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 ands, 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 - "hilbert"
 Hilbert's Square-Filling Curve"Hilbert's Square-Filling Curve" by The 3DXM Consortium In 1890 David Hilbert published a construction of a continuous curve whose image completely fills a square, which was a significant contribution to the understanding of continuity. Although it might be considered to be a pathological example, today, Hilbert's curve has become well-known for a very different reason---every computer science student learns about it because the algorithm has proved useful in image compression. See more fractal curves on the 3D-XplorMath Gallery. --- adapted from "About Hilbert's Square Filling Curve" by Hermann Karcher
 "Hilbert Cube 512""Hilbert Cube" is a space-filling recursive curve in 3 dimensions in analogy to the famous Hilbert curve in the plane. Special care has been taken never to place more than 3 coplanar line segments in sequence. At the largest recursion step the geometry has been slightly altered so as to obtain a closed loop. In the proper parallel projection one can see that the 2 halves of this sculpture are connected by only 2 tube segments. This piece of art gives me the association of an abstract, constructivist model of the human brain. See more views of the "Hilbert Cube 512". --- Carlo Sequin

 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