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Math ImageryThe 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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"Aristolochia Grandiflora," by S. Louise Gould, Central Connecticut State University, New Britain (2008)Inkjet print on treated silk, quilted and sparsely beaded to emphasize symmetries, 20" x 21.5". "My artwork usually connects textiles or paper with mathematical, specifically geometric ideas. 'Aristolochia Grandiflora' is a floral fractal. When I first saw the plant at Frederik Meijer Gardens in Grand Rapids in full bloom in May, it seemed a natural subject for exploring the seventeen wallpaper patterns in the plane. Starting with a photograph that I had taken in the garden, I sampled sections of the plant image and used KaleidoMania to generate samples of each of the seventeen wallpaper patterns. These were printed on 8.5 by 11 inch treated silk pages and folded, cut, pieced, quilted and beaded to create mathematical art to wear." --- S. Louise Gould, Associate Professor, Department of Mathematical Sciences, Central Connecticut State University, New Britain, CT Apr 14, 2009
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"Extrapolated Icosahedron," by Bradford Hansen-Smith (2008)52 folded 9" paper plate circles, 13"x13"x13". "Forty circles have been folded, reformed to an in/out variation of a truncated tetrahedron, then octahedronally joined in pairs, and arranged in an icosahedron pattern. This revealed an interesting form of the icosadodecahedron with open pentagon stars. In this case twelve circles were reformed and added to suggest mouth-like openings found in sea anemones or in opening flower buds. This gives function to the open pentagons. Much of what I explore with folding circles are the structural functions of geometry found in life forms that correlate to the movement forms of the folded circle." --- Bradford Hansen-Smith, Independent consultant, geometer, author, sculptor, Chicago, ILApr 14, 2009
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"Skelug," by Bradford Hansen-Smith (2007)28 folded circles, 16"x6"x5". "Nine inch paper plate circles are folded and reformed into multiple units that have been arranged in one of many possible combinations of joining. Consistently following the development it began to take on a skeleton-like appearance and by decreasing the diameters of the circles it began to form a twisting conical helix, much like a sea slug, thus the name Skelug. Most all of my explorations with the circle start with folding three diameters, developing the equilateral triangular grid, reforming and joining multiples, which often reveals structural forms observable in nature." --- Bradford Hansen-Smith, Independent consultant, geometer, author, sculptor, Chicago, ILApr 14, 2009
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"Black and Blue Ricochet Trio," by Gary R. Greenfield, University of Richmond, VA (2008)Digital print, 14" x 24". "Many of my computer generated algorithmic art works are based on visualizations that are inspired by mathematical models of physical and biological processes. These three side-by-side black and blue "ricochet compositions" were generated by placing particles on each of the sides of a 16-gon, assigning them starting angles, and then letting each move in a straight line until it encounters an existing line segment at which point it is reflected--the ricochet--and then paused so that the next particle may take its turn. Further, if a particle ricochets off its own path, then the area it has just enclosed is filled using the requisite black or blue drawing color that particles were alternately assigned." --- Gary R. Greenfield, Associate Professor of Mathematics and Computer Science, University of Richmond, Richmond, VAApr 14, 2009
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"Trefoil Knot Minimal Surface," by Nat Friedman, Professor Emeritus, University of Albany - SUNY (2006)Limestone, 9" diameter by 4" depth. "This sculpture was carved from a circular piece of limestone. The form is based on the shape of the soap film minimal surface on a configuration of a wire trefoil knot. There is a nice interaction of the form and space with light and shadow." --- Nat Friedman, Professor Emeritus, University of Albany - SUNY
Apr 14, 2009
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"The Net," by Mehrdad Garousi (2008)Digital art print, 24" x 18.5". "This image exhibits a very complex, yet ordered series of lonely fibers that are woven in each other. This generated lacy net is not flat and goes to infinity at the center and also many times in each of its main arms. Another wonderful mathematical and artistic representation is where hexaploid weaving is modified into a triple one without cutting or deleting any fibers. Self similarity is the main property of this work, as any small hole in the main arms is nearly similar to the whole image. Having experimented with other media, I chose mathematical fractal image making as one of the newest and most wonderful common areas between mathematics and art." --- Mehrdad Garousi, Freelance fractal artist, painter and photographer, Hamadan, IranApr 14, 2009
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"Spiral Mobius," by Nat Friedman, Professor Emeritus, University of Albany - SUNY (2006)Stoneware, 12" x 8" x 12". "This sculpture was made by starting with a cut circular band of clay and then bending and twisting before rejoining the cut ends. Props were used to preserve the shape while drying. The form was then sanded, low fired, sanded, and then high fired." --- Nat Friedman, Professor Emeritus, University of Albany - SUNY Apr 14, 2009
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"The PowerStar: Synergetic Sacred Geometry, " Warren Scott Fentress (2008)MagneBlocks, 20" x 20" x 20". "Platonic fundamental shapes like the tetrahedron and pyramid, which are culminated recursively into 'powered tetrahedrons & pyramids', are arranged into pentagonal forms that mimic the 5-fold geometry of flowers. I invented MagneBlocks because of the bicameral mind resonating with the fundamental consciousness waveforms that permeate spacetime." --- Warren Scott Fentress, Imaginatuer, Brookfield, CT
Apr 14, 2009
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"Cornrow," Stephen Luecking, DePaul University, Chicago, IL (2008)Giclee print, 13" x 13". "Images begin as super ellipses constructed from bezier curves in which the weight and position of the control points are randomized, using a random number generator to induce eccentricity. The eccentric curves are then layered subjected to various improvised Boolean and path edits. The results are not intended to be read as mathematical objects, thus the randomizing and improvising procedures. Rather the goal is to seek out visual tensions implicit in the relationship between the curves and the tondo format, between the wholeness of the circle and the fragmentation in its interior." --- Stephen Luecking, Professor of Computer Graphics, School of Computing and Digital Media, DePaul University, Chicago, ILApr 14, 2009
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"Twice Iterated Knot No. 1," by Robert Fathauer, Tessellations Company (2008)Third Prize, 2009 Mathematical Art Exhibition. Digital print, 19" x 12". Fathauer makes limited-edition prints inspired by tiling, fractals, and knots. He employs mathematics in his art to express his fascination with certain aspects of our world, such as symmetry, complexity, chaos, and infinity.

