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 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.
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Home > 2009 Mathematical Art Exhibition
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"Recursive Construction for Sliding Disks," Adrian Dumitrescu, University of Wisconsin, Milwaukee (2008)
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Digital print, 11" x 5". "Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk slides in the plane without intersecting any other disk, so that its center moves along an arbitrary (open) continuous curve. One can easily show that 2n moves always suffice, while the above construction shows pairs of configurations that require 2n-o(n) moves for this task, for every sufficiently large n. Disks in the start configuration are white, and disks in the target configuration are shaded. " --- Adrian Dumitrescu, University of Wisconsin, Milwaukee
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