2024 Joint Mathematics Meetings
Frank A. Farris
Artists
Frank A. Farris
Professor of Mathematics and Computer Science
Santa Clara University
San Jose, CA
Statement
My art represents an ongoing discussion of the question, "What do mathematical objects look like?" I like to make it seem as if mathematics is both approachable and mysteriously beautiful. My process leads me to apply mathematical knowledge to create art that could not be made without mathematics. This piece was made in Rhino with Grasshopper, with a little help from Photoshop. In the Fall of 2019, I attended the semester-long workshop called Illustrating Mathematics at the Institute for Computational and Experimental Research in Mathematics (ICERM).
Artworks
Tangent Tiling Curves: Circular and Hyperbolic
51.0 x 61.0 cm
Digital print on aluminum
2023
Imagine a particle tracing the boundary of a single tile on a tiling of the sphere, starting at a vertex. Make that curve the succession of tangent vectors of new curve, starting at the origin: a tangent tiling curve. Tracing one face of the cube from each vertex yields four piecewise circular curves ending at the same point. The full cube gives six quartets. The dodecahedron gives twelve sets of five curves.
The curves on the right use tilings in the geometry of space-time. The hyperboloid shown is the set of unit time-like vectors. In gold are the tangent tiling curves for a tile with four angles of 72 degrees. These represent travelers beginning and ending at the same time/place and illustrate the twin paradox.