Aaron Fenyes

Postdoctoral fellow
University of Toronto, Department of Mathematics
Toronto, Ontario, Canada
For me, drawing pictures of the two-dimensional surfaces I study isn't just a treat, or a way to communicate; it's a research tool I couldn't do without. I use hand-drawn sketches to get a feel for how geometric objects behave—to see which ways they can move and bend and still look true to life. I use computer drawings to explore unfamiliar objects I can't yet see well enough to sketch, and to see familiar objects with more clarity than my intuition can provide. The drawings in my first submission come from software I wrote to test the results I proved in my Ph.D. thesis. I hope they'll show you a glimpse of what I find most beautiful about my field.
84 x 56 cm
Digital print
These pictures are two different views of the same hyperbolic surface. The surface is divided into four colored triangles, all the same shape and size. To make the picture above, I unrolled the surface onto the hyperbolic plane. The four triangles, repeated over and over, form a tessellation. Below, I flattened the surface out, concentrating all its curvature at the centers of the triangles. Then I cut it into a polygon, with the triangle centers at the vertices. The triangles have collapsed to tripods whose legs spiral around the surface, filling it up as densely as the rational numbers fill the real line. (The technical details of the flattening process are sketched in Subhojoy Gupta's "Asymptoticity of grafting and Teichmüller rays.")
8, 13, 21?
22 x 33 cm
Digital photo print
[To be framed as a triptych.] A pineapple's florets fall into three families of spirals. Urban legend has it that if you tie a string around a pineapple and count the spirals from each family passing through it, you'll typically get three successive Fibonacci numbers. Many plants' florets follow the same pattern, and many models have been proposed over the years to explain why (see Mughal and Weaire, 2017, for a recent one). I bought this pineapple from a Waterloo, Ontario Valu-Mart in 2010, intending to make it a poster child for the "three Fibonacci numbers" rule. Unfortunately, between photographing it and eating it, I forgot to count the spirals. Now I'll never know whether it followed the rule I'm using its image to illustrate.