(2 3 7) Triangles and Klein's Quartic
(2 3 7) Triangles and Klein's Quartic My new favorite t-shirt arrived in the mail today, designed by Henry Segerman. This design and many others with mathematical themes are available at Henry's website. http://www.segerman.org/tshirts.html I used the "create" version of the shop to slightly alter the size and color. http://math-art-create.spreadshirt.com/us/US/Shop/ So what is this design? In short, it is a tiling of (2 3 7) triangles. The (2 3 7) designates a Schwarz triangle. It means the 3 angles of each triangle are π/2, π/3, and π/7. Schwarz triangles can tile the sphere, Euclidean plane, or hyperbolic plane depending on the choice of the 3 angles. (2 3 7) triangles tile the hyperbolic plane, and Henry has drawn these triangles in the Poincare disk model, cutting off the model at some radius from the origin. My G+ banner is a similar representation of (2 3 7) triangles tiling the disk, but with a different choice of cutoff and as a 3D printed model. I prev