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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 "Unlikely Tetrahedron (View 1)," by Gwen Fisher (www.beadinfinitum.com)Materials: size 15° seed beads, 3 mm bugle beads, 3 mm Swarovski crystal, thread. 34 mm on an edge. I applied the beading techniques I used to turn Impossible Triangles into beaded art objects to a tetrahedron. The Unlikely Tetrahedron generates no corresponding optical illusion. The faces form three distinct paths that twist around the sculpture in unexpected ways. Each beam includes all three colors of faces, with one color on two opposite faces. Like a Möbius band, as you follow a path around the piece, sometimes when you get back to a beam, you return to the opposite face. Thus, it feels like you have to travel around the sculpture twice just to get back to where you started. --- Gwen Fisher (www.beadfinitum.com)
 "Unlikely Tetrahedron (View 2)," by Gwen Fisher (www.beadinfinitum.com)Materials: size 15° seed beads, 3 mm bugle beads, 3 mm Swarovski crystal, thread. 34 mm on an edge. I applied the beading techniques I used to turn Impossible Triangles into beaded art objects to a tetrahedron. The Unlikely Tetrahedron generates no corresponding optical illusion. The faces form three distinct paths that twist around the sculpture in unexpected ways. Each beam includes all three colors of faces, with one color on two opposite faces. Like a Möbius band, as you follow a path around the piece, sometimes when you get back to a beam, you return to the opposite face. Thus, it feels like you have to travel around the sculpture twice just to get back to where you started. --- Gwen Fisher (www.beadfinitum.com)
 "Unlikely Dodecahedron (View 1)," by Gwen Fisher (www.beadinfinitum.com)Materials: size 15° and 11° seed beads and thread. 23 mm on an edge, 58 mm diameter. I applied the beading techniques I used to turn Impossible Triangles into beaded art objects to a dodecahedron. The Unlikely Dodecahedron generates no corresponding optical illusion. The faces form ten distinct paths that twist around the sculpture in unexpected ways. --- Gwen Fisher (www.beadfinitum.com)
 "Unlikely Dodecahedron (View 2)," by Gwen Fisher (www.beadinfinitum.com)Materials: size 15° and 11° seed beads and thread. 23 mm on an edge, 58 mm diameter. I applied the beading techniques I used to turn Impossible Triangles into beaded art objects to a dodecahedron. The Unlikely Dodecahedron generates no corresponding optical illusion. The faces form ten distinct paths that twist around the sculpture in unexpected ways. --- Gwen Fisher (www.beadfinitum.com)