Peter Kagey

Peter Kagey in a Rhombic Dodecahedron made from Truncated Octahedra

Hello! I’m Peter!

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  • Saved video tweets (Part 1/4)

    As I discussed previously, I’m going through my old saved tweets and documenting them as I move to Bluesky (@peterkagey.com). Here are four of those tweets (all of which had video/GIF embeddings):

    Peter Huxford on a cubic curve determined by 9 points

    I posted about this demo on Bluesky. My guess is that it is in response to a post that was drawing conic sections through five points.

    I’d like to see an applet that shows an analogous setup for an algebraic curve of arbitrary degree \(n\) that is described by \(\binom{n+2}{2}-1\) points in the plane. (Let me know if you know about one!)

    Play around with the demo yourself on on a (hacked version) of Desmos hosted on Peter Huxford’s academic website.

    Vincent Pantaloni on folding a dodecahedron

    This demonstration takes two dodecahedral half-nets and a rubber band, and *pop* turns it into a dodecahedron with a geodesic going around it—no glue or tape required!

    Paula Beardell Krieg on “Rolling Oloid”

    Some of my favorite saved tweets are the ones that I have a different perspective on now than I had when I first saved it. In particular, this demo suggested by Juan Carlos (@jcponcemath.bsky.social) and Paula Beardell Krieg (@paulakrieg.bsky.social) now reminds me of a project my students did in the “Making Mathematics” topics class that I taught at Harvey Mudd College in Spring 2024. Check out the link to my students’ blog post below.

    See the Geogebra demo, where you can change the camera angle.

    And here’s the link to my students’ project that I had promised in the lede. (The students gave the art to me as a gift, and I now have it in my office at Cal Poly Pomona!)

    Sphericoin Art

    Rob on building LEGO at the Tate Modern

    This is Olafur Eliasson’s “The cubic structural evolution project”, 2004 at the Tate Modern.

    I first learned about this artist when my wife took me to Olafur Eliasson: OPEN at The Geffen Contemporary at MOCA a few months ago, just a few stops south of our house along the A Line Metro.

    As an example of my own experience with the Baader-Meinhof phenomenon, I recently Olafur Eliasson appear in the article “The Space Club Invasion” about a indoor playplace in Brooklyn for Instagram parents on Curbed, which you should read!

    Space Club is a phenomenon in itself — half McDonald’s PlayPlace, half Olafur Eliasson installation, built for selfie-ing parents as much as their children.

    “The Space Club Invasion”

  • Some Saved Tweets

    I’ve been off Twitter for a while now, but I thought it would be useful to archive my saved posts somewhere. Here are a subset of my saved posts, which I think are mostly self-explanatory.

  • An M.C. Escher-inspired poster

    I wanted an excuse to use Harvey Mudd’s large format printer, so I made a movie-sized (27″×40″) poster for my office based on the second term of OEIS sequence A368138(n): \(A368138(2) = 154\). The idea here is that you have a a collection of tiles like , which you can rotate and mirror; you then choose a \(n \times n\) grid of these tiles, and repeat that pattern infinitely over the plane. I recently learned that this particular example (for \(n = 2\)) was first enumerated in a 1996 paper by Dan Davis, On a Tiling Scheme from M. C. Escher, in The Electronic Journal of Combinatorics.

    In my paper, “Counting Tilings of the \(n \times m\) Grid, Cylinder, and Torus,” we give a method for counting these kinds of problems in full generality. While revising the paper, I learned from Doris Schattschneider’s 1990 book Visions of Symmetry (pp 44-48) that the artist M.C. Escher was perhaps the first person to attempt counting this. (In particular, Escher successfully enumerated A368145(2) = 23.)

    Figure 3 from Bill Keehn’s and my paper “Counting Tilings of the \(n \times m\) Grid, Cylinder, and Torus“, which illustrates that there are many equivalent choices when repeating a \(2 \times 2\) pattern when ignoring the boundary.

    Notice how the whitespace and the black space are \(180^\circ\) rotations of each other. Ami Radunskaya pointed out to me that this looks like “op art.”

    If you had to choose one of these patterns to tile your bathroom floor, which would you pick?