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.
"Four Right Angles: Ascent (left) and Cantilever (right)," by Nat Friedman (Albany, NY)
17" L x 11" H x 7 D", Steel, 2010
A sculpture is defined as a form in a position relative to a fixed horizontal plane (base, ground). To hypersee an outdoor sculpture, one walks around it to see overall views and close up detail views from different viewpoints as well as in different light conditions at different times. If two sculptures consist of the same form in different positions, then the sculptures are said to be congruent. Congruent sculptures can look so completely different that one does not realize the sculptures are congruent. A hypersculpture is a group of congruent sculptures, and a more complete presentation of the sculptural possibilities of a form. In order to hypersee a form, one presents it as a hypersculture. This hypersculpture Four Right Angles consists of two vertical and three horizontal congruent sculptures and is discussed in an article of the same title in the Spring, 2011 issue of Hyperseeing, www.isama.org/hyperseeing/ . The two vertical sculptures Ascent and Cantilever are shown here. The form consists of four identical angle iron sections welded together. Each section is 5" x 5" x 6 ½" and ½" thick. --- Nat Friedman (Professor Emeritus, University at Albany, NY, Founder and Director of ISAMA, http://www.isama.org)