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"Crystal Morphohedron," by Stephen Wilmoth (University of California, Berkeley)6" x 6"x 6" closed, 6" x 6"x 18" opened, Clear acrylic, 1970
My work is directed at demonstrating the amazing interrelationship of the Regular Polyhedrons (Platonic Solids plus Kepler/Poinsot), and the Golden Ratio (1.618). Blending these together creates the three dimensional projection of the Fibonacci numbers. I call this phenomenon the Morphohedron. Transparent Dodecahedron that open to reveal clear cube inside that opens to allow a tetrahedron/octahedron to come out, which opens to reveal the inner icosahedron. All the Regular Solids (Platonic Solids) are here harmoniously nested.  Stephen WilmothMay 16, 2013


"Convergence?", by Robert Spann (Washington, DC)11" x 14" including frame, Digital Print, 2012
Computer graphics allows one to see both the numerical and aesthetic properties of dynamical systems. Recently I became interested in the properties of complex functions in which a complex variable is raised to a complex, rather than an integer exponent. I have also been analyzing complex polynomials that have no attracting fixed points. This image is produced by applying Newton's method for root finding to the complex function (z^(2+3i).09)*(z^(23i) .09).The white areas are points in the complex plane where this function does not converge to any root. The background is produced using Perlin noise functions.  Robert SpannMay 16, 2013


"Double Boy Klein Bottle," by Carlo Séquin (University of Califnornia, Berkeley)6" x 8" x 7", FDM Model (blue ABS plastic), 2012
Boy's surface, a compact model of the projective plane, with a small disk removed is topologically equivalent to a Möbius band. Every Klein bottle can be composed of two Möbius bands that are glued together by their edges. In this model a Klein bottle is created by gluing together two mirror images of a 3fold symmetrical Boy surface with a disk removed from its pole. The result is a Klein bottle with S6 symmetry, showing six of the "inverted sock" openings characteristic of the classical Klein bottle.  Carlo SéquinMay 16, 2013


"Seifert surfaces for torus knots and links," by Saul Schleimer (University of Warwick, UK) and Henry Segerman (University of Melbourne, Australia)Four pieces: 111mm x 111mm x 105mm, 125mm x 130mm x 99mm, 125mm x 125mm x 118mm, 103mm x 103mm x103mm, PA 2200 Plastic, SelectiveLaserSintered, 2012
As elegantly discussed in Ghys' 2006 ICM plenary talk, the natural parameterization of the Seifert surface for the trefoil knot uses Eisenstein series of lattices in the plane. This was generalized by Milnor to all (p,q) torus knots; he replaces Eisenstein series by certain fractional automorphic forms. Tsanov reduces the construction of these forms to finding an analytic description of the universal covering of the orbifold S^2(p,q,infinity) by the hyperbolic plane. Mainly following Lehner, we find a Fourier series for the covering map. Combining these ideas, we obtain a map from a hyperbolic triangle T_H, with angles pi/p, pi/q, and 0, to a domain T_S in S^3; rigid symmetries of T_S in S^3 generate the Seifert surface. Using SchwarzChristoffel theory we uniformize T_H by a Euclidean triangle T_E having angles pi/p, pi/q and pi(11/p1/q). In this way we transfer decorations on T_E to the Seifert surface; for these sculptures we use a subdivision of T_E into 15 congruent triangles.  Saul Schleimer and Henry SegermanMay 16, 2013


"Pointed Planes and Bézier Beaks," by Harry RubinFalcone (Oberlin College, Oberlin, OH)15.5" x 20", Digital Print, 2012
Each figure is created with a series of Bézier curves. Because there is space between each curve, you can see some parts of the curves behind the others, which gives each figure a translucent and three dimensional look. The curves can be thought of as lying on a plane, which means each figure is a representation of a foldedover plane that comes to a point.  Harry RubinFalconeMay 16, 2013


"Starry Pines," by Charles Redmond (Mercyhurst University, Erie, PA)16" X 16", Generated by code written in the Context Free Art language, no photoediting software used, 2011
Every program written in the Context Free Art language may be considered to be a context free grammar for creating images. Thus, when one programs in this language, one is "inventing" grammars. Any image produced with such a grammar may be considered to be a legal sentence in the grammar. If randomness is introduced into the program, then there are many different legal sentences or images, and one is producing generative art. When I created Starry Pines, I was studying tree creation with Context Free Art while at the same time experimenting with a technique of mine for creating star clusters and galaxies. I put them together for this work, along with a recursive icy swirl added to the rules for the trees.  Charles RedmondMay 16, 2013


"White hyperbolic disk," by Gabriele Meyer (University of Wisconsin, Madison)20" x 17" x 17", Polyester yarn and shaped line, 2012
This started out as a white disk crocheted in a spiral fashion. By making more than the necessary stitches, it takes on this characteristic wavy form. The hyperbolic disk is the most basic form of a hyperbolic surface, other possible shapes include blossoms and algae. I particularly like the play of light and shadow on this hyperbolic surface. That's the reason why I made this one just pure white. The holes created by double and triple stitches allow further light and shadow play.  Gabriele MeyerMay 16, 2013


