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.

 "A Fractal Circle Pattern on the {3,12} Polyhedron," by Doug Dunham (University of Minnesota - Duluth, MN)Printed cardboard, 50 x 30 x 30 cm, 2015 The goal of my art is to create aesthetically pleasing repeating hyperbolic patterns. One way to do this is to place patterns on (connected) triply periodic polyhedra in Euclidean 3-space. This polyhedron is constructed by placing regular octahedra on all the faces of another such octahedron, so there are 12 equilateral triangles about each vertex. Each of the triangular faces has been 90% filled by a fractal pattern of circles provided by John Shier. The polyhedron consists of red and blue "diamond lattice" polyhedra and purple octahedra that connect the red and blue polyhedra. Each of the red and blue polyhedra consists of octahedral "hubs" connected by octahedral "struts", each hub having 4 struts projecting from alternate faces. The red and blue polyhedra are in dual position with respect to each other - they form interlocking cages. Each purple connector has a red and a blue octahedron on opposite faces. --- Doug Dunham Mar 09, 2016
 "A Steiner Chain Trapped Inside Two Sets of Villarceau Circles," by Francesco De Comité (Univeristy of Lille, France)Digital print on cardboard, 60 x 80 cm, 2015 Manipulation of digital images, and use of ray-tracing software can help you to concretize mathematical concepts. Either for giving you an idea of how a real object will look or to represent imaginary landscapes only computers can handle. Here, ring cyclides are images of tori under sphere inversion. If certain conditions are fulfilled, a torus can contain a set of tangents spheres. Since the tangency property is preserved by inversion, this set of tangent spheres find its place inside the cyclide. --- Francesco De Comité Mar 09, 2016
 "Poincaré’s 'Pas de deux'," by Jean Constant (Hermay, Santa Fe, NM)Mathematics and mathematical visualizations are meaningful at many scientific and technological levels. They are also an endless source of inspiration for artists. The following artworks are part of the 12-30 project – one mathematical image a day for one year, 12 mathematical visualization software, January 1st, 2015 – December 31, 2015. See the 365 images portfolio and a printed compilation of the work will be available in the coming months at Hermay.org. --- Jean ConstantMar 09, 2016
 "Intrinsic Regularity," by Conan Chadbourne (San Antonio, TX)Archival inkjet print, 60 x 60 cm, 2015 This image presents a visualization of the Steiner triple system S(2,3,7). This system, which is combinatorially equivalent to the Fano plane, consists of seven three-element subsets (or blocks) drawn from a seven element set such that any pair of elements occur in exactly one block, and any two blocks have exactly one element in common. --- Conan Chadbourne Mar 09, 2016
 "Tangent Discs I," by Anne Burns (professor emerita, Long Island University Brookville, NY)Digital print, 30 x 30 cm, 2015 I am interested in the connections between mathematics, art and nature, especially the concept of evolution. Thus my mathematics interests are dynamical systems, differential equations and any area that deals with states that evolve with time. This image is an iterated Function System consisting of a group of (six) Mobius Transformations acts on six discs, five of which are tangent to the unit circle, to its two neighboring discs and to a sixth disc centered at the origin. --- Anne Burns Mar 09, 2016
 "A Radin-Conway Pinwheel Lace Sampler," by Douglas G. Burkholder (Lenoir-Rhyne University Hickory, NC)Digital Print, 50 x 50 cm, 2015 This artwork evolved from a search for beauty and patterns within Conway and Radin’s non-periodic Pinwheel Tiling of the plane by 1x2 right triangles. The Pinwheel tiling can be created by repeatedly subdividing every triangle into five smaller triangles. This lace resulted from alternately subdividing triangles and removing triangles. Triangles are removed based upon their location in the next larger triangle. First, on the macro level, the five distinctive removal rules are applied one to each row. This removal rule is especially easy to see in the bottom row. These same five rules are then applied, on the micro level, to the columns. The remaining triangles form a sampling of twenty-five styles of lace generated by the Pinwheel tiling. --- Douglas G. BurkholderMar 09, 2016
 "Hyperbolic Afghan {3, 7}," by Heidi Burgiel (Bridgewater State University, Bridgewater, MA)KnitPicks Shine Sport yarn: 60% cotton 40% modal, 7 x 44 x 44 cm, 2015 "Hyperbolic Afghan {3, 7}" illustrates a tiling of the hyperbolic plane by triangles, 3 at a vertex, in crocheted cotton. Adapting techniques developed by Joshua and Lana Holden, the piece is not assembled from flat triangles but instead approximates constant curvature over its entire surface. Its coloration, inspired by William Thurston's rendition of the heptagon tiling underlying the Klein quartic, suggests the identifications required to construct that surface as a quotient of the hyperbolic plane. --- Heidi Burgiel Mar 09, 2016
 "Dragon Curve Double Knit Scarf," by Rachelle Bouchat (Indiana University of Pennsylvania, Indiana, PA)Merino Wool Yarn, 137 x 18 cm, 2015 This double knit scarf brings together the recursive construction of a fractal, the dragon fractal, as well as the recursive construction of an integer sequence, the Fibonacci sequence. The main panels of the scarf are based on a pattern developed from the eleventh iteration of the dragon fractal. Moreover, the striping pattern in between the main panels is illustrative of the Fibonacci sequence with color changes after 1 row, after another 1 row, after 2 rows, after 3 rows, after 5 rows, and with another color change after 8 rows. As this is a double knit pattern, the back side of the scarf is shown in the reverse color pattern. --- Rachelle Bouchat Mar 09, 2016
 "The Jordan Curve Theorem," by Robert Bosch (Oberlin College Oberlin, OH)Lasercut woods, 15 x 45 cm, 2015 The Jordan Curve Theorem states that when a simple closed curve is drawn in the plane, it will cut the plane into two regions: the part lies inside the curve (here, the slightly darker-colored inset piece of wood), and the part that lies outside it (here, the slightly brighter and thicker frame). --- Robert Bosch Mar 09, 2016
 "Rainbow Brunnian Link Cowl," by sarah-marie belcastro (MathILy, Holyoke, MA)Knitted wool (various sources) and printed photographs, 30 x 30 x 7 cm, 2015 The central property of the Borromean rings--that removing any component unlinks the remaining components, which collectively form the unlink--generalizes to the class of Brunnian links. The Rainbow Brunnian Link Cowl has seven components rather than the three components of the Borromean rings. All linking is intrinsic, rather than introduced post-construction via grafting. The Rainbow Brunnian Link Cowl is also a garment that can be worn two different ways, which are pictured alongside that cowl in the exhibit. --- sarah-marie belcastro Mar 09, 2016
 From "Serenity to Monkey-Mind and Back (Two Twisted Tessellated Transforming Tori)," by Ellie Baker (Lexington, MA) Printed polyester crepe de chine, bead crochet (glass beads and thread), 70 x 50 cm, 2015 This infinity scarf and bead crochet necklace are twin tori. The fabric design is (an elongated version of) the infinitely repeating planar pattern that a tiny explorer could map by charting the surface of the necklace in all directions (the universal cover of the beaded rope). The two colors, identical tessellated wave motifs, gradually transform from "calm" to "busy." The pattern at each step has an increasing "busyness" quotient (a measure of how much the individual beads in a fundamental tile differ in color from neighboring beads). The scarf, sewn from a parallelogram to create a mobius-like twisted torus, has a small hole in one seam so that it can be turned inside out to explore the puzzling behavior of torus inversions. --- Ellie Baker Mar 09, 2016