David Bachman and Henry Segerman

Professor of Mathematics; Associate Professor of Mathematics
Pitzer College; Oklahoma State University
Claremont, CA; Stillwater, OK

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.

Henry Segerman is an associate professor in the Department of Mathematics at Oklahoma State University. His interests include 3D printing, virtual reality, and spherical video.

Cannon-Thurston Ball
Cannon-Thurston Ball
15 x 15 x 15 cm
3D printed gypsum

The "figure 8 knot" is the second simplest knot you can tie in a piece of rope. It is well known that it's complement has a hyperbolic structure. If you make the knot out of wire and dip that in a vat of soapy water, the soap film surface you see is its "fiber." Inside the sculpture you can see one lift of the fiber to the Poincare ball, a model of hyperbolic space. The coloring on the outside depicts an approximation of the Cannon-Thurston map, indicating the number of lifts between each point and the chosen fiber.