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.

Image search results - "Origami,"
 "Fiddler Crab, opus 446" crease pattern, by Robert J. Lang. Copyright Robert J. Lang (www.langorigami.com).Crease patterns (CPs) provide a one-step connection from the unfolded square to the folded form, compressing hundreds of creases, and sometimes hours of folding, into a single diagram! A CP can sometimes be more illuminating than a detailed folding sequence, conveying not just "how to fold," but also how the figure was originally designed. Mathematical and geometric CPs usually show all the creases, but representational origami rarely shows every crease in the finished form, as it would make the crease pattern impossibly busy. Instead, the crease pattern gives the creases needed to fold the "base," that is, a geometric shape that has the right number and arrangements of flaps. It is still left up to the folder to add thinning and shaping folds. See the final "Fiddler Crab" origami work in this album.
 "Night Hunter, opus 469" crease pattern, by Robert J. Lang. Copyright Robert J. Lang (www.langorigami.com).Crease patterns (CPs) provide a one-step connection from the unfolded square to the folded form, compressing hundreds of creases, and sometimes hours of folding, into a single diagram! A CP can sometimes be more illuminating than a detailed folding sequence, conveying not just "how to fold," but also how the figure was originally designed. Mathematical and geometric CPs usually show all the creases, but representational origami rarely shows every crease in the finished form, as it would make the crease pattern impossibly busy. Instead, the crease pattern gives the creases needed to fold the "base," that is, a geometric shape that has the right number and arrangements of flaps. It is still left up to the folder to add thinning and shaping folds. See the final "Night Hunter" origami work in this album.

 2 files on 1 page(s)

 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