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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"Geodesic Cuboctahedron 7 frequency," by Magnus Wenninger (Saint John’s Abbey, Collegeville, MN)Papercraft, 12 inches in diameter, 2009. "Geodesic domes are well known as architectural structures, but generally they exhibit only triangular grids. My main interest, however, has been in having geometric patterns projected onto a spherical surface. The icosahedron is most frequently used for this purpose, but other polyhedrons can serve just as well for the same purpose. 'Geodesic Cuboctahedron 7 frequency' is the cuboctahedron in a 7 frequency basket weave pattern with 6 squares of one color and 12 rectangles of 6 other colors projected onto the surface of the cuboctahedron’s circumsphere." More information about the techniques I use to produce my artistic patterns on a spherical surface can be found in the Dover publication of my book Spherical Models (1999), originally the Cambridge University Press publication of Spherical Models (1979). Robert Webb’s Stella program is now my computer program par excellence. --- Magnus Wenninger (Saint John’s Abbey, Collegeville, MN) http://www.saintjohnsabbey.org/wenninger/
"Meditations on f(x,y)= (x^2)/2 + xy/2 – (y^4)/8," by Richard Werner (Santa Rosa Junior College, Santa Rosa, CA)2010 Mathematical Art Exhibition Third Prize.
Plastic and wood, two pieces, each 6”x7”x7”, 1998. The two pieces give alternate views of the same three-dimensional surface. The sculpture has been used for classroom illustrations of the concept of partial derivatives as well as integration of functions of two variables. Since the construction is with clear plastic, a myriad of delightful views of intersecting curves can be found allowing the viewer to hypersee the surface. "I have been a recreational wood worker and sculptor for much of my life. As a mathematics teacher, I have always been captivated by the beauty of the subject and have wanted to enhance the visual concepts in whatever way I can. The two activities were destined to meet. The first mathematical art that I made was intended mainly for classroom demonstrations. The response was very positive and I began to branch out. New materials, especially metal, have captured my interest. The work that I do now is becoming a blend of my interest in math and my love of nature, with a little bit of steam-punk influence creeping in as well." --- Richard Werner (Santa Rosa Junior College, Santa Rosa, CA)
"Julia's Loops," by Jennifer Ziebarth (California College of the Arts, Oakland, CA)Digital print, 16" x 13", 2009. This fractal image is based on a Julia set, visible in dark blue along the intersections of the loops. The loops, which all begin and end on the Julia set, also exhibit self-similarity, and hint at the existence of more small loops hidden behind the larger loops. "I have always been fascinated with repetition, abstraction, and the search for pattern, and this is what drew me to mathematics. As a mathematical artist, this love of repetition and detail has lead me to fractal art. As a mathematician teaching at an art college, some of my work is pedagogical in the sense of illustrating mathematical concepts in aesthetically pleasing ways; some of it is purely visual play." --- Jennifer Ziebarth (California College of the Arts, Oakland, CA)