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 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)Oct 22, 2015

"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)Oct 22, 2015

"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)Oct 22, 2015

"Fish," by Hamid Naderi YeganehThis image is like a fish. It shows 1,000 line segments. For i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-2cos(4πi/1000), (1/2)(cos(6πi/1000))^3) and (-(2/15)sin(6πi/1000), (4/5)sin(2πi/1000)). --- Hamid Naderi YeganehSep 16, 2015

"Boat," by Hamid Naderi YeganehThis image is like a sailing boat. It shows 2,000 line segments. For each k=1,2,3,...,2000 the endpoints of the k-th line segment are: (cos(6πk/2000)-i cos(12πk/2000))e^(3πi/4) and (sin((4πk/2000)+(π/8))+i sin((2πk/2000)+(π/3)))e^(3πi/4). --- Hamid Naderi Yeganeh Sep 16, 2015

"A Bird in Flight (2015)," by Hamid Naderi Yeganeh This image is like a bird in flight. It shows 500 line segments. For each i=1,2,3,...,500 the endpoints of the i-th line segment are: ((3/2)(sin((2πi/500)+(π/3)))^7, (1/4)(cos(6πi/500))^2) and
((1/5)sin((6πi/500)+(π/5)), (-2/3)(sin((2πi/500)-(π/3)))^2). ---
Hamid Naderi Yeganeh Sep 16, 2015

"10,000 Circles," by Hamid Naderi YeganehThis image shows 10,000 circles. For each i=1,2,3,...,10000 the center of the i-th circle is:
((cos(38πi/10000))^3, sin(10πi/10000)) and the radius of the i-th circle is: (1/3)(sin(16πi/10000))^2. --- Hamid Naderi Yeganeh Sep 16, 2015

"A Strawberry Lemon Spiral," by Frank A. Farris, Santa Clara University, CAInk jet on paper, 2015.

This image started life as a wallpaper pattern with symmetry group p2, based on a photograph of strawberries with a cut of lemon. After scaling it correctly, I applied the complex exponential map to wind it around the origin, creating a spiral of yellows, greens, and reds. I particularly enjoy how the lemon became a string of yellow wax beans, while the strawberries turned into peppermint candies. --- Frank Farris Sep 02, 2015