Frank A Farris

Professor of Mathematics and Computer Science
Santa Clara University
San Jose, California, USA
Inspired by joining the Illustrating Mathematics semester at the Institute for Computational and Experimental Research in Mathematics (ICERM), I am passionate about promoting the role of mathematical art in the broader community. Mathematical artists do more than reach out to non-mathematicians. We make important contributions to mathematical research, exposition, and education. Recent work involves creating patterns invariant under various group actions using Grasshopper in Rhino. The shapes may then be staged in scenes with texture mapping and ray tracing, or printed as sculptures.
A Hyperboloid from 14 Laced Hyperboloids
A Hyperboloid from 14 Laced Hyperboloids
31 x 38 cm
Digital print
Preparing to teach differential geometry, I was studying the hyperboloid of one sheet and realized that I could match the rulings on one large hyperboloid with rulings on much smaller hyperboloids with the potential to fit nicely around the larger shape. This is a departure from my usual work in that the only symmetry is 14-fold rotational symmetry. I created the shape in Rhino with Grasshopper, using techniques from both my 2021 and 2020 Bridges papers to create the apparent weaving of the laces on the hyperboloid. I added small beads as caps at the tops and bottoms of strands to give a finished appearance. Two views are provided facilitate understanding the shape.