Tag: Math

Robot Walks
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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…

Zimin Words and Bifixes
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One of the earliest contributions to the OnLine 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
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This is the fourth in my installment of My Favorite Sequences. This post discusses sequence A263135 which counts pennytopenny connections among \(n\) pennies on the vertices of a hexagonal grid. I published this sequence in October 2015 when I was thinking about hexagonalgrid analogs to the “Not Equal” grid. The squaregrid analog of this sequence…

My Favorite Sequences: “Not Equal” Grid
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This is the third installment in a recurring series, My Favorite Sequences. This post discusses OEIS sequence A278299, a sequence that took over two years to compute enough terms to add to the OEIS with confidence that it was distinct. This sequence is discussed in Problem #23 of my Open Problems Collection, which asks for…

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 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…

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));…