Three mathematical bathroom floors

chez Kuperberg-Zieve

Downstairs bathroom

My dad made this floor maybe in 1997. It shows our conjecture for the best packing of regular pentagons in the plane. What we did not know at first is that other people have also discovered this packing, e.g. the physicist Subir Sachdev.

Master bathroom

A Sacramento area contractor (Patrick Montgomery and his assistant Mike) put in this floor for us in the summer of 2007 following my design. The design is inspired by, and is a simplification of, mosaic tiles in the Alhambra in Spain.

Kids' bathroom

Patrick and Mike put in this floor too. This design is a quasiperiodic tiling discovered by Robert Ammann. It's like the more famous Penrose tiling by rhombuses, except that it has 8-fold symmetry instead of 5-fold symmetry.