Schmidt Arrangement of the Eisenstein Integers - Katherine Stange

Schmidt Arrangement

This picture drawn by Katherine Stange shows what happens when we apply fractional linear transformations $ z \mapsto \frac{a z + b}{c z + d} $ to the real line sitting in the complex plane, where $a,b,c,d$ are Eisenstein integers that is, complex numbers of the form $ m + n \exp(2 \pi i/3) $ with $m,n$ being integers.

Hammersley Sofa - Claudio Rocchini

Hammersley Sofa

The moving sofa problem asks: what is the shape of largest area that can be maneuvered through an L-shaped hallway of width 1? This animated image made by Claudio Rocchini shows one attempt to solve this problem.