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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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# "Broken Dishes, Mended Edges," by Margaret Kepner (Washington, DC)

## 6" x 16", Archival Inkjet Print, 2011 The traditional quilt pattern “Broken Dishes” and certain edge-matching puzzles share a common visual element – a square subdivided along its main diagonals to form 4 right triangles. This work presents 4 puzzle solutions using this visual element in a format suggesting Broken Dishes quilts. Edge-matching puzzles based on the square were introduced by MacMahon in the 1920s. One challenge was to arrange a set of 24 three-colored squares (all the possibilities) in a rectangle with same colors matching on the edges and a single color appearing around the border. If this is generalized to four colors, the complete set of puzzle pieces jumps to 70. These can be arranged in a 7x10 rectangle, providing a nice quilt proportion. This set of four designs is based on different matching “rules” ranging from strict matching to random placement, while maintaining the border requirement. To produce richer colors, each design is overlaid with a translucent scrim of the next design in the sequence. --- Margaret Kepner (Artist, Washington, DC)

 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