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.

 "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
 "Wormhole," by Kerry Mitchell. ©Kerry MitchellThis work was created using a technique very similar to that used in Penrose Pursuit image, also in this album. However, instead of drawing the lines forming the pursuit curves, this image was rendered buy shading the areas inside of the tiles. --- Kerry MitchellSep 29, 2015
 "Proud," by Kerry Mitchell. ©Kerry MitchellThis image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration. I often find simple images to be the most compelling. I like to let the structure be the focal point, not necessarily the coloring methods of the color palette. --- Kerry MitchellSep 29, 2015
 "Penrose Pursuit, 2011," by Kerry Mitchell. ©Kerry MitchellThis is a tessellation of Penrose tiles. In this set, there are two different tile shapes, a fat rhombus and a thin rhombus. Penrose tiles are remarkable because they can be arranged (as they are here) such that the tiling never repeats, no matter how many tiles are used. Also, each tile is filled with four pursuit curves, the dark curves from each corner to a point near the center of the tile. Imagine a mouse in each corner of the tile. At the same time, each mouse begins moving toward (pursuing) the next mouse. The tracks of the mice are pursuant curves. --- Kerry MitchellSep 29, 2015
 "Naturally Textured 5, 2013," by Kerry Mitchell. ©Kerry MitchellThis image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration. --- Kerry MitchellSep 29, 2015
 "Lincoln," by Kerry Mitchell. ©Kerry MitchellThis Lincoln image was created with math. The image is made up of 500 square tiles of five different types. Typically, I use these tiles to create a sona image, which is a continuous, closed curve around an array of points, such that the curve goes around each point once. In Lincoln, the dots are removed for clarity. The width of the curve was changed on every tile to mimic the grayscale level of that part of the portrait. --- [url=http://www.kerrymitchellart.com/]Kerry Mitchell[url]Sep 29, 2015
 "Great Wave," by Kerry Mitchell. ©Kerry MitchellThe genesis of this image has nothing to do with waves; it is a representation of the complex numbers that can be expressed using the base 1 + i. Yet, the spirals inherent in the arithmetic are suggestive of Hokusai's 'The Great Wave Off Kanagawa'. --- Kerry MitchellSep 29, 2015
 "Curiosity," by Kerry Mitchell. ©Kerry MitchellThis image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration. "Curiosity" celebrates both the unsung measure of central tendency, the harmonic mean, and the Curiosity rover’s landing on Mars in August 2012. --- Kerry MitchellSep 29, 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
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 Art & Music, MathArchives Geometry in Art & Architecture, by Paul Calter (Dartmouth College) Harmony and Proportion, by John Boyd-Brent International Society of the Arts, Mathematics and Architecture Journal of Mathematics and the Arts Mathematics and Art, the April 2003 Feature Column by Joe Malkevitch Maths and Art: the whistlestop tour, by Lewis Dartnell Mathematics and Art, (The theme for Mathematics Awareness Month in 2003) MoSAIC - Mathematics of Science, Art, Industry, Culture Viewpoints: Mathematics and Art, by Annalisa Crannell (Franklin & Marshall College) and Marc Frantz (Indiana University) Visual Insight, blog by John Baez