Author: peterkagey

My Favorite Sequences: A261865
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This is the first installment in a new series, “My Favorite Sequences”. In this series, I will write about sequences from the OnLine Encyclopedia of Integer Sequences that I’ve authored or spent a lot of time thinking about. I’ve been contributing to the OnLine Encyclopedia of Integer Sequences since I was an undergraduate. In December…

Richard Guy’s Partition Sequence
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Neil Sloane is the founder of the OnLine 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 πestimating Twitter bot: Part III
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In the final part of this threepart series, I’ll give technical stepbystep 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 πestimating Twitter bot: Part II
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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 πestimating Twitter bot: Part I
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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
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Problems 21, 66, and 116 in my Open Problem Collection concern polytopes with lattice coordinates—that is, polygons, polyhedra, or higherdimensional 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
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My friend Alec Jones and I wrote a Python script that takes a twodimensional sequence in the OnLine Encyclopedia of Integer Sequences and uses it to create a onebitperpixel (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
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Back in May, I participated in The Big LockDown MathOff from The Aperiodical. In the MathOff, I went headtohead against Colin Beveridge (who has, handsdown, 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
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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 oneline Commodore 64 BASIC program: 10 PRINT CHR$(205.5+RND(1));…