Math ImageryThe connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius ands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.

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Home > Carlo Séquin :: Mathematical Images
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"Poincare FishDish," by Carlo Sequin, University of California, Berkeley

A tiling with regular heptagons does not fit into the Euclidean plane, since 3 times the dihedral angle of the heptagon exceeds 360 degrees. But if we are willing to introduce a progressive scale factor, then the whole hyperbolic plane can be fit into the Poincaré disc. Here is a visualization of a {7,3} tessellation where 3 heptagons join at every vertex, using a tiling motif inspired by the famous Dutch artist M.C. Escher. Each heptagon is cut into 7 identical pizza slices with irregular boundaries in the shape of fish that properly interlock with one another. See more tiling patterns on the Poincare disc. --- Carlo Sequin

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