
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 awardwinning 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 mathematicsorigami, computergenerated
landscapes, tesselations, fractals, anamorphic art, and
more.
Jump to one of the galleries


Last additions 
"Sierpinski Tringle at Brean Down," by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down, UK.  Simon Beck (https://www.facebook.com/snowart8848/Aug 19, 2014


"Serpinski Triangle at PeiseyVallandry," by Simon Beck (https://www.facebook.com/snowart8848/)Pattern made in snow with snowshoes at PeiseyVallandry.   Simon Beck (https://www.facebook.com/snowart8848/)Aug 08, 2014


"Mandelbrot set in the sand, view two" by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down in the U.K. Find a time lapse video of the creation at http://youtu.be/MVzGyAAtHiU  Simon Beck (https://www.facebook.com/snowart8848/) Aug 08, 2014


"Mandelbrot set in the sand," by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down in the U.K. Find a time lapse video of the creation at http://youtu.be/MVzGyAAtHiU  Simon Beck (https://www.facebook.com/snowart8848/) Aug 08, 2014


"Hopf Knott, " by Peter Sittner (Kensington, MD)13.5" x 13.5" x 13.5", red oak, 2013
Hopf Knott is the offspring of two forms that have intrigued me for some time, the Hopf Link and the Borromean Rings. While the sculpture may appear to be a series of connected Hopf Links, it is actually two sets of Borromean Rings, an inner set and an outer set. Of course, the "rings" are stretched to make the crossings possible and shaped to resemble Hopf Links. The 6 outermost points correspond to the vertices of a regular octahedron.  Peter Sittner
May 05, 2014


"Dance of Stars I, " by Reza Sarhangi (Towson University, Towson, MD)12" X 12" X 12", heavy paper, 2013
"I am interested in Persian geometric art and its historical methods of construction. "
Dance of Stars I is one of the KeplerPoinsot polyhedra, the Small Stellated Dodecahedron, with Schläfli Symbol (5/2, 5). It has been ornamented by the sâzeh modular tiles, that are used in a majority of tiling that conform to local fivefold symmetries. In an article that appeared in Science, the authors proposed the possibility of the use of a set of tiles, girih tiles, by the medieval craftsmen, for the composition of the underlying pattern. Ink outlines for these girih tiles appear in panel 28 of the Topkapi scroll. I used girih tiles and left the dashed outlines in the final tessellation. I also included rectilinear patterns that appear as an additional smallbrick pattern in the decagonal Gunbadi Kabud tomb tower in Maragha, Iran.  Reza Sarhangi
May 05, 2014


"Longest Crease J, " by Sharol Nau (Northfield, MN)10" x 10" x 10", book sculpture, 2013
"A classical calculus problem, the socalled Paper Creasing Problem, deals with extremizing the length of the crease formed when a rectangular sheet of paper is altered by folding one corner, say the lower righthand corner, to the opposite edge. The length of the crease depends on the distance the active corner is from the upper lefthand corner."
This sculpture formed by folding individual pages is an example of the variety of the threedimensional forms which can be obtained by incremental changes in the length of the crease from page to page and by extending the points that can be used.  Sharol Nau (http://www.sharolnau.com)
May 05, 2014


"Jose, " by So Yoon Lym (Paterson, NJ)22" x 30", acrylic on paper, archival pigment print, 2009
"The Dreamtime is inspired by the Aboriginal stories and visions of creation. Each braided pattern, carried by the students, is a map of the ancient universe, a topographical palimpsest of the world in pattern: valleys, mountains, forests, oceans, rivers, streams. "
The link to Dr. Ron Eglash's website on cornrow hairbraiding best details the mathematic content behind my hair and braid paintings. Professor Eglash's website called "Transformational geometry and iteration in cornrow hairstyles" outlines one aspect of his research in ethnomathematics and cybernetics. Ethnomathematics "aims to study the diverse relationship between math and culture." More information:  So Yoon (http://www.soyoonlym.com/works/dreamtime/)
May 05, 2014


"Untitled, " by Jack Love (graduate student, George Mason University, Fairfax, VA)Spherical, 18" in diameter, mediumdensity fiberboard, 2013
"The Platonic solids have been the inspiration for the pieces I have created thus far. My work explores the structure of these objects and their relationships to one another, and attempts to express this structure in a way that is aesthetically appealing. "
Take either the icosahedron or dodecahedron and center it at the origin. Project its vertices outward from the origin onto the surface of a sphere surrounding it, giving a collection of points on a sphere. Draw a great circle through two points if they are images of two adjacent vertices in the original polytope. Each of these great circles is partitioned into arcs by its intersection with the other great circles thus produced. The arcs come in three lengths and are projections of the edges of, respectively, an icosahedron, a dodecahedron, and a third polytope whose facets are rhombic. This model exhibits this construction. The convex arcs correspond to the icosa, the concave to the dodeca, and the straight to the rhombic.  Jack Love
May 05, 2014


