, <em>invert</em> the functions. So we solve<br />
\[<br />
y = mx + b \iff y-b = mx \iff y/m - b/m = x \iff x = (1/m) y - b/m<br />
\] that is, if $k = 1/m$ and $c = -b/m$, then $(m,b)$ and $(k,c)$ represent the same line in the two sheets. So to "glue" the sheets together, we glue every $(m,b)$ in the <em>mb</em>-plane to $(1/m,-m/b)$ in the <em>kc</em>-plane. Obviously the sheets need to be made of some very stretchable material, because it is going to be awfully hard to glue points together. Actually it's pretty hard to physically do this so don't try this at home, but just try to imagine it (don't you just love thought experiments?). For example, points in the <em>mb</em>-plane $(1,1)$, $(2,2)$, $(3,3)$, and $(4,4)$ get glued to the corresponding points $(1,-1)$, $(1/2,-1)$, $(1/3,-1)$, and $(1/4,-1)$. You glue them in a very weird way, but if you suppose for a moment, that you allow all sorts of moving, rotating, shrinking, stretching in this process (<em>topological</em> deformations), but without tearing, creasing, or collapsing, you can preseve the "shape" of this space, and yet make it look like something more familiar. This would be our new catalogue of lines. In addition, the catalogue has an additional property: nearby points in the catalogue translate to very similar-looking lines.<br />
<br />
<h4>
So, What Is It?</h4>
One should wonder what kind of overall "shape" our nice spiffy catalogue has, after gluing together the two possible charts we've made for it. As it turns out, its shape is the <em>Möbius strip! </em>That's right, the classic one-sided surface (without, as it turns out, its circle-boundary). <br />
<br />
That is to say, if you give me a point on the <em>Möbius strip</em>, it specifies one and only one line in the plane. One would not, initially, be able see why non-orientability enters the picture. But a little interpretation is in order. First, if we take a particular line and rotate it through 180 degrees, we get the same line back. Everything in between gives every possible (finite) slope. It so happens that as far as slopes of lines is concerned, $\infty=-\infty$, and if you go "past" this single <i>projective infinity,</i> as they call it, you go to negative slopes. In other words, if you start on a journey on rotating a line through 180 degrees, from vertical back to vertical, you come back to the same line, except with orientation reversed (because what started out as pointing up now points down).<br />
<br />
<div style="text-align: center;">
<span style="text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dww-z7g_4nKH-TlZZK-qV1UyISfFqXWVI9yj08v1wX8ToN2nbE86_FbNfD1p4eVnZHTLZDS2cKtakXP-y1w4Q' class='b-hbp-video b-uploaded' frameborder='0'></iframe></span></div>
<br />
If you fix an origin and declare that it correspond to a certain special line in the plane, and then select a "core circle" for the Möbius strip, then as you travel around this circle, the distance traveled represents rotation angle for this special line. Traveling from the origin along the core circle and making one full loop should correspond to rotating the special line by 180 degrees. If you instead move up or down on the core circle, you instead end up sliding the line along a perpendicular direction, without changing its angle. So moving up and down the strip corresponds to parallel sliding of lines, and moving around the strip along a circle corresponds to rotating a line.<br />
<br />
<h4>
The Derivation</h4>
The specific formula we use is \[<br />
F(m,b) = \left(\cot^{-1} m, \frac{b}{\sqrt{m^2 + 1}}\right),<br />
\] which sends the line to the angle it makes with the $y$-axis, and its signed perpendicular distance to the origin (the sign is determined by $b$). For the other chart, \[
F(k,c) = \begin{cases}\left( \cot^{-1} \left( \frac{1}{k}\right), \dfrac{c}{\operatorname{sgn}(-k)\sqrt{k^2+1}}\right) \quad & \text{ if } k \neq 0 \\<br />
(0,-c) & \quad \text{ if } k = 0<br />
\end{cases}<br />
\] We'll show how we got this in an update to this post, or perhaps a "Part 2." This can be readily checked by simply substituting the transition charts for $(m,b)$ and $(k,c)$. However, the extra case for $k=0$ here is simply gotten by taking the limit as $k$ goes to zero <i>from above</i> in the other case. What proves that it is a Möbius strip is that, if we take the limit as $k$ goes to zero <i>from below, </i>it will approach $(\pi,c)$ instead of $(0,-c)$. This would make it discontinuous, unless we decide to <i>identify</i> $(\pi,c)$ with $(0,-c)$: the $c$ going to $-c$ means we take the strip at $\pi$ and flip it around to glue it to the strip at $0$ (see <a href="http://www.nestedtori.com/2012/10/an-unexpectedly-delightful-application.html">this post</a> for another example of defining a Möbius strip this way). Technically, we need an infinitely wide Möbius strip for this, but we can always scrunch it down into a finite-width strip without its boundary circle (using something like arctangent). It's just that the closer you get to the edge, the quicker things go off to infinity.<br />
<br />
The animation is an example "path" through "line space," The blue dot travels around the white circle, and the line in the plane that corresponds to it is the blue line. The red line is a reference line perpendicular to the blue one, and always passes through the origin. The distance the blue dot from the core circle (in turquoise) indicates how far from the origin that the blue and red lines intersect. Because of the "scrunching down," though, the closer to the edge of the strip we get, the more dramatic the change in distance the blue line is from the origin. Here it is again in the plane with the Möbius strip as a picture-in-picture reference:<br />
<br />
<div style="text-align: center;">
<span style="text-align: center;"><span style="text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dz9CwsuTiJK4V1CW5AoPaToQoanxMn3zpx5pe0jU_tgOXCFo9Yko7As8SSrevpFylntr9e71He0hPth1OWXUg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></span></span><br />
<span style="text-align: center;"><span style="text-align: center;"><br /></span>
</span><br />
<div style="text-align: left;">