"The starting point for this iterated knot is a nine-crossing knot that has been carefully arranged to allow seamless iteration. Four regions of this starting knot are replaced with a scaled-down copy of the full starting knot, incorporated in such a way that the iterated knot is still unicursal. These same four regions are then replaced with a scaled-down copy of the iterated knot, resulting in a complex knot possessing self similarity." --- Robert Fathauer, Small business owner, puzzle designer and artist, Tessellations Company, Phoenix, AZ
Apr 14, 2009
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"Cob," by Stephen Luecking, DePaul University, Chicago, IL (2008)Giclee print, 13" x 13". "Images begin as super ellipses constructed from bezier curves in which the weight and position of the control points are randomized, using a random number generator to induce eccentricity. The eccentric curves are then layered subjected to various improvised Boolean and path edits. The results are not intended to be read as mathematical objects, thus the randomizing and improvising procedures. Rather the goal is to seek out visual tensions implicit in the relationship between the curves and the tondo format, between the wholeness of the circle and the fragmentation in its interior." --- Stephen Luecking, Professor of Computer Graphics, School of Computing and Digital Media, DePaul University, Chicago, IllinoisApr 14, 2009
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"Overlapping Circles I," by Anne Burns, Long Island University, Brookville, NY (2008)Digital print, 13" x 12". "This is an iterated function system made up of Mobius Transformations, programmed in ActionScript. I began my studies as an art major; later I switched to mathematics. In the 1980's I bought my first computer and found that I loved programming and could combine my all of my interests: art, mathematics, computer programming and nature." --- Anne Burns, Professor of Mathematics, Long Island University, Brookville, NYApr 14, 2009
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"Rhombic Triacontahedron III," by Vladimir Bulatov (2007)Metal sculpture, 4.0" diameter. "Stellation of rhombic triacontahedron with 30 identical rhombic faces makes base for this sculpture. All internal intersections of rhombic faces were carefully eliminated by cutting away parts of rhombuses. The resulting 3D body was given organic shape by replacing straight faces with smooth subdivided surface. My artistic passions are purely mathematical images and sculptures, which express a certain vision of forms and shapes, my interpretations of distance, transformations and space. In my opinion, mathematics is not simply a profession, but rather a way of thinking, a way of life." --- Vladimir Bulatov, Independent Artist, Corvallis, ORApr 14, 2009
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"Rhombic Dodecahedron I," by Vladimir Bulatov (2008)Metal sculpture, 4.5" diameter. "The base of this sculpture is rhombic dodecahedron (polyhedron with 12 rhombic faces with cubical symmetry). Each of the 12 faces was transformed into a curved shape with 4 twisted arms, which connects to other shapes at vertices of valence 3 and 4. The boundary of the resulting body forms quite a complex knot. My artistic passions are purely mathematical images and sculptures, which express a certain vision of forms and shapes, my interpretations of distance, transformations and space. In my opinion, mathematics is not simply a profession, but rather a way of thinking, a way of life." --- Vladimir Bulatov, Independent Artist, Corvallis, ORApr 14, 2009
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"Recursive Construction for Sliding Disks," Adrian Dumitrescu, University of Wisconsin, Milwaukee (2008)Digital print, 11" x 5". "Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk slides in the plane without intersecting any other disk, so that its center moves along an arbitrary (open) continuous curve. One can easily show that 2n moves always suffice, while the above construction shows pairs of configurations that require 2n-o(n) moves for this task, for every sufficiently large n. Disks in the start configuration are white, and disks in the target configuration are shaded. " --- Adrian Dumitrescu, University of Wisconsin, Milwaukee Apr 14, 2009
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