Math ImageryThe 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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"A Piece of Hyperspace," by Sarah Mylchreest and Mark Newbold2295 viewsThe quilt depicts a polyhedron known as the Great Triambic Icosidodecahedron. It was paper-pieced by Sarah Mylchreest from a design generated by Mark Newbold using his "Hyperspace Star Polytope Slicer" Java applet. It won a ribbon in the 2002 Vermont Quilt Festival. The site has a description of the quilt pattern.

--- Photograph and image copyright 2005 by Mark Newbold,
"Poincare," by Mary Candace Williams. Quilt copyright 2005 Mary Candace Williams; photograph by Robert Fathauer.2201 viewsThis is a hyperbolic design so it is as if a sphere was mapped onto a plane. The printed fabric has distorted spheres. This quilt is unusual in that it is pieced from the outside to the center.

--- Mary Candace Williams
"ParaStar8," by Mary Candace Williams. Quilt copyright 2003 Mary Candace Williams; photograph by Robert Fathauer.2003 viewsThis quilt is is the third in a series of quilts based on the approximation of a parabola by drawing a series of straight lines. There were eight divisions of the orginal block which was then mapped onto a rhombus and repeated eight times for the complete quilt. The star part of the design was enhanced by the use of shades of color.

--- Mary Candace Williams
"Spirolateral_{6}^{1,3,4} ," by Mary Candace Williams. Quilt copyright 2005 Mary Candace Williams; design is copyright Robert Krawczyk; photograph by Robert Fathauer.1654 viewsThe challenge of doing a quilt that has only rotational symmetry and uncommon angles lies in a technique called partial seaming. The printed fabric has a lot of pursuit curves overlaide on top of one another and shows a lot of contrast with the black of the spirolateral.

--- Mary Candace Williams
"Symmetry Mobius," by Mary Candace Williams; photograph by Annette Emerson.1227 viewsIn order to keep the mobius as a band, I used only the eleven symmetries that are not based on a hexagon. The fabric was chosen for its mathematical content. -- Mary Candace Williams
"Tumbling Escher," by Mary Candace Williams. Quilt copyright 2006 By Mary Candace Williams; photograph by Annette Emerson.1038 viewsIf you look at the quilt at a perpendicular angle you have a traditional diamond tessellation known as Tumbling Block. From the side, however, it rises up and back into the quilt; thus a nod to Escher's "Reptiles" in which the drawn lizard rises up and out and back into the drawing board. --- Mary Candace Williams

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American Mathematical Society