<span style="text-align: center;">The more general object here we are describing is closely related to the notion of <i>Grassmannian manifold</i>, which are all $k$-dimensional subspaces in an $n$-dimensional vector space (the only difference is that Grassmannians only consider spaces through the origin).</span></div>
</div>
<span style="text-align: center;">
</span>Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-48757998725360116492015-09-18T17:13:00.000-07:002015-09-18T17:21:58.676-07:00Two Classic Clifford Tori Animations<div>
After much rummaging around my hard drive, I finally found some Clifford tori animations from my old site that clearly give a much better sense of how the (stereographically projected) tori change as the angle $\varphi$ changes from $0$ to $\pi/2$ (in the notation of the <a href="http://www.nestedtori.com/2015/09/clifford-circles.html">last</a> 2 <a href="http://www.nestedtori.com/2015/09/clifford-tori.html">posts</a> on this subject). Here, we've used the Clifford circles to see its effect on them as well.</div>
<div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dytVQNWO5wi7TithsqVm1hybz1kESUnFqpfHPRuW5yosW9XH9WBI1ie2Noj-iDP4OvVZVDEFXGjGb5wePvprw' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<div>
<br /></div>
<div>
It starts off with the first degenerate case of one single unit circle, and expands from there. We see that it eventually comes very close to the other degenerate case, that of the straight line, the $z$-axis.</div>
<div>
<br /></div>
<div>
Our next video requires more explanation. This time, we take one particular torus, namely the one of identical radii $\frac{1}{\sqrt{2}}$ (in the video, these two particular circles are highlighted red and blue). Now, a $3$-sphere, like any sphere, can be <i>rotated</i> (by a matrix, or a whole path of matrices, in $SO(4)$). Thus, of course, such a rotation can always be realized as a rigid motion of the ambient $4$-space containing this $3$-sphere. It is possible to continuously rotate it so that the torus within has beginning and ending configurations that look the same, <i>except that the red and blue circles have been swapped</i>. If we restrict ourselves to $3$-space, such a rigid motion is impossible, but if we allow ourselves to let the torus pass through itself, then it, too, can be done. However, visualizing the $3$-sphere version in stereographic projection, with a $4$-space rotation, we effectively allow ourselves to distort distances (actually the $4$-space distance is <i>not</i> distorted; the distortion we see is an artifact of the stereographic projection), and add a "point at infinity," so a continuous rotation is allowed to take things through that point. The rotation of the ambient $3$-sphere does not preserve our usual set of nested tori, as can be seen by letting a matrix in $SO(4)$ act directly on the coordinates of our parametrization: it jumbles up all the components. So, of course, the torus undergoes a completely different kind of motion than in our previous "expander" video.</div>
<div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzJA3di12M1zHA1RVxBUTgaph2g3_yh4-vFdDAnN58mZ3rj8vCMERd8btuZjle5ZSXszamf1jaJYg6K38P5JQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<div>
<br /></div>
<div>
<div>
What happens is we inflate our inner tube, so a part of it gets puffed up to infinity, and wraps back around, turning the torus inside-out. In fact, after wrapping back around, we're "inflating" the <i>outside</i> of the torus. Or equivalently, getting back to donuts with frosting, the dough gets bigger and bigger, and when wrapping back around, almost all of space (plus a point at infinity) is dough, and the frosting bounds an inner-tube-shaped pocket of air.</div>
<div>
<br /></div>
Anyway, the full turning inside-out (which also swaps the red and blue circles, as promised) occurs exactly halfway through the movie (the rotation continues to restore the torus to its original state in the second half). Notice how the stripes on the torus which started out horizontal now are vertical, and what used to be the "apple core" shape which surrounds the donut hole now has become a "donut segment." Plus it just looks totally awesome!</div>
</div>
</div>
Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-40507281791039059642015-09-11T14:11:00.004-07:002015-09-15T20:49:35.922-07:00Clifford Circles<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjZOxE77jDHbUuxMo3PWvp6ZAbSE490Lt_6rKG4Y5tsY2Ma8uLln0yQLZDv0ZqgyYeoTb4OB4OYOdui2SdJByy7pxdSpnvlRKrp4KdqUr0SvM5wK_BTOJc2yPrAmPMqYpjLQki64AUFFA/s1600/clifford+tori+--+new.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="560" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjZOxE77jDHbUuxMo3PWvp6ZAbSE490Lt_6rKG4Y5tsY2Ma8uLln0yQLZDv0ZqgyYeoTb4OB4OYOdui2SdJByy7pxdSpnvlRKrp4KdqUr0SvM5wK_BTOJc2yPrAmPMqYpjLQki64AUFFA/s640/clifford+tori+--+new.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">30 Clifford circles with with $\varphi = \pi/8$ and $\theta_0$ ranging from $0$ to $2\pi$</td></tr>
</tbody></table>
A discussion about <a href="http://nestedtori.blogspot.com/2015/09/clifford-tori.html">Clifford tori</a> would never be complete without a corresponding discussion about <i>Clifford circles</i>. These were featured as the logo of the UCSD math site for many years (not the case anymore, though, but I saved a screenshot!):<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizg2zl8FWz2MLl9EQZtOhWKcBnV9qLl0jXGZQm7qWNm4nJNxjiBwqnzQKZ_tMjPOobbLv9_iZXRO9e6H_QVIcPQIXc0J-g95_bxANJmoXSf5OxPecijI0KgbN2yUA3sQvduPW9tq5jJ4w/s1600/Screen+shot+2015-09-03+at+2.08.28+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="92" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizg2zl8FWz2MLl9EQZtOhWKcBnV9qLl0jXGZQm7qWNm4nJNxjiBwqnzQKZ_tMjPOobbLv9_iZXRO9e6H_QVIcPQIXc0J-g95_bxANJmoXSf5OxPecijI0KgbN2yUA3sQvduPW9tq5jJ4w/s320/Screen+shot+2015-09-03+at+2.08.28+PM.png" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Just as the Clifford tori foliate $S^3$, the Clifford circles foliate each of the Clifford tori. As part of ongoing efforts to revisit algebraic topology, this example is one of the best to explore. We begin with classical mapping, called the <i><a href="https://en.wikipedia.org/wiki/Hopf_fibration">Hopf fibration</a>, </i>which maps $S^3$ to $S^2$ by</div>
\[<br />
p\begin{pmatrix}x_1\\x_2\\x_3\\ x_4\end{pmatrix} =\begin{pmatrix}2(x_1 x_3 + x_2 x_4)\\ 2(x_2 x_3 -x_1x_4)\\ x_1^2 + x_2^2 -x_3^2 -x_4^2\end{pmatrix}.<br />
