2019 Icerm Illustrating Mathematics

# David Bachman, Saul Schleimer, and Henry Segerman

## Artists

## Statement

David Bachman is a professor at Pitzer College in Claremont, CA. David studies geometry and topology, and enjoys creating 3D sculptures that illustrate these ideas. Saul Schleimer is a geometric topologist, working at the University of Warwick. His other interests include combinatorial group theory and computation. He is especially interested in the interplay between these fields and additionally in the visualization of ideas from these fields. Henry Segerman is an Associate Professor in the Department of Mathematics at Oklahoma State University. His interests include geometry and topology, 3D printing, virtual reality, and spherical video.

## Artworks

Four "views" of the inside of finite-volume hyperbolic three-manifolds. Each three-manifold contains a surface; when a “light ray” leaves your eye it becomes darker when it crosses the surface in the positive sense and lighter when it crosses in the negative sense. The elaborate patterns come from the complicated geometry and topology of the ambient three-manifold. The four-manifolds (in reading order) are m004, s227, s776, and s000 from the SnapPy census.