The 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 bands, 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.
DART ... as a very simple game by Jo Niemeyer 2010 . Two dart players, A and B, are facing this "image", whose area is split 1 : 0.618.. into white and black. This two basic elements are rotated in 90° increments. The winner is, who aims first a black part. Since we have two equal partners and an uneven distribution of the "target", one would think, that this is not a fair game. But it is! Because A as the "majority", and consequently B as the "minority", transferred their inequality onto the "court". The ratio of the two playing partners is 1:1. With this harmonious proportionality there is exactly the same chance to win for both players A and B! The Swiss mathematician Hans Walser mentions for the justice condition, the formula p = 1/2*(3-sqrt(5)). And with sqrt(5), we have the golden section in this game, which ensures equity between different partners. This is also a very fair game! Or a piece of art, which ensures harmony and balance. --- Jo Niemeyer (http://www.jo.niemeyer.com)