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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 > Chaim Goodman-Strauss :: Symmetries
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"Calla Lily 32 infinity," by Chaim Goodman-Strauss, University of Arkansas (http://mathbun.com/main.php)
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The group SL_2(Z) acts on the hyperbolic plane discretely, producing patterns of symmetry type 23 infinity, such as the one shown here. Similarly, the 2-fold cover GL_2(Z) acts with symmetry type *23 infinity. This image is from "The Symmetries of Things", by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss (AK Peters, 2008).
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