2023 Bridges Conference Art Exhibition

# Eve Torrence

## Artists

## Statement

I enjoy creating sculptures that allow me to share the beauty of geometry and topology with a general audience. I usually work with inexpensive materials, such as paper, felt, and craft foam, which allows me to evolve my pieces through many iterations. These materials also adapt well to workshops so I can share my discoveries and designs. I hope to communicate that mathematics is accessible and interesting to people who may have never had the opportunity to be inspired by mathematics.

## Artworks

The colorful part of this sculpture shows Heffter’s 1891 maximally complete 9-color map on a 3-hole torus. Heawood's formula says that every map on a genus-3 surface can be colored with at most nine colors. The map is complete since every colored region shares a boundary line with each of the other 8 regions. Heffter described this map using a table of numbers, making the structure hard to understand. The black and white tubes are attached to the 9-color map in 3 places, creating a genus-5 surface. These two additional regions each touch all the regions of Heffter's map. Any map on a genus-5 surface can be colored with at most 11 colors, hence the complete sculpture is a maximally complete 11-color map.