Category Archives: Uncategorized

Proofs and theorems without words

Introduction In the figure below, a regular hexagon with side length 12 is tiled with “lozenges,” sort of like triangular dominoes, each consisting of a pair of unit-length equilateral triangles joined at a common side. Each lozenge is in one … Continue reading

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Hilbert halftone art

Introduction This post was motivated by a recent attempt to transform a photograph into a large digital print, in what I hoped would be a mathematically interesting way. The idea was pretty simple: convert the (originally color) image into a … Continue reading

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Probability of playable racks in Scrabble

Introduction Earlier this year, I spent some time calculating the probability of a Scrabble “bingo:” drawing a rack of 7 tiles and playing all of them in a single turn to spell a 7-letter word. The interesting part of the … Continue reading

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Analysis of Bingo

Introduction Suppose that Alice and Bob play a game for a dollar: they roll a single six-sided die repeatedly, until either: Alice wins if they observe each of the six possible faces at least once, or Bob wins if they … Continue reading

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Digits of pi and Python generators

Introduction This post was initially motivated by an interesting recent article by Chris Wellons discussing the Blowfish cipher. The Blowfish cipher’s subkeys are initialized with values containing the first 8336 hexadecimal digits of , the idea being that implementers may … Continue reading

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Floating-point agreement between MATLAB and C++

Introduction A common development approach in MATLAB is to: Write MATLAB code until it’s unacceptably slow. Replace the slowest code with a C++ implementation called via MATLAB’s MEX interface. Goto step 1. Regression testing the faster MEX implementation against the … Continue reading

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What is (-1&3)?

This is just nostalgic amusement.  I recently encountered the following while poking around in some code that I had written a disturbingly long time ago: What does this code do?  This is interesting because the switch expression is a constant … Continue reading

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