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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# "A Fractal Circle Pattern on the {3,12} Polyhedron," by Doug Dunham (University of Minnesota - Duluth, MN)

## Printed cardboard, 50 x 30 x 30 cm, 2015 The goal of my art is to create aesthetically pleasing repeating hyperbolic patterns. One way to do this is to place patterns on (connected) triply periodic polyhedra in Euclidean 3-space. This polyhedron is constructed by placing regular octahedra on all the faces of another such octahedron, so there are 12 equilateral triangles about each vertex. Each of the triangular faces has been 90% filled by a fractal pattern of circles provided by John Shier. The polyhedron consists of red and blue "diamond lattice" polyhedra and purple octahedra that connect the red and blue polyhedra. Each of the red and blue polyhedra consists of octahedral "hubs" connected by octahedral "struts", each hub having 4 struts projecting from alternate faces. The red and blue polyhedra are in dual position with respect to each other - they form interlocking cages. Each purple connector has a red and a blue octahedron on opposite faces. --- Doug Dunham

 Art & Music, MathArchives Geometry in Art & Architecture, by Paul Calter (Dartmouth College) Harmony and Proportion, by John Boyd-Brent International Society of the Arts, Mathematics and Architecture Journal of Mathematics and the Arts Mathematics and Art, the April 2003 Feature Column by Joe Malkevitch Maths and Art: the whistlestop tour, by Lewis Dartnell Mathematics and Art, (The theme for Mathematics Awareness Month in 2003) MoSAIC - Mathematics of Science, Art, Industry, Culture Viewpoints: Mathematics and Art, by Annalisa Crannell (Franklin & Marshall College) and Marc Frantz (Indiana University) Visual Insight, blog by John Baez