2023 Bridges Conference Art Exhibition
Diana Davis
Artists
Diana Davis
Instructor in Mathematics
Phillips Exeter Academy
Exeter, NH, USA
Statement
I am a research mathematician studying billiards and flat surfaces. Since 2014, with Samuel Lelièvre, I have been working to study periodic billiard paths on regular polygons, starting with the regular pentagon. We have made our pictures of periodic pentagon paths into jewelry and T-shirts, to bring the beauty of mathematics to more people. We are always thinking about how to make abstract ideas into beautiful tangible objects.
Artworks
A Celtic-knotted periodic path on a pentagon billiard table
27.0 x 28.0 x 2.0 cm
nylon cord, felt, wood, brass screws, acrylic, papier-mâché, paint
2023
When a billiard ball bounces around a table shaped like a regular pentagon, it makes a beautiful pattern. Here we have shown a periodic billiard path with 10 bounces, using nylon cord. We realized that if we added crossings to the path, we could make it into a Celtic knot: a knot where the crossings alternate over, under, over, under as you follow the cord along its path. We think that this makes a beautiful fusion art piece, blending a dynamical system (billiards) with a classical art form (Celtic knots).
Our plans to make this piece using a laser cutter were dashed when the laser cutters in both of our accessible Fab Labs were out of order, so we ended up making the entire piece with traditional tools!