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# Category Archives: geometry

## Apollonian gaskets and Descartes’ Theorem II

In a few previous posts I wrote about “kissing sets” of four mutually tangent circles, and the fact that their signed bends satisfy Descartes’ Theorem, (Remember that the signed bend of a circle is like the curvature , except that … Continue reading

## Apollonian gaskets and Descartes’ Theorem

In my previous post, I explained a recursive procedure for drawing Apollonian gaskets. Given any three mutually tangent circles, there are exactly two other circles which are mutually tangent to all three (forming what we called a “kissing set”). This … Continue reading

## Apollonian gaskets

In my last post I showed off this tantalizing picture: This pattern of infinitely nested circles is called an Apollonian gasket. Over the next post or two I’ll explain some cool math behind actually constructing them. Mostly I will state … Continue reading

Posted in geometry, pattern, pictures, recursion
Tagged Apollonian, gasket, recursion, tree
4 Comments

## An amazingly symmetric icosahedron edge coloring

In my last post I showed off the stellated icosahedron I made out of folded paper: I also claimed that it uses a very particular and elegant color scheme. When I set out to make it, I did some googling … Continue reading

## Origami stellated icosahedron!

Continuing what I started in December, I finally finished making a stellated icosahedron out of 30 Sonobe units. Each Sonobe unit corresponds to an edge of the icosahedron, and interlocks with three others to give the whole thing a remarkable … Continue reading

Posted in geometry, group theory
Tagged icosahedron, making, objects, origami, sonobe, stellated
4 Comments

## Link: Chat Noir

Just a link for you today: Chat Noir is a fun game where you try to trap a cat before it escapes. It’s quite mathematical, too. Can you figure out strategies for trapping the cat? Can you always win, or … Continue reading