Category Archives: geometry

Orthogons and orthobraces

One of these days soon I will get back to writing about primality tests, but for now I am having fun getting sidetracked on orthogons! In a previous post I gave rules for when two orthogons will be considered the … Continue reading

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Properties of orthogons II

In my previous post I proved three out of the four properties of orthogons I originally stated. Now let’s prove the final property: Every sequence of an even number of X’s and V’s, with exactly four more X’s than V’s, … Continue reading

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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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Orthogonal polygons

It’s time to say more about PWW #21, in which I exhibited things like this: Quite a few commenters figured out what was going on, and mentioned several nice (equivalent) ways to think about it. Primarily, the idea is to … Continue reading

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Post without words #21

Posted in combinatorics, geometry, posts without words | Tagged , , | 16 Comments

Paper torus with Villarceau circles

I made another thing! This is a torus, made from 24 crescent-shaped pieces of paper with slots cut into them so they interlock with each other. I followed these instructions on cutoutfoldup.com. There is also a template with some ideas … Continue reading

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Computing sums of primitive roots

Remember this picture? It, and other pictures like it, express the fact that for a given , if we take the primitive roots for each of the divisors of , together they make up exactly the set of all th … Continue reading

Posted in geometry, pictures | Tagged , , , , , , | 9 Comments