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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"Hyperbolic Twist: Forever in Memory," by Charlotte Henderson (A.K. Peters, Natick, MA)

Acrylic yarn and glass beads, 6 × 6 × 4 inches (3d work), 2010 This model is a hyperbolic Möbius band. The starting “spine” consists of 20 chain stitches, and the outer single edge has over 1600 single crochet stitches. The negative curvature of the surface allows the width of the band to be much greater than if the curvature were zero. The surface can move freely through the “hole” in the center. The bead work highlights the nonorientability of the surface. In isolated sections, it looks as if the beads are on two sides of the band; but if one traces the line of beads, one will return to the chosen starting point having traced all of the beads. The same amount of yarn is used for the red and the pink, to display the exponential growth of the surface. (There is a greater amount of white yarn, to have a constant final row for aesthetic purposes.) The color scheme arose from the fact that, at an earlier construction stage, the silhouette of the model resembles a heart. --- Charlotte Henderson

 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