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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"Walnut Star," by David Reimann (Albion College, Albion, MI)Walnut veneer and brass fasteners, 38 x 38 x 38 cm, 2015

I am interested in creating patterns that convey messages at multiple levels and scales using a wide variety of mathematical elements and media. This form is based on the small rhombicosidodecahedron, an Archimedean solid with 120 edges. The underlying polyhedral edges have been replaced by 4.75 cm squares made from laser-cut paper-backed walnut veneer and connected at their corners with brass split-pin fasteners. The 62 faces (squares, hexagons, and pentagons) and 60 vertices of the underlying polyhedron are transformed into open negative space. The expansion of linear edges into squares results in a sphere-like shape with 20 knobs. --- David Reimann

Mar 09, 2016
"OSU Triptych No. 2," by Robert OrndorffPaper and acrylic, 20 x 46 cm, 2015
Honorable Mention, 2016 Mathematical Art Exhibition

My paper folding art is math plus paper. Folded paper is simply tangible math. This is a permanent manifestation of an ephemeral artwork, namely, one solution for a specific one-straight-cut problem. Such problems are usually stated as follows: How must one fold a paper rectangle into a flat figure such that one straight cut through all of the layers will produce a given planar straight-line graph? Here the problem has been solved with paper and then represented in acrylic. To a significant degree the work relies on transmitted and reflected light, and so it never looks the same twice. The figure (the letters "OSU") has been divided into three frames. The crease patterns for the left and right letters are pedestrian but that for the central letter is sublime. --- Robert Orndorff
Mar 09, 2016
"Shield 1," by Kerry Mitchell (Phoenix, AZ)Digital print on aluminum panel, 40 x 40 cm, 2014

My work is composed primarily of computer generated, mathematically-inspired, abstract images. I draw from the areas of geometry, fractals and numerical analysis, and combine them with image processing technology. This image was created using a dynamic version of the Chaos Game algorithm. The Chaos Game is a simple example illustrating chaotic motion and strange attractors. It is typically implemented using three anchor points, which become the vertices of a Sierpinski triangle. The Dynamic Chaos Game allows the anchor points to move each iteration. Here, the image comprises seven panels. In each, the three anchor points slid along line segments, with different speeds. The pixels were then colored according how frequently that point was visited during the iteration. --- Kerry Mitchell
Mar 09, 2016
"Ovoid Bead with three Hyperbolic Axes as a Lamp," by Gabriele Meyer (University of Wisconsin, Madison)Photograph, 2016

I like to crochet hyperbolic surfaces. This object started as a hollow ovoid, top and bottom missing. I then crocheted three vertical axes down the sides. These three axes are the basis for the hyperbolic crochet. The object is hung from the ceiling.
I then entered a light tube. The photograph was taken in the dark without flash. --- Gabriele Meyer
Mar 09, 2016
"Hexahedron 2," by Dorothy McGuinness (Everett, WA)Watercolor paper, acrylic paint, polyester thread, 38 x 38 x 38 cm, 2014

I create forms art of diagonal twill and structures not normally found in the basketry world. My medium for this unique work is watercolor paper, which I've painted and cut into very narrow uniform strips to achieve the precision I seek. I am very much interested in the math and geometric constraints of the work. Using hundreds of strips of paper at a time, I explore new structural forms. An interpretation of a hexahedron using diagonal twill to form a woven sculptural basket. --- Dorothy McGuinness
Mar 09, 2016
"Catalan Connections: Level Four," by Margaret Kepner (Washington, DC)Archival inkjet print, 40 x 60 cm, 2015

I enjoy exploring the possibilities for conveying ideas in new ways, primarily visually. I have a background in mathematics, which provides me with a never-ending supply of subject matter. The Catalan numbers are a sequence of positive integers that provide answers to certain combinatorial questions. For example, in how many ways can a polygon with n+2 sides be cut into triangles? A hexagon (setting n=4) can be triangulated in fourteen different ways, so the 4th Catalan number is 14. Other types of problems also lead to the Catalan numbers: counting binary trees, balancing parentheses, finding paths through a grid, shaking hands in a circle, etc. This piece is composed of diagrams representing seven different problems; for each of these, the answer is the 4th Catalan number. The solution sets for the problems are displayed in diagonal bands. The columns indicate correspondences between elements in different solution sets. --- Margaret Kepner
Mar 09, 2016
"45 Poppies," by Karl Kattchee (University of Wisconsin-La Crosse)Digital print, 18 x