Nick Mendler

Student of Mathematics
University of San Francisco
San Francisco
I'm fascinated by the variety of tessellations possible in hyperbolic space. While in normal Euclidean geometry there are finitely many possible structures for a tessellation, hyperbolic geometry offers infinitely many tilings. Its appearance was made famous by Escher, less well known however is that the Poincare disc is a map for an infinite non-Euclidean space. Furthermore, only a finite portion of the space can fit into our 3-Dimensional world. Portions of surface which do have intrinsic hyperbolic geometry are often small, so that patterns can't be well illustrated on them. Remarkably, the Poincare disc model maps the entire space into the unit circle. I've always wanted to draw a tiles to tessellate the hyperbolic plane!
5 Squares
25 x 25 cm
Watercolor and Pen and Ink scan processed with Python for inkjet print
I've been relatively mystified by hyperbolic geometry for as long as I can remember. I am now beginning to generate patterns and understand the concept of intrinsic geometry, however every corner of the subject seems to be a surprise or have a non-intuitive answer. My drawing for the tessellation reflects the way I find hyperbolic space to be enigmatic and magical.