Frank A Farris
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.
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.