"Blue Sun," by Mojgan Lisar (Enschede, The Netherlands) and Reza Sarhangi (Towson University, MD)16" x 16", combination of hand painting and computer work, 2012
The Blue Sun is a collage of two different Persian works of art, both with deep mathematical roots: Tiling and Tazhib. The mosaic design on the back is a twolevel selfsimilar tiling that has been made based on the decagram. This structure possesses a 10fold rotational symmetry. This symmetry can be expanded in all directions using the five Sâzeh motifs introduced in "Polyhedral Modularity in a Special Class of Decagram Based Interlocking Star Polygons" by Reza Sarhangi, the 2012 Bridges Proceedings. The tiling at the center presents the tiling of a decagram that follows the same rules as the larger tiling in the back. The front image is a decagram Tazhip. In a traditional Persian Tazhib, one can find mathematical ideas and concepts, such as symmetries, spirals, polygons and star polygons.  Mojgan Lisar and Reza Sarhangi May 16, 2013


"Inlaid Wooden Box of Makoto Nakamura's Tessellations," by Kevin Lee (Normandale Community College, Saint Paul, MN)4" x 4" x 4", Wood: Cherry, Maple, Walnut, Oak, Butternut, Mahogany, 2012
Best textile, sculpture, or other medium, 2013 Mathematical Art Exhibition
Makoto Nakamura has created a collection of tessellation designs that rival M. C. Escher’s collection. The six designs on this box represent the asymmetric, isohedral Heesch tile types: TCCTC, TG1G2TG2G1, TCCTGG, C3C3C3C3C3C3, and CC4C4C4C4.  Kevin LeeMay 16, 2013


"540º," by Ayelet Lindenstrauss Larsen (Indiana University, Bloomington)1" x 8" x 8", Cotton, silk, dissolvable muslin, 2003
This Möbius band is twisted three times, each time by 180 degrees, before its short sides are attached to each other. Topologically, it is the same as the usual Möbius band where the band is twisted only once before attaching the short sides to each other; it is just embedded in 3space in a different way. The edge of a Möbius band consists of one long circle. If you follow the edge of this Möbius band, you will go through the colors of the rainbow, from red to purple, and then transition to red through redpurple and begin the cycle again.  Ayelet Lindenstrauss LarsenMay 16, 2013


"Meandering Eightfold Path," by Margaret Kepner (Washington, DC)Flat: 18" x 18"; Folded: 3" x 6" x 0.5", Archival Inkjet on Paper, 2012
This work is a modified version of an earlier design – The Eightfold Path. Colors have been added, and the flat 2D print has been deconstructed into a folding book format. The underlying design is a visual presentation of the five nonisomorphic groups of order eight: C8, C2 x C4, C2 x C2 x C2, D4, and Q8. It employs a visual vocabulary derived from a traditional quilt pattern, Drunkard’s Path. Each of the small shapes used in the design is a quarter circle in a square, scaled so that its area equals the square’s residual area. The 36page book structure is created from a single sheet of paper through a series of cuts and folds. A continuous meander folding path is followed, with varying length foldsequences, and no beginning nor end. When it is fully folded up, the book assumes a doublesquare footprint. A smallerscale meander path, which would result in a continuous 144page book, is expressed through color accents.  Margaret Kepner May 16, 2013


"Super Buckyball of Genus 31," by BihYaw Jin (National Taiwan University, Taipei)20" x 20" x 20", Plastic beads, 2011
Joining with students and teachers of the Taipei First Girls High School in November 2011, we made two bead models of super buckyball, a polyhedron of genus 31. Each vertex in this model is itself a buckyball punched with three holes and then connects to three neighbored vertices by three shortest carbon nanotubes. We can also view structure as the second level Sierpinski buckyball, which can be extended arbitrarily to infinity.  BihYaw JinMay 16, 2013


Fractal Cylinder 2, by Daniel Gries (Hopkins School, New Haven, CT)11.5" x 22", Giclee print from JavaScriptgenerated digital image, 2012
In Fractal Cylinder 2, curves are drawn along waist curves, colored by a radial gradient. Low alpha values create differing densities and transparency.  Daniel GriesMay 16, 2013


"Quejido Design III," by Gary Greenfield (Prof Emeritus, University of Richmond, VA)10.5" x 10.5" (unframed), Digital Print, 2012
Between 19681972 Spanish artist Manuelo Quejido collaborated with computer programmers at the University of Madrid in order to execute a series of stateoftheart computer generated “sequence” designs consisting of patterns of disks. As an homage, Quejido Design III realizes one of these patterns using stateoftheart agent based methods. Here, agents are virtual ants modeled after the species T. albipennis that collect dispersed grains of sand in order to form circular nest walls. By using two different colors for sand grains and by assigning to each virtual ant a center, radius, and color, a uniform density grid of sand grains selforganizes into a pattern which, up close, has no color symmetry, but from a distance is perceived of as being color preserving under various symmetry operations.  Gary Greenfield May 16, 2013


"Window into Infinity: A Sample of the Murhombicuboctahedron," by S. Louise Gould (Central Connecticut State University, New Britain)6.5" x 6.5" x 6.5", Embroidery on cotton fabric, 2012
This is an extension of the work I have done with fabric polyhedra. "The Symmetries of Things" written by Conway, Burgiel and GoodmanStrauss has provided many pathways to explore and it was the inspiration for this piece. This Archimedean infinite polyhedra is constructed of regular hexagons and squares. It illustrates the symmetry *642. Each vertex has 4 squares and one hexagon surrounding it. This model uses squares of four colors to show how the model moves into space. Each of the modules is constructed from a "net" of embroidered squares and hexagons. The nets were designed on Geometer's Sketchpad then digitized using 4D Professional Software and stitched on a Viking Topaz embroidery sewing machine. The pictures show the object from three different directions.  S. Louise GouldMay 16, 2013



