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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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# "Catalan Connections: Level Four," by Margaret Kepner (Washington, DC)

## Archival inkjet print, 40 x 60 cm, 2015 I enjoy exploring the possibilities for conveying ideas in new ways, primarily visually. I have a background in mathematics, which provides me with a never-ending supply of subject matter. The Catalan numbers are a sequence of positive integers that provide answers to certain combinatorial questions. For example, in how many ways can a polygon with n+2 sides be cut into triangles? A hexagon (setting n=4) can be triangulated in fourteen different ways, so the 4th Catalan number is 14. Other types of problems also lead to the Catalan numbers: counting binary trees, balancing parentheses, finding paths through a grid, shaking hands in a circle, etc. This piece is composed of diagrams representing seven different problems; for each of these, the answer is the 4th Catalan number. The solution sets for the problems are displayed in diagonal bands. The columns indicate correspondences between elements in different solution sets. --- Margaret Kepner

 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