Tag Archives: proof

Properties of orthogons I

First things first: from now on, when talking about polygons with only right angles, instead of calling them “orthogonal polygons” I’m going to start calling them “orthogons”, which sounds cool, is much less clunky than “orthogonal polygons”, and doesn’t seem … Continue reading

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Fermat’s Little Theorem: proof by group theory

It’s time for our third and final proof of Fermat’s Little Theorem, this time using some group theory. This proof is probably the shortest—explaining this proof to a professional mathematician would probably take only a single sentence—but requires you to … Continue reading

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Fermat’s Little Theorem: proof by necklaces

It’s time for our second proof of Fermat’s Little Theorem, this time using a proof by necklaces. As you know, proof by necklaces is a very standard technique for… wait, what do you mean, you’ve never heard of proof by … Continue reading

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Now on mathstodon.xyz

Christian Lawson-Perfect and Colin Wright have set up an instance of Mastodon—a decentralized, open-source Twitter clone—as a place for mathy folks to be social. It’s appropriately named mathstodon.xyz, and because it’s open-source they were able to easily hack in support. … Continue reading

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Computing optimal play for the greedy coins game, part 4

Last time I explained a method for computing best play for instances of the greedy coins game, which is feasible even for large games. This general approach is known as dynamic programming and is applicable whenever we have some recursively … Continue reading

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Computing optimal play for the greedy coins game, part 3

In a previous post we saw how we can organize play sequences in the greedy coins game into a tree. Then in the last post, we saw how to work our way from the bottom of the tree upward and … Continue reading

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Computing optimal play for the greedy coins game, part 2

I want to explain in more detail how we can think about computing the best possible score for Alice in the greedy coins game, assuming best play on the part of both players. I glossed over this too quickly in … Continue reading

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