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.
"RUBIK's new clothes," by Anna Viragvolgyi (Mathematician, Budapest, Hungary)
Stirol cube with plastic foil, 2,5"x2,5"x2,5", 2009. Example of extending pattern of "48 different squares" over the surface of RUBIK's 4x4x4. Each square of the set appears twice on the 96 tiles of the cube. There are various symmetries on the sides of the cube and between the sides also. So there is more than one coherent and continuous arrangement. "I deal with diagonally striped, coloured squares. [These squares assign a restricted de Bruijn sequence S(k,n). There are [k(k-1)^(n-1)]/2 distinct squares, where k is the number of colours, n is the number of stripes.] Last year I studied the geometric shape of arrangements of the squares [in case of k=3, n=6, S(3,6)=48] with coherent pattern on the plane. Presently my aim is filling surfaces of solid figures with these squares. Here is one of them." --- Anna Viragvolgyi (Mathematician, Budapest, Hungary) email@example.com