JIangmei Wu
Paper folding is an exciting area of art and design. Folding a piece of paper can be simple and doesn’t require any sophisticated tools. However, to model the morphology and to understand the intrinsic properties found in paper folding scientifically is very difficult and requires sophisticated tools of mathematics and computer science. As an artist, I'm interested in how paper folding can be expressed mathematically, physically, and aesthetically, how it can be done with different material and making techniques, and how these aspects work together with the conceptual space in which they occur.
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 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.