\]<br />
In fancy-schmancy homotopy-theory speak, $p$ is a generator of $\pi_3(S^2)$. Considering our previous parametrization $F$ from <a href="http://nestedtori.blogspot.com/2015/09/clifford-tori.html">last time</a>:<br />
\[<br />
F\begin{pmatrix}\varphi \\ \alpha \\ \beta\end{pmatrix} = \begin{pmatrix} \cos \alpha \cos \varphi \\ \sin\alpha\cos\varphi \\ \cos\beta\sin\varphi \\ \sin\beta\sin\varphi \end{pmatrix},<br />
\]<br />
we recall that the last coordinate of $p$ is simply $A^2 - B^2$, or $\cos^2(\varphi) - \sin^2(\varphi)$. Although I tell my students to not bother memorizing trigonometric identities, we derived that from a $\sin^2 \alpha + \cos^2 \alpha = 1$ and $\sin^2 \beta + \cos^2 \beta = 1$. We can further simplify that last coordinate to $\cos(2\varphi)$.<br />
<br />
The key property that we want to demonstrate is that each point of $S^2$ corresponds to a whole circle in $S^3$ (for any $\boldsymbol \xi$ in $S^3$, the circle in question is the inverse image $p^{-1}(\boldsymbol\xi)$), and that each of these circles corresponding to distinct $\boldsymbol \xi$, though disjoint, are nevertheless linked together.<br />
<br />
To do this, we visit the first two coordinates:<br />
\[<br />
2(x_1x_3 + x_2x_4) = 2(\cos\alpha \cos\varphi \cos\beta \sin\varphi+ \sin\alpha\cos\varphi \sin\beta\sin\varphi)<br />
\] \[= 2\sin\varphi\cos\varphi(\cos\alpha\cos\beta +\sin\alpha\sin\beta) = \sin(2\varphi) \cos(\alpha-\beta),\] where the last equation is gotten either by trolling the back of a calculus book for some trig identities, or using complex numbers. Similarly,<br />
\[<br />
2(x_2x_3 - x_1x_4) = 2(\sin\alpha \cos\varphi \cos\beta \sin\varphi- \cos\alpha\cos\varphi \sin\beta\sin\varphi)<br />
\] \[= 2\sin\varphi\cos\varphi(\sin\alpha\cos\beta -\cos\alpha\sin\beta) = \sin(2\varphi) \sin(\alpha-\beta).\]<br />
All together, we have \[<br />
p \circ F\begin{pmatrix}\alpha\\ \beta\\ \varphi\end{pmatrix} = \begin{pmatrix}\sin(2\varphi)\sin(\alpha-\beta) \\ \sin(2\varphi)\cos(\alpha-\beta) \\ \cos(2\varphi)\end{pmatrix}.<br />
\]<br />
Letting $\theta = \alpha-\beta$, we see that this looks almost like our standard parametrization of a $3$-sphere, except that the polar angle $\varphi$ is off by a factor of $2$. No matter, it's still a sphere; we just have to take care to remember that the range of <i>this</i> $\varphi$ is $[0,\pi/2]$ rather than $[0,\pi]$. This confirms, incidentally, that $p$ really maps onto the sphere, rather than merely mapping into some amorphous blob in $\mathbb{R}^3$, as one can only assume at first, because the destination of the map $p$ has $3$ coordinates. The important thing to realize is that given <i>any </i>$\boldsymbol \xi$ in $S^2$, there is a unique $\varphi_0$ in $[0,\pi/2]$ and $\theta_0$ in $[0,2\pi]$ that correspond, under the usual parametrization, to $\boldsymbol \xi$. So, to calculate $p^{-1}(\boldsymbol \xi)$, we have to see how much we can change $\alpha$, $\beta$, and $\varphi$ in order to always get $(\varphi_0,\theta_0)$. By our above computations, this is easy: $\alpha$ and $\beta$ must satisfy $\alpha - \beta = \theta_0$, and $\varphi = \varphi_0$ is already completely determined. So our only degree of freedom here is $\alpha-\beta$: given some point in the fiber $p^{-1}(\boldsymbol \xi)$, <i>if we add the same thing to both $\alpha$ and $\beta$,</i> we will stay in the fiber. This means the fiber has a parametrization that looks like<br />
\[<br />
\beta \mapsto F\begin{pmatrix}\theta_0 + \beta \\ \beta \\ \varphi_0\end{pmatrix} = \begin{pmatrix} \cos (\theta_0 + \beta) \cos \varphi \\ \sin(\theta_0 + \beta)\cos\varphi \\ \cos\beta\sin\varphi \\ \sin\beta\sin\varphi \end{pmatrix}.<br />
\]<br />
We finally finish things off by composing with the stereographic projection $P$ as before:<br />
\[<br />
\beta \mapsto \frac{1}{1-\sin\beta\sin\varphi } \begin{pmatrix}\cos (\theta_0 + \beta) \cos \varphi \\ \sin(\theta_0 + \beta)\cos\varphi \\ \cos\beta\sin\varphi \end{pmatrix}.<br />
\]<br />
Plotting this out, this gives us the nice circles shown at the start of the post. We'll continue to explore the properties of $p$ and its visualizations as we move along in algebraic topology.Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-40361259202160590582015-09-09T20:31:00.000-07:002015-09-15T20:49:07.713-07:00Some Cool Views of Projective SpaceWhile finally revisiting one of the geometry books on my shelf, Glen Bredon's <i><a href="https://books.google.com/books/about/Topology_and_Geometry.html?id=wuUlBQAAQBAJ&hl=en">Topology and Geometry</a>, </i>I encountered an exercise about showing that the projective space is homeomorphic to the <i>mapping cone</i> of a map that doubles a circle on itself (the complex squaring map $z \mapsto z^2$). The mapping cone has a nice visualization, first as a <i>mapping cylinder</i>, which takes a space $X$ and crosses it with the interval $I$ to form $X \times I$ (thus forming a "cylinder"), and then glues the bottom of it to another space $Y$ using a given continuous map $f : X \to Y$. Finally, to make the cone, it collapses the top to a single point. Of course, this can be visualized as deforming the bottom part of $X \times I$ through whatever contortion $f$ does, which might include self-intersection (and of course, it could be more gradual). So I used a good old friend, <a href="http://nestedtori.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">parametrizations</a>, to help set up an explicit example. Take a look!<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy14jS6HUiIh9Daswd1aOWMreaUdzRagc5NKaO2-u6E4ut3dZ_3y_gJA_vxPQysdgADYPDk-3kz_BfLx9PR7vEW1Hn10G2cGDb4ceHb4AT3bcM7kEWZM28AsQ42j6fx4GjlK-b-rKzrpM/s1600/molar+projective+space-2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="491" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy14jS6HUiIh9Daswd1aOWMreaUdzRagc5NKaO2-u6E4ut3dZ_3y_gJA_vxPQysdgADYPDk-3kz_BfLx9PR7vEW1Hn10G2cGDb4ceHb4AT3bcM7kEWZM28AsQ42j6fx4GjlK-b-rKzrpM/s640/molar+projective+space-2.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">An immersion of projective space into $\mathbb R^3$. Shown as a mesh to make the self-intersecting portion visible. Looks a little like a molar, although one would hope I take good enough care of my teeth to not have that many holes in it…</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeEitwew5cY-BFEkL4msO3EYY3FcFMHMrrLLS3_1v5eD7m17ogmwuK1kXxqu_YXeWBmrL7TJp-z81pIMnsh0yPyV06YyJX6CzjVOWc_aRlsioPbdvyhXn9LXYbu9_MMyva6cRFKE3t4ZY/s1600/molar+projective+space-3.