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 ands, 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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"Interlaced Hearts," by Matjuska Teja Krasek (2001)Digital print, 12.6" x 11.9". Kraskek's interest is focused on the shapes' inner relations, on the relations between the shapes and between them and a regular pentagon. Her artworks also illustrate properties such as golden mean relations, self similarity, ten- and fivefold symmetry, Fibonacci sequence, inward infinity and perceptual ambiguity. She employs contemporary computer technology as well as classical painting techniques.

"The implicit decagon constituted of five smaller decagons expresses tenfold and fivefold rotational symmetry. The image where golden heart-like shapes are exposed shows self-similarity, the richness of relations between the decagons, pentagonal stars, Penrose rhombs, kites and darts with the golden ratio used several times as a scale factor." --- Matjuska Teja Krasek, Freelance artist, Ljubljana, Slovenia, EU
Apr 14, 2009
"Wave (32)," by Goran Konjevod, Arizona State University, Tempe, AZ (2006)First Prize, 2009 Mathematical Art Exhibition. One folded square sheet of paper, 10" x 10" x 5". "The wave is one of the pleat tessellations that continues to amaze me even years after I first folded it. The peculiar symmetry and the tension caused by locking the edges causes two of its corners to bulge in opposite directions, while the remaining two corners remain fairly flat. As in the simple bowl, the pleat sequences all begin at the edges and proceed towards the center of the sheet, but the difference is that all horizontal pleats are oriented the same way, and similarly all the vertical pleats." --- Goran Konjevod, Assistant Professor of Computer Science and Engineering, Arizona State University, Tempe, AZApr 14, 2009
"Spiral Squares," by Iftikhar Husain, University High School, Newark, NJ (2008)Digital print, 8" x 8". "The artwork 'Spiral Squares' was originally created on a TI-84 Plus graphing calculator. The design was uniquely created by using two equations only of linear function with restricted domain. These two equations have different parameters of the equation of each line segment, such as slope, y-intercept, domain x-left value, and domain x-right value, organized in a table. Each line segment is drawn by picking up its respected parameter value from the table. Once all the values from the table are exhausted the complete spiral square will appear on the calculator screen. The artwork is simple but truly illustrates the mathematical concepts. A single Spiral Square was then created on a computer using Geometer Sketchpad software. The artwork, shown here, is the simple translation effect of the single spiral square horizontally and vertically thrice." --- Iftikhar Husain, Mathematics Teacher and Tech-Coordinator, University High School, Newark, NJApr 14, 2009
"(10,3)-a Twice," by George Hart, Stony Brook University, Stony Brook, NY (2008)Nylon (selective laser sintering), 3.5" x 3.5" x 3.5". "This is a sculptural interpretation, made by selective laser sintering, of two copies of the (10,3)-a lattice. Modern layered fabrication processes allow the construction of two interlocked components which are free to move slightly relative to each other, within the constraints of their being linked. The two copies are congruent, though mirror images. Each interpenetrates the tunnels of the other in a surprisingly complex manner. The 5x5x5 selection from the infinite lattice was made in such a way that the sculpture can stand vertically on a corner. See more works at" --- George Hart, Research Professor, Stony Brook University, Stony Brook, NYApr 14, 2009
"(10,3)-a," by George Hart, Stony Brook University, Stony Brook, NY (2008)Nylon (selective laser sintering), 3.5" x 3.5" x 3.5". "This is a sculptural interpretation of the (10,3)-a crystal lattice, which has been well known to crystallographers and mathematicians for decades. However I have adapted it by wrapping it in a smooth surface which maintains its high genus topology while giving an organic sensibility. A 4x4x4 block has been selected from the infinite lattice in such a way that it can stand upright on a corner with a 3-fold axis vertical. Viewing the sculpture from different vantage points reveals a rich set of dramatically different tunnels along varying projections. For additional information and images, see" --- George Hart, Research Professor, Stony Brook University, Stony Brook, NYApr 14, 2009
"Simple Bowl (32)," by Goran Konjevod, Arizona State University, Tempe, AZ (2006)One folded square sheet of paper, 5" x 5" x 4". "This is one of the simplest pieces in my ongoing series of bowls formed by pleat tessellations. Every fold is a straight line segment parallel to an edge of the square sheet, and no fold is ever undone. The curved surface is purely a result of the intrinsic tension in the sheet of paper trying to unfold itself. This simple bowl is constructed by using alternating pairs of vertical and horizontal pleats, from the edges toward the center." --- Goran Konjevod, Assistant Professor of Computer Science and Engineering, Arizona State University, Tempe, AZApr 14, 2009
"A Strange Dream," by Karl Kattchee, University of Wisconsin - La Crosse (2008)Oil crayon on paper, 20" x 24". "This drawing is composed of round shapes, mainly. The arrangement of the round shapes is itself round, so that roundness is occurring on multiple levels. On the other hand, the drawing depicts multiple levels of thinking or being, like a sleeper who dreams within his dream within his dream. A Strange Loop, in the sense of Hofstadter, is evident." --- Karl Kattchee, Associate Professor of Mathematics, University of Wisconsin-La Crosse, La Crosse, WIApr 14, 2009
"Crane," by Zdenka Guadarrama, Rockhurst University, Kansas City, MO (2008)Mobile--Gauze, papyrus, silver and wood, 10" x 10" x 15". "'Crane' represents the continuous dimensional transition from a point, represented by a silver sphere, to a line, a plane and finally a crane. This transition is depicted in parallel to the evolution of the creative process which starts with an idea, represented by the same silver sphere, and which through refinements and trials culminates in the bird as well. [My] projects consist in artistic explorations that happen in parallel to the teaching/learning of mathematics (measure theory or complex analysis, for example). I search to generate art using mathematics and art inspired in the mathematics that I share with my students in order to motivate them to learn more mathematics, to make some extra connections, and to create some art of their own." --- Zdenka Guadarrama, Assistant Professor of Mathematics, Department of Mathematics and Physics, Rockhurst University, Kansas City, MOApr 14, 2009
"A Mathematician's Nightmare," by JoAnne Growney (2008)Laser print on paper, 15 1/2" x 17 1/2" . "The poem, 'A Mathematician's Nightmare,' introduces a version of the unsolved Collatz Conjecture which asserts that when prescribed operations are iterated on any positive integer, the sequence produced will eventually reach 1. The prescribed operations are these, for any starting positive integer n: if n is even, replace n by n/2 (i.e., decrease n by half); if n is odd, replace n by (3n+1)/2 (i.e., increase n by half and round up to the next integer); my exhibit-entry displays both the poem and a graph of the sequence of iterations applied to the integer 27." --- JoAnne Growney, Poet, Professor Emerita, Department of Mathematical Sciences, Bloomsburg University. Residence: Silver Spring, MDApr 14, 2009
"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
"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
"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
"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
"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
"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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