"Magic Square 8 Study: A Breeze over Gwalior," by Margaret Kepner (Washington, DC)20" x 20", archival inkjet print, 2013
"I enjoy exploring the possibilities for conveying ideas in new ways, primarily visually. I have a background in mathematics, which provides me with a neverending supply of subject matter. "
This work is based on a magic square of order 8, expressed in a visual format similar to a traditional quilt pattern. The magic square, known as the Gwalior Square, is an 8x8 array of numbers from 0 to 63, such that every row and column adds up to 252, the 'magic constant.' The two main diagonals, as well as every broken diagonal, also sum to 252. The numbers in the square are represented in base 2 and base 4. Nested squares serve as the number places in the base systems, and suggest the Log Cabin quilt structure. For each of the 64 squares, half is shown in base 2 and the other half in base 4. The squares are oriented to create the 'pinwheel' quilt pattern. This pattern groups together 2x2 arrays of 4 numbers, all of which sum to 126.  Margaret Kepner (http://mekvisysuals.yolasite.com)
May 05, 2014


"Evolution of the Twin Tornados, " by Hartmut F. W. Höft (professor emeritus, Eastern Michigan University, Ann Arbor, MI)7.5" x 9" (10.5" x 12" framed), archival photographic digital paper, 2013
"I like to experiment with simple planar geometric figures. Starting with one outline I move it, rotate it, and change its proportions. "
In this picture 12 images are arranged in a spiral. A primordial sea in the center starts the process. One parameter of the spine function increases, then stays constant, while the other increases and then decreases again. As the sequence progresses along the spiral the spine function increases in complexity so that the images billow out like clouds and then start separating into two funnels as the second parameter decreases again. Each image on the spiral is composed of 289 ellipses with a closed spine curve though it does not appear to be closed since the axes of the elipses decrease to zero at the bottom. The graphics were rendered in Mathematica 8 and printed on archival, photographic digital paper.  Hartmut F. W. Höft (http://people.emich.edu/hhoft/)
May 05, 2014


"View of the platycosm a2, decorated with AMS, " by Charles Gunn (Technisches Universität Berlin, Germany)18" x 18", print of computer image, 2013
"I enjoy exploring two and threedimensional tessellations  euclidean, spherical and hyperbolic, especially the "insider's" view of such spaces. I have been experimenting recently with alternative perspective rendering based on a spherical canvas surrounding the viewer. "
This is an insider's view of the platycosm a2. ("Platycosm" is John Conway's term for a compact euclidean 3manifold.) This platycosm is generated by a translation, a glide reflection and a screw motion with order2 rotational part, in three mutually perpendicular directions. The fundamental domain is a cube, whose edges are rendered via the textured beams. The "geometry" consists of the initials AMS, in honor of one of the hosting orgranizations of the art show. The image is rendered conformally from the viewable sphere of an insider positioned in the scene. I sometimes call this "sixpoint perspective" rendering since one may see vanishing points not just in the x,y, and z directions but also in the x, y, and z directions.  Charles Gunn (http://page.math.tuberlin.de/~gunn)
May 05, 2014


"Blue Torus, " by Faye E. Goldman (Ardmore, PA)10" x 10" x 2.5", strips of ribbon, 2011
Honorable Mention
2014 Mathematical Art Exhibition
"I was drawn to modular origami by its structure and mathematical properties. More recently I found the Snapology technique by H. Strobl, which allows great creativity with very few rules using only strips of material… It has provided insights into mathematical ideas. "
This toroid shape is made from over 2400 strips of ribbon. It was the first nonconvex shape I've made. I love the fact that there needs to be as many heptagons making the negative curvature in the center as there are pentagons around the outside.  Faye Goldman (http://www.FayeGoldman.com)
May 05, 2014


"ThreeFold Development, " by Robert Fathauer (Tessellations, Phoenix, AZ)13" x 13" x 13", ceramics, 2013
Best textile, sculpture, or other medium
2014 Mathematical Art Exhibition
"I'm endlessly fascinated by certain aspects of our world, including symmetry, chaos, and infinity. Mathematics allows me to explore these topics in distinctive artworks that I feel are an intriguing blend of complexity and beauty. "
This sculpture is based on the first five generations of a fractal curve. The starting point is a circle, and the first iteration produces a threelobed form. With each iteration, the number of lobes is tripled. The spacing between features is essentially constant throughout a layer, while the threefold symmetric boundary of the curve becomes increasingly complex. A hexagonal version of this curve is found in Benoit Mandelbrot's book "The Fractal Geometry of Nature". This hyperbolic surface is reminiscent of naturallyoccurring corals. It was inspired in part by a 3Dprinted model created by Henry Segerman. (For more information on this work see http://mathartfun.com/shopsite_sc/store/html/Art/FractalCurveSculp.html .  Robert Fathauer (http://robertfathauer.com)
May 05, 2014


"Lorenz Attractor in Flow, " by Marc Chamberland and Chris French (Grinnell College, Grinnell, IA)12cm x 12cm x 12cm, 3D printer, 2013
"Most people view mathematics as a collection of tools and procedures and get mired in the mechanics. Mathematical art communicates the essential beauty found in mathematics. "
The Lorenz attractor is the limiting set of a threedimensional system of differential equations modeling atmospheric convection. Discovered by Ed Lorenz in 1962, this set has become an attractive symbol for chaotic dynamics. The art work was created by modifying Mathematica code developed by Knill and Slavkovsky. An important new component was to have the curve which generates the shape continuously change color. This allows the observer to see the flow of motion as the attractor is generated.  Marc Chamberland and Chris French
May 05, 2014


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