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeEitwew5cY-BFEkL4msO3EYY3FcFMHMrrLLS3_1v5eD7m17ogmwuK1kXxqu_YXeWBmrL7TJp-z81pIMnsh0yPyV06YyJX6CzjVOWc_aRlsioPbdvyhXn9LXYbu9_MMyva6cRFKE3t4ZY/s640/molar+projective+space-3.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A cutaway view, now as a more solid surface, basically illustrating it now as a mapping cylinder (it is homeomorphic to projective space minus a disk, which is a Möbius strip). Anyone know a good glassblower so we can make vases that look like this?</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIsigHiZeDGEG5nVognxkwng6abSbSgMMSlm1U1kPO-0-17F3oXL0xcB__nS3B2hXbJc4w5iGf_DTx9HYlLuC0UqxpZGtwxVhr4Jusvr5NtvBeOhBTkqCfo95Z1KYKrUmAiFNUFuTSIyc/s1600/molar+projective+space-cutaway.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="493" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIsigHiZeDGEG5nVognxkwng6abSbSgMMSlm1U1kPO-0-17F3oXL0xcB__nS3B2hXbJc4w5iGf_DTx9HYlLuC0UqxpZGtwxVhr4Jusvr5NtvBeOhBTkqCfo95Z1KYKrUmAiFNUFuTSIyc/s640/molar+projective+space-cutaway.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A view from the open top, allowing us to see the self-intersecting part of the surface from above</td></tr>
</tbody></table>
<span id="goog_1536413794"></span>The equation, in "cylindrical coordinates", is $r = (2z+\cos\theta) \sqrt{1-z^2}$ for $0\leq z \leq 1$ (for the closed surface), $0 \leq z \leq 0.97$ (for the cutaway), and $0 \leq \theta \leq$ (what else?) $2\pi$. I say it in scare quotes because technically, it allows negative values of $r$. For fun, though (and to make it totally legit, even if you have qualms about negative radii), we rewrite it as a (Cartesian) parametrization (by substituting for $r$):<br />
\[<br />
\begin{pmatrix} x \\ y \\ z\end{pmatrix} = \begin{pmatrix} (2u + \cos v)\sqrt{1-u^2} \cos v\\ (2u + \cos v) \sqrt{1-u^2}\sin v \\ u\end{pmatrix}<br />
\]<br />
with $0\leq u \leq 1$ or $0.97$, and $0 \leq v \leq 2\pi$.<br />
<br />
The motivation for this is that the equations $r = a + \cos\theta$, as $a$ varies, goes from a loop traversed once to a loop that folds over itself exactly in a $2:1$ manner:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbryMoPC7Y5JyBroRP2SW4i_yWXoGoFSp4PtguGzjHPSUEWeDdtXDkY28510-AYGvgEJncAaw0-kB1CdAQ3ikYWOKMv-O0L7my9WUjLDw3AMq0xbcAFKazS308DEckyJTquZr8dhetXSc/s1600/g4410.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbryMoPC7Y5JyBroRP2SW4i_yWXoGoFSp4PtguGzjHPSUEWeDdtXDkY28510-AYGvgEJncAaw0-kB1CdAQ3ikYWOKMv-O0L7my9WUjLDw3AMq0xbcAFKazS308DEckyJTquZr8dhetXSc/s640/g4410.png" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
but now visualized stacked on top of one another. Then to collapse the top, we shrink the diameter by a function that vanishes at $1$ and approaches $0$ at infinite slope to make it smooth (topologically speaking, it is valid to let it collapse to a corner point, though). Flowers, however, are not included (you'll have to fiddle with things like $r = \cos(k\theta)$ if you want that…)<br />
<br />Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-74842018177124216472015-09-05T17:35:00.000-07:002015-09-06T14:19:52.305-07:00Distributing Points on Spheres and other ManifoldsOne of the classic problems of random-number generation and generally representing probability distributions is the problem of <i>uniform distribution of points on a </i>($2$-)<i>sphere</i> (we, of course, clarify the dimension, having gone on too many extradimensional journeys lately—but we'll quickly see that these methods are good for those cases too!). Namely, how does one pick points at random on a sphere such that every spot on it is equally likely? Naïvely, one tries to jump to latitude and longitude. But this is because we are trained to think of the sphere in terms of parametrizations (yes, <a href="http://nestedtori.blogspot.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">we like those</a>, obviously, but they are only a <i>means</i> of representation but not the be-all and end-all of geometric objects), and not in terms of quantities defined directly on the sphere itself. <i>Uniform</i> for points directly on the sphere need not correspond to uniform with respect to some real parameters defining those points. After all, the whole point of parametrization is to distort very simple domains into something more complicated. What will happen, for example, with latitude and longitude, if one distributes points uniformly in latitude, i.e., the interval $[-\pi/2,\pi/2]$ and then also distributes points uniformly in longitude, the interval $[-\pi,\pi]$, then, after mapping to the corresponding points on a sphere, one will get points concentrated near the poles:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcIUJfsifyvF5BVauU7qtHQYMxvhHdV-x5wGUgiwsrDSOn7rSneeqyw6hYPu4e2BAerv-ZUDbrS3IS6Mg5UKsDZItcLP3BNYK_Ibsj2yMNwhFb7cgSa2HqPFGU9j0fxTp__abhbjB_qiY/s1600/sphere-non-unif.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcIUJfsifyvF5BVauU7qtHQYMxvhHdV-x5wGUgiwsrDSOn7rSneeqyw6hYPu4e2BAerv-ZUDbrS3IS6Mg5UKsDZItcLP3BNYK_Ibsj2yMNwhFb7cgSa2HqPFGU9j0fxTp__abhbjB_qiY/s400/sphere-non-unif.png" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Sphere with a distribution of 2000 points, uniform in latitude and longitude, generated by MATLAB. Notice it clusters at the poles. (Here the north pole of the sphere is tipped slightly out of the plane of the page so we can see the points getting denser there. Click to enlarge.)</td></tr>
</tbody></table>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
