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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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# "The Path Crumpled Paper Takes," by Jeanette Powers, Rockhurst University, Kansas City, MO (2008)

## Ink and paper, 11" x 15". "A classic example to explain fractal dimension is the piece of crumpled paper. In this example, one takes a sheet of paper to be 2 dimensional (ignoring the very thin thickness). This then is a good representation of the mathematical plane. However, if we crumple the paper into a ball, as seen below the frame, it seems to take on a volume, or third dimension. Now, there is a meta-level to the inter-dimensionality of this system. If one flattens the paper back into the two dimensional sheet of paper, then one can draw a continuous line ( in blue) of all the folds that happened during the crumpling process. Now a line is considered to be one dimensional, but is the space this line takes up really best described with only one dimension?" --- Jeanette Powers, Student, Physics and Math Department, Rockhurst University, Kansas City, MO

 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