Peter Kagey

Author: peterkagey

  • My Favorite Sequences: A261865

    My Favorite Sequences: A261865

    —

    by

    peterkagey

    This is the first installment in a new series, “My Favorite Sequences”. In this series, I will write about sequences from the On-Line Encyclopedia of Integer Sequences that I’ve authored or spent a lot of time thinking about. I’ve been contributing to the On-Line Encyclopedia of Integer Sequences since I was an undergraduate. In December…

  • Richard Guy’s Partition Sequence

    Richard Guy’s Partition Sequence

    —

    by

    peterkagey

    Neil Sloane is the founder of the On-Line Encyclopedia of Integer Sequences (OEIS). Every year or so, he gives a talk at Rutgers in which he discusses some of his favorite recent sequences. In 2017, he spent some time talking about a 1971 letter that he got from Richard Guy, and some questions that went…

  • A π-estimating Twitter bot: Part III

    A π-estimating Twitter bot: Part III

    —

    by

    peterkagey

    In the final part of this three-part series, I’ll give technical step-by-step instructions for how to wire up our Twitter bot, @BotfonsNeedles, to Docker and deploy it on the free tier of AWS Lambda, so that it can run until the end of time. I’ll also include some tips that I wish I knew when…

  • A π-estimating Twitter bot: Part II

    A π-estimating Twitter bot: Part II

    —

    by

    peterkagey

    This is the second part of a three part series about making the Twitter bot @BotfonsNeedles. Click here for Part I. In this part, I’ll explain how to use the Twitter API to post the images to Twitter via the Python library Tweepy, and keep track of all of the Tweets to get an increasingly…

  • A π-estimating Twitter bot: Part I

    A π-estimating Twitter bot: Part I

    —

    by

    peterkagey

    This is the first part of a three part series about making the Twitter bot @BotfonsNeedles. In this part, I will write a Python 3 program that uses a Monte Carlo method to approximate \(\pi\) with Buffon’s needle problem, and produces an image with the Python library Pillow In the second part, I’ll explain how…

  • Polytopes with Lattice Coordinates

    Polytopes with Lattice Coordinates

    —

    by

    peterkagey

    Problems 21, 66, and 116 in my Open Problem Collection concern polytopes with lattice coordinates—that is, polygons, polyhedra, or higher-dimensional analogs with vertices the square or triangular grids. (In higher dimensions, I’m most interested in the \(n\)-dimensional integer lattice and the \(n\)-simplex honeycomb). This was largely inspired by one of my favorite mathematical facts: given…

  • Parity Bitmaps from the OEIS

    Parity Bitmaps from the OEIS

    —

    by

    peterkagey

    My friend Alec Jones and I wrote a Python script that takes a two-dimensional sequence in the On-Line Encyclopedia of Integer Sequences and uses it to create a one-bit-per-pixel (1BPP) “parity bitmaps“. The program is simple: it colors a given pixel is black or white depending on whether the corresponding value is even or odd.…

  • Stacking LEGO Bricks

    Stacking LEGO Bricks

    —

    by

    peterkagey

    Back in May, I participated in The Big Lock-Down Math-Off from The Aperiodical. In the Math-Off, I went head-to-head against Colin Beveridge (who has, hands-down, my favorite Twitter handle: @icecolbeveridge). Colin wrote about using generating functions to do combinatorics about Peter Rowlett’s toy Robot Caterpillar. Coincidentally and delightfully, I wrote about using generating functions to…

  • Regular Truchet Tilings

    Regular Truchet Tilings

    —

    by

    peterkagey

    I recently made my first piece of math art for my apartment: a 30″×40″ canvas print based on putting Truchet tiles on the truncated trihexagonal tiling. I first became interested in these sorts of patterns after my former colleague Shane sent me a YouTube video of the one-line Commodore 64 BASIC program: 10 PRINT CHR$(205.5+RND(1));…