This occurs essentially because, for example, at different latitudes, a degree of longitude can be a very different physical distance (~70 miles at the equator and goes to zero at the poles): the <i>numerical</i> correspondence does not match up to other more relevant physical measures. In more fancy-schmancy speak, uniformity in latitude and longitude (or the equivalent spherical $\varphi$ and $\theta$) means uniformly in some imaginary rectangle that we deform to a sphere. Actually, without much work, we can already intuitively see what we have to do to achieve uniformity on the sphere in terms of those coordinates: make the distribution <i>thin out</i> when the latitude indicates we're near the poles, i.e., we want the distribution of points in the parameter rectangle to look like this:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEpt2TqOj7KRU2sT9dZGRXmrd_wrBDJuMPiGaxW975YPPOZBJR39w_uISJ9C3pK_sdIOKUuy7zdFp4fBgMbaT4CHRIUzyoR2yFFgPdDdIwCdCApRibVvyEwW7NZ8ej2XY7XNG8sBjqmTw/s1600/++.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="478" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEpt2TqOj7KRU2sT9dZGRXmrd_wrBDJuMPiGaxW975YPPOZBJR39w_uISJ9C3pK_sdIOKUuy7zdFp4fBgMbaT4CHRIUzyoR2yFFgPdDdIwCdCApRibVvyEwW7NZ8ej2XY7XNG8sBjqmTw/s640/++.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Nonuniform distribution of points on the parameter rectangle $(\theta,\varphi)$. Notice the points get more sparse at the top and bottom, corresponding to $\varphi$ at its extreme values.</td></tr>
</tbody></table>
How do we express this in formulas? We need to take a look at the area element. The naïve uniform distribution gives $\frac{1}{2\pi^2}d\varphi\; d\theta$, $\frac{1}{2\pi^2}$ times the area element of the rectangle $[0,\pi]\times[0,2\pi]$, where the $1/2\pi^2$ is there to make the integral come out to $1$, as required for all probability densities. But anyone who has spent a minute in a multivariable calculus class probably got it drilled into their heads that the area element of the <i>sphere</i>, namely, that which measures the area of a piece of sphere of radius $r$, is $r^2 \sin \varphi\; d\varphi\; d\theta$ (or $r^2\sin \theta\; d\theta\; d\phi$ if you're using the physicists' convention… that's a whole 'nother headache right there). We'll take $r = 1$ here, and of course, we have to now multiply by $\frac{1}{4\pi}$ to make the density integrate to $1$. It is reasonable that actual physical area <i>would</i> correspond to an actual uniform distribution, because the area of some plot of land on a sphere will be the same no matter how the sphere is rotated: to distribute one sample point per square inch everywhere on a sphere would indeed truly give a uniform distribution. So this gives us the solution: we can still uniformly distribute in "longitude" $\theta \in [0,2\pi)$ (which accounts for the factor of $\frac{1}{2\pi} d\theta$), since the area element doesn't have any functional dependence on $\theta$ other than $d\theta$. For the $\varphi$, however, we need to weight the density, in such a manner that if we take $d\varphi$ for the moment to be the classical interpretation as an infinitesimal or just small increment in $\varphi$, the proportion of points landing between $\varphi$ and $\varphi+ d\varphi$ is approximately $\frac{1}{2}\sin\varphi \;d\varphi$ (the $\frac{1}{2}$ comes from removing the previous factor of $1/2\pi$ from the total $1/4\pi$). But that, we recognize, as $\frac{1}{2}d(-\cos \varphi)$, so if we <i>define</i> a new variable $u = -\cos \varphi$, then our area form is $\frac{1}{2} du\; \frac{1}{2\pi} d\theta$. Thus if we <i>uniformly distribute </i>$u$ in $[-1,1]$ (an interval of length $2$, so justifying the $\frac{1}{2}$), and <i>only then</i> calculate $\varphi = \cos^{-1}(-u)$ (and uniformly distribute $\theta$ in $[0,2\pi]$ as before), we do in fact get a uniform distribution on the sphere.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggcpOCcCtvH69UrsDJrwCRcpUKTJsGPyhZ_U91qPoVDG1sQa36s1v6B8Q7I7-ebFvXQTtoOhlsFgJoxSRKtc0u5LiVlsXo3EuMixdPF55MJbTEhODGxQ4TVWQwgjdNzyAzG0xWbNAfbRg/s1600/sphere-unifdist.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="475" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggcpOCcCtvH69UrsDJrwCRcpUKTJsGPyhZ_U91qPoVDG1sQa36s1v6B8Q7I7-ebFvXQTtoOhlsFgJoxSRKtc0u5LiVlsXo3EuMixdPF55MJbTEhODGxQ4TVWQwgjdNzyAzG0xWbNAfbRg/s640/sphere-unifdist.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Sphere with a uniform distribution of 2000 points (click to enlarge), generated by MATLAB</td></tr>
</tbody></table>
<h4>
</h4>
<h4>
</h4>
<h4>
So What's the More General Thing Here?</h4>
As veteran readers might have expected, this situation is not as specific as it may seem. Transforming probability density functions (pdfs), even just on a line, sometimes seems very mysterious, because it doesn't work the same way as other coordinate changes for functions one often encounters. It is <i>not</i> enough to simply evaluate the pdf at a new point (corresponding to the <i>composition</i> of the pdf with the coordinate change). Instead what is reported in most books, and sometimes proved using the Change of Variables theorem, is some funny formula involving a lot of Jacobians. But this is the <i>real </i>reason: it's because the natural object associated to probability densities is a <i>top-dimensional differential form</i> (actually, a differential <i>pseudoform</i>, which I have spent some time advocating, for the simple reason that modeling things in a geometrically correct manner really clarifies things—just think, for example, how one may become confused by a right-hand rule?). A way to view such objects, besides as a function times a standardized "volume" form, is a <i>swarm, </i>which is precisely one of these distributions of points (although they don't <i>have</i> to be random, generating them this way is an excellent way to get a handle on it).<br />
<br />
If we have some probability distribution on our space, and near some point it is specified (parametrized) by variables $x = (x_1, x_2,\dots,x_n)$, then the pdf should (locally) look like $\rho(x_1,x_2,\dots,x_n) dx_1 dx_2\dots dx_n$. Most probability texts, of course, just consider the $\rho$ part without the differential $n$-form part $dx_1\dots dx_n$. But when transforming coordinates to $y$ such that $x = f(y)$, then the standard sources simply state that $\rho$ in the new coordinates is $\rho(f(y)) \left|\det \left(\frac{\partial f}{\partial y}\right)\right|$. But <i>really</i>, it's because the function part $\rho(x)$ becomes $\rho(f(y))$ as a function usually would, and the $dx_1 \dots dx_n$ becomes $\left|\det \left(\frac{\partial f}{\partial y}\right) \right| dy_1\dots dy_n$. In total, we have the transformation law<br />
\[<br />
\rho(x_1,\dots,x_n) dx_1 \dots dx_n=\rho(f(y_1,\dots,y_n)) \left|\det \left(\frac{\partial f}{\partial y}\right) \right| dy_1\dots dy_n.<br />
\]<br />
