The 2017 Mathematical Art Exhibition Awards were made at the Joint Mathematics Meetings last week “for aesthetically pleasing works that combine mathematics and art.” The three chosen works were selected from the exhibition of juried works in various media by 73 mathematicians and artists from around the world.
“Torus,” one of my folded light art, was awarded Best textile, sculpture, or other medium. I’m interested in how paper folding can be expressed mathematically, physically, and aesthetically. Torus is folded from one single sheet of uncut paper. Gauss’s Theorema Egregium states that the Gaussian curvature of a surface doesn’t change if one bends the surface without stretching it. Therefore, the isometric embedding from a flat square or rectangle to a torus is impossible. The famous Hévéa Torus is the first computerized visualization of Nash Problem: isometric embedding of a flat square to a torus of C1 continuity without cutting and stretching. Interestingly, the solution presented in Hévéa Torus uses the fractal hierarchy of corrugations that are similar to pleats in fabric and folds in origami. In my Torus, isometric embedding of a flat rectangle to a torus of C0 continuity is obtained by using periodic waterbomb tessellation.
The work is made of Hi-tec Kozo Paper and measures 45 x 45 x 20 cm.