Peter Kagey

Author: peterkagey

  • Saved video tweets (Part 1/4)

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    peterkagey

    As I discussed previously, I’m going through my old saved tweets and documenting them as I move to Bluesky (@peterkagey.bsky.social). 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…

  • Some Saved Tweets

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    peterkagey

    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

    An M.C. Escher-inspired poster

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    peterkagey

    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…

  • Triangle Center Patterns

    Triangle Center Patterns

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    peterkagey

    I made a video that illustrates a particularly interesting “discrete state random dynamical system,” which was inspired by a Tweet (and a mistake) that I saw. First, be hypnotized by this video, which I recommend you watch in 4K, and then scroll down to read about the inspiration and the cool math going on under…

  • How to Make Animated Math GIFs: LaTeX + TikZ

    How to Make Animated Math GIFs: LaTeX + TikZ

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    peterkagey

    The first animated GIF that I ever made was made with the LaTeX package TikZ and the command line utility ImageMagick. In this post, I’ll give a quick example of how to make a simple GIF that works by layering images with transparent backgrounds on top of each other repeatedly. TikZ code In our first…

  • XOR Triangles

    XOR Triangles

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    peterkagey

    In this post, I’ll explore the math behind one of my Twitter bots, @xorTriangles. This bot was inspired by the MathOverflow question “Number triangle,” asked by user DSM posted in May 2020. (I gave an overview of my Twitter bots @oeisTriangles in my post “Parity Bitmaps from the OEIS“. And if you want to build…

  • Robot Walks

    Robot Walks

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    peterkagey

    I’ve gotten a lot of mathematical inspiration from Project Euler questions, but perhaps the question that has gotten me thinking the most is Project Euler Problem 208: Robot Walks. In this problem, a robot takes steps either to the right or the left, and at each step, it turns \(\frac 15\) of the way of…

  • Pour Le Science and the anti-Sum-Product Problem

    Pour Le Science and the anti-Sum-Product Problem

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    peterkagey

    In March 2021, I got an out-of-the-blue email from OEIS editor Michel Marcus which totally delighted me. He wrote: This afternoon I went to the library.And I was browsing “Pour La Science” the French version of the Scientific American.And here is what I saw. I like the mysterious tone. He included this photo of an…

  • Zimin Words and Bifixes

    Zimin Words and Bifixes

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    peterkagey

    One of the earliest contributions to the On-Line Encyclopedia of Integer Sequences (OEIS) was a family sequences counting the number of words that begin (or don’t begin) with a palindrome: Let \(f_k(n)\) be the number of strings of length \(n\) over a \(k\)-letter alphabet that begin with a nontrivial palindrome” for various values of \(k\).…

  • My Favorite Sequences: A263135

    My Favorite Sequences: A263135

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    peterkagey

    This is the fourth in my installment of My Favorite Sequences. This post discusses sequence A263135 which counts penny-to-penny connections among \(n\) pennies on the vertices of a hexagonal grid. I published this sequence in October 2015 when I was thinking about hexagonal-grid analogs to the “Not Equal” grid. The square-grid analog of this sequence…