The usual interpretation of the $n$-form $\rho(x) dx_1 \dots dx_n$ is simply that, when integrated over some region of space, gives the total quantity of whatever such a form is trying to measure (volume, mass, electric charge, or here, probability).<br />
<br />
<h4>
Another Curious Example</h4>
<div>
One perennial interesting example is the computation of two independent, normally distributed random variables (with mean $0$ and variance $\sigma^2$), and considering the distribution of their <i>polar coordinates</i>. For one variable, the normal distribution is, using our fancy-schmancy form notation,<br />
\[<br />
\rho(x)\; dx = \frac{1}{\sqrt{2\pi \sigma^2}} e^{-x^2/2\sigma^2} dx<br />
\]<br />
From the definition of independence, two normally distributed variables have a density obtained by multiplying them together:</div>
\[ \omega = \rho(x)\rho(y) \; dx\;dy = \frac{1}{2\pi\sigma^2} e^{-(x^2 + y^2)/2\sigma^2} dx\;dy.\]<br />
So if we want the distribution in polar coordinates, where $x = r \cos \theta$ and $y = r \sin \theta$, this means we transform the form part as the usual $dx\;dy = r\; dr\; d\theta$, and write the density part as $\frac{1}{2\pi\sigma^2}e^{-r^2/2\sigma^2}$. In total,<br />
\[<br />
\omega = \frac{1}{2\pi\sigma^2} r e^{-r^2/2\sigma^2} dr \; d\theta<br />
\]<br />
This factors back out into two independent pdfs (i.e., $r$ and $\theta$ are independent random variables) as<br />
\[<br />
\omega = \left(\frac{1}{\sigma^2} r e^{-r^2/2\sigma^2} dr\right) \left( \frac{1}{2\pi} d\theta\right)<br />
\]<br />
which means we can take $\theta$ and uniformly distribute it in $[0,2\pi]$ as before. To get $r$, we can proceed by two ways. First, we could imitate what we did earlier with the sphere: use integration by substitution or the Chain Rule, to deduce that $\frac{1}{\sigma^2} r e^{-r^2/2\sigma^2} dr= d\left(- e^{-r^2/2\sigma^2}\right)$, and thus, making the substitution $v = - e^{-r^2/2\sigma^2}$, we now have $\omega = \frac{1}{2\pi} dv\; d\theta$. The range of $v$ has to be in $[-1,0)$, since $e^{-r^2/2\sigma^2}$ goes to zero as $r \to \infty$ and has a maximum at $1$. With this, we uniformly distribute $v \in [-1,0)$ and invert the function:<br />
\[<br />
r=\sqrt{-2\sigma^2 \log (-v)}.<br />
\]<br />
<br />
Alternatively, we can substitute $u = r^2/2\sigma^2$ (and the inverse, $r = \sqrt{2\sigma^2 u}$). Then $du = (r/\sigma^2) dr$, and $\frac{1}{\sigma^2} re^{-r^2/2\sigma^2} dr = e^{-u} du$, with $u \geq 0$. This means $u$ is distributed as an exponential random variable with parameter $\lambda = 1$. However, this is often computed using uniform $[0,1]$ variables as well, for which we simply end up using something similar to the above method. Still, however, it gives another way of <i>understanding</i> the distributions: it certainly is very interesting that two <i>normally distributed</i> random variables <i>becomes</i>, via such an ordinary transformation such as polar coordinates, (the square root of) an exponentially distributed random variable and a uniform random variable.<br />
<br />
What about <i>three</i> independent normally distributed variables (with mean zero and all the same variance)? It turns out the $r$ coordinate is not so easy (it's a gamma distribution), but the $\varphi$ and $\theta$ variables yield a uniform distribution on the sphere! However, it shouldn't be too surprising: given three independent such variables, there should be no bias on their directionality in $3$-space. We can also turn this around to give ourselves an alternate method of uniformly distributing points on a sphere (since normal random variables are very easy to generate): take three such variables, consider it a point in $\mathbb R^3$, and divide by its magnitude (I thank Donald Knuth's <i>Art of Computer Programming</i>, Volume 2 for this trick; it has an excellent discussion on random number generation).Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com0tag:blogger.com,1999:blog-5950074794465831898.post-11416410820009554392015-09-01T14:49:00.002-07:002020-11-27T16:07:43.731-08:00Clifford Tori<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjepUgpV_UKyuABw0pQhqZSmvq7uUXqyAzvj0bHwQHXDq2hrFioM5fB6LhcFOU6ugW1osyuh_VUmXmyu8myZhho52oFhJAKT0bzHK5cRFYfoAvvP2bfp2GcGKU7DVSNxwbS167QWsHFECU/s1600/morenestedtori-green-xxl.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="342" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjepUgpV_UKyuABw0pQhqZSmvq7uUXqyAzvj0bHwQHXDq2hrFioM5fB6LhcFOU6ugW1osyuh_VUmXmyu8myZhho52oFhJAKT0bzHK5cRFYfoAvvP2bfp2GcGKU7DVSNxwbS167QWsHFECU/s400/morenestedtori-green-xxl.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
As part of the ongoing celebration that is the relaunch, here, we finally give the long-awaited in-depth look at the site's namesake hinted at in <a href="http://nestedtori.blogspot.com/2012/10/welcome-to-nested-tori.html">the opening post</a>. Perhaps surprisingly in a post that ostensibly is about tori, we begin our story with a different well-known (and hopefully loved) family of spaces: the spheres. The $1$- and $2$-dimensional spheres hardly need introduction, being undoubtely the first curved geometrical objects that one studies, the ordinary circle and sphere (which for mathematicians, only refers to the <i>boundary</i> <i>surface</i>, not the interior, of a ball, so is $2$-dimensional). These shapes of course appear all the time in nature, since they satisfy many optimality properties. Much, of course, has been written about their "<a href="https://books.google.com/books/about/Perfect_Form.html?id=8uWPG0QK0UIC">perfect form</a>."<br />
<div>
<br /></div>
<div>
Higher-dimensional spheres are easy to define: <i>the set of all points a given distance from a given point</i>. Where, of course, "all points" start out as being in some higher dimensional space, say, <i>n</i>. High-dimensional spheres have interesting applications, such as in statistical mechanics, where the dimension of the state space in question is on the order of $10^{24}$ (every particle gets its own set of 3 dimensions! Again, this is why state space is awesome). Spheres occur in this context because the total energy of the system remains constant, so the sum of the squares of all their momenta has to be constant—namely, the momenta are all a certain "distance" from the origin. As crazy as it may sound, it is, at its root, a description (using <a href="http://nestedtori.blogspot.com/2015/08/hamiltonian-mechanics-is-awesome-double.html">Hamiltonian mechanics</a>) of many more than the two particles that we spent a whole <a href="http://nestedtori.blogspot.com/2015/08/the-configuration-space-of-double.html">5-part series</a> talking about! But of course, it'd take us a bit far afield to explore this (at least in this post; we should eventually feature some statistical-mechanical calculations here, because it is illustrative of how we can deal with overwhelmingly large-dimensional systems and, rather amazingly, be able to extract useful information from it!).</div>
<div>
<br /></div>
<div>
So let's get back to nearly familiar territory: $n = 3$, the $3$-sphere $S^3$ (the boundary of a ball in 4-dimensional space $\mathbb{R}^4$). Being $3$-dimensional, one would think we can visualize it or experience it viscerally somehow. As noted by <a href="http://press.princeton.edu/titles/6086.html">Bill Thurston</a>, the key to visualization of $3$-manifolds is to imagine living inside a universe that is shaped like one (this is also elaborated upon, working up from $2$-dimensional examples, by <a href="https://books.google.com/books?id=Lurp6nB4LtQC&dq=isbn:0824707095&hl=en&sa=X&ved=0CB4Q6AEwAGoVChMI-bHdifLRxwIVSQOSCh1b8gn9">Jeffrey Weeks</a>, with <a href="http://www.geometrygames.org/CurvedSpaces/index.html">interactive demos</a>). This isn't so straightforward to visualize (literally), because it is a curved 3-dimensional space. There are a number of ways of doing this; they give the essence of $S^3$ by understanding it in terms of some more familiar objects from lower dimensions, such as slicing by hyperplanes, and of course, by tori.<br />
<br /></div>
<div>
<div>
<h4>
The Clifford Tori as a Foliation of $S^3$</h4>
</div>
<div>
So where do tori (nested or not) come in? Let's get back to the defining formula of $S^3$,</div>
</div>
\[<br />
x_1^2 + x_2^2 + x_3^2 + x_4^2 = 1.<br />
\]
If we consider groups of $2$ terms, $x_1^2 + x_2^2 = A^2$, and $x_3^2 + x_4^2 = B^2$, we have, $A^2 + B^2 = 1$. But for each fixed $A$ and $B$ satisfying that relation, we get two circles: one for the coordinates $(x_1,x_2)$ and another for the coordiantes $(x_3,x_4)$. We can use this information to help <i><a href="http://nestedtori.blogspot.com/2015/08/parametric-pasta-relaunch-of-nested-tori.html">parametrize</a></i> $S^3$. Let's first ask: what are some familiar things satisfying $A^2+B^2 = 1$? If we let $A = \cos \varphi$ and $B = \sin \varphi$, then $A$ and $B$ will always satisfy this relation for any $\varphi \in \mathbb{R}$: so $\varphi$ is one possible parameter of this system, and the full possible range of $A^2$ and $B^2$ is assumed by letting $\varphi$ vary from $0$ to $\frac \pi 2$. This gives us:
\[<br />
x_1^2 + x_2^2 =\cos^2 \varphi<br />
\] and \[ <br />
x_3^2 + x_4^2 = \sin^2 \varphi.<br />
\]<br />
In other words, as $\varphi$ varies, the two sets of coordinates represent one circle that grows in radius, and another that shrinks, in such a way that the sum of the squares of the two radii are always $1$. This realizes the $3$-sphere as a collection of sets of the form $S^1(A) \times S^1(B) = S^1(\cos\varphi) \times S^1(\sin\varphi)$, the Cartesian product of circles of radius $A$ and $B$. But what is the Cartesian product of two circles? A torus. These tori fill up all of $S^3$ (except for two degenerate cases: two circles, corresponding to the Cartesian product of a unit circle and a single point—a circle of radius $0$). The technical term for this is that they <i>foliate</i> $S^3$ (from the Latin <i>folium</i> for "leaf"). They are called <i>Clifford tori</i>. Hard as it may be to believe, their intrinsic geometry, as inherited from $\mathbb{R}^4$ is <i>flat </i>(although this is not true of their <i>extrinsic</i> geometry). It means that if we have a sheet of paper, we could lay it flat on a Clifford torus in $\mathbb{R}^4$ (you can't do that in $\mathbb{R}^3$ with your garden-variety donut-shaped torus). However, a full study of the geometry of these tori will have to wait for another time. Here, we will be content to <i>visualize</i> them (which, unfortunately, will not preserve that flat geometry we are claiming they have). For the visualization, we use another tool, the <i>stereographic projection.</i> Before we get to that, we finally note that, for each given $\varphi$, each of the circles $S^1(\cos \varphi)$ and $S^1(\sin\varphi)$ can be further parametrized with other angles; we take<br />
\[<br />
(x_1,x_2) = (\cos \alpha \cos \varphi, \sin \alpha \cos \varphi)<br />
\] and \[<br />
(x_3,x_4) = (\cos \beta \sin \varphi, \sin \beta \sin \varphi),<br />
\]<br />
where $0\leq \alpha,\beta \leq 2\pi$. So this means we have parametrized $S^3$ by 3 variables, $(\varphi,\alpha,\beta)$ varying over $[0,\pi/2]\times [0,2\pi]\times [0,2\pi]$.<br />
<br />
<h4>
<a name="stereo">The Stereographic Projection</a></h4>
<div>
There's a way to project (almost) the whole $3$-sphere into ordinary $3$-space $\mathbb{R}^3$. To understand how we can project the $3$-sphere (minus a point) into $3$-space, let's look at the analogous problem for the $2$-sphere, first. It so happens that the stereographic projection is extremely useful in that case as well, and is the source for many arguments involving "the point at infinity" in complex analysis. The way it works is to imagine screwing in a light bulb at the top of a sphere resting on a plane, and given a point on a sphere, its shadow cast on the plane by this light is the corresponding plane (shown in the figure below for a line: the dots connected by the blue rays correspond).<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsyQV89wpQQxlnnOPczwoqoFpa-ImvSk_vILVH4ZjW6n0irRlUOf2uKYpI352E_G83beCAJv8jPNiLHyAR5SDQEl5z5xFtoG2q0vjodSc74nJFz01EB6gQXcdAuV1TI3Kvfs1WL6JrWhU/s1600/projective-line-diagram.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsyQV89wpQQxlnnOPczwoqoFpa-ImvSk_vILVH4ZjW6n0irRlUOf2uKYpI352E_G83beCAJv8jPNiLHyAR5SDQEl5z5xFtoG2q0vjodSc74nJFz01EB6gQXcdAuV1TI3Kvfs1WL6JrWhU/s640/projective-line-diagram.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Some corresponding points for the stereographic projection of a circle (here of radius $\frac 1 2$) to a line.</td></tr>
</tbody></table>
Notice that the closer it gets to the top, the farther out the rays go (thus, the farther out the corresponding point). And the top point falls on a horizontal line, which will never intersect the corresponding plane of projection: it is said to be sent to the "point at infinity". But the thing is, that extra point at infinity is, at least for the plane as we've defined it, truly <i>extra</i>, so the stereographic projection <i>really</i> simply maps the sphere <i>minus one single point</i> to the plane. In formulas, for a sphere of radius $\frac{1}{2}$ centered at $(0,0,\frac{1}{2})$, this is<br />
\[<br />
\left(\frac{x}{1-z},\frac{y}{1-z}\right).<br />
\]<br />
Of course, if we want to map the <i>unit</i> (radius 1 and origin-centered) sphere, we have to do a little finessing with an extra transformation, namely, $(x',y',z') = (2x, 2y, 2z-1)$. It <i>so happens</i> that we get the exact same formula back, just a different domain:<br />
\[<br />
\left(\frac{x}{1-z},\frac{y}{1-z}\right) = \left(\frac{\frac{1}{2}x'}{1-\frac{1}{2}z'-\frac{1}{2}},\frac{\frac{1}{2}y'}{1-\frac{1}{2}z'-\frac{1}{2}}\right) =\left(\frac{x'}{1-z'},\frac{y'}{1-z'}\right).<br />
\]<br />
For this reason, many people start off with this formula for the unit sphere instead. The <i>picture</i> associated to this actually is nice: it projects rays of light from the top, through the sphere, and onto a plane that <i>slices</i> the sphere exactly in half at its equator. The consequence is that the light hits the corresponding point in the plane first before reaching a point in the lower hemisphere (but, mathematically, we keep the mapping as always from the sphere to the plane, regardless which the light beam would hit first). It should also be noted that the inverse mapping, of course, will be different (we won't be needing the inverse mapping here, but it is also useful in other contexts, and can be derived using elementary, if tedious, means, via messy algebra).<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLWD3dkLUfDg5gckVS0u70ME3eL_9KK03yx2DuujVt7s6_2qQKvIb6NT_lY4cLGw1dbXphsIYIW7MkUU_SaLsKxqYt7pdI3heQfcI83mJLS_Papt3qzJxnf52QTdIvqB1Ye_0MrLzo9NY/s1600/Screen+shot+2015-08-31+at+6.23.10+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLWD3dkLUfDg5gckVS0u70ME3eL_9KK03yx2DuujVt7s6_2qQKvIb6NT_lY4cLGw1dbXphsIYIW7MkUU_SaLsKxqYt7pdI3heQfcI83mJLS_Papt3qzJxnf52QTdIvqB1Ye_0MrLzo9NY/s640/Screen+shot+2015-08-31+at+6.23.10+PM.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Stereographic projection of the unit, origin-centered sphere to the plane containing its equator. The projection associates the point $P$ to the point $Q$.</td></tr>
</tbody></table>
<br />
So we generalize this formula: for the unit 3-sphere, given as $x_1^2 + x_2^2 + x_3^2 + x_4^2 = 1$, we have a stereographic projection $P$ of all of its points except the point $(0,0,0,1)$, to $\mathbb{R}^3$, as follows:<br />
\[<br />
P \begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4\end{pmatrix} =\frac 1 {1-x_4}\begin{pmatrix} x_1\\ x_2 \\ x_3\end{pmatrix}.<br />
\]<br />
In order to visualize our Clifford Tori, then, we recall the parametrization derived above:<br />
\[<br />
\begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4\end{pmatrix} = F\begin{pmatrix}\varphi \\ \alpha \\ \beta\end{pmatrix} = \begin{pmatrix} \cos \alpha \cos \varphi \\ \sin\alpha\cos\varphi \\ \cos\beta\sin\varphi \\ \sin\beta\sin\varphi \end{pmatrix}.<br />
\]<br />
The two circles that we want are when $\alpha$ and $\beta$ vary, so if we select a few values of $\varphi$ and draw the surface by the parametrization with the remaining variables, we will get different tori for each value of $\varphi$. <i>But</i>, of course, this still gives the torus as being in $\mathbb R^4$. So we compose this with the stereographic projection: for fixed $\varphi$, and letting $\alpha, \beta$ vary, we consider parametrizations<br />
\[<br />
\Phi \begin{pmatrix} \varphi \\ \alpha \\ \beta \end{pmatrix} = P \circ F\begin{pmatrix} \varphi \\ \alpha \\ \beta \end{pmatrix} = \frac{1}{\sin\beta\sin\varphi} \begin{pmatrix} \cos \alpha \cos \varphi \\ \sin\alpha\cos\varphi \\ \cos\beta\sin\varphi \end{pmatrix}.<br />
\]<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht4etKIgp5AfdSLMjVs6NDpBgNw07lz3SWCipNCUZC8D6CWuCkqkDAi5b7egIkcMuZw3-OjVF5XfNu4hFEReucP4STvre45n8uqSLPFRnubheyysco13792CCU_dmao4oFNwlls2geLmc/s1600/clifford+tori.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht4etKIgp5AfdSLMjVs6NDpBgNw07lz3SWCipNCUZC8D6CWuCkqkDAi5b7egIkcMuZw3-OjVF5XfNu4hFEReucP4STvre45n8uqSLPFRnubheyysco13792CCU_dmao4oFNwlls2geLmc/s400/clifford+tori.jpg" width="400" /></a></div>
<br />
<br />
These are the tori given in the <a href="http://nestedtori.blogspot.com/2012/10/welcome-to-nested-tori.html">opening post</a> (the tori are deliberately shown incomplete, with $\beta$ not going full circle, so that you can see how they change with different $\varphi$ and that they are <i>nested</i>. Note that this transformation does not preserve sizes, so even though we said that "one circle gets bigger as the other gets smaller", this is not what happens in the projection. Think of a sphere with circles of latitude; they grow from one pole to the equator and shrink back down from the equator to the other pole, but their stereographic projections to the plane just keep growing. The other view of this, and the site's logo, is simply a cutaway view of the stereographic projections by one vertical plane. As a note of thanks, bridging years, one of the sources of inspiration for learning about Clifford tori and their visualizations has come from Ivars Peterson's <i><a href="https://books.google.com/books?id=BhkrN0vL9aYC&source=gbs_book_other_versions">The Mathematical Tourist</a></i>. (He maintains a<a href="http://mathtourist.blogspot.com/" target="_blank"> blog</a> as well).<br />
<br />
We should finally note that this is <i>not</i> the same parametrization as our usual <a href="http://nestedtori.blogspot.com/2012/10/fun-equations-of-torus-fenics-part-2.html">torus of revolution</a>. Parametrizations are not unique. The Clifford tori have many interesting, topologically important properties that will certainly be fodder for future posts.<br />
<h4>
</h4>
</div>
Chrishttp://www.blogger.com/profile/18171898639160337398noreply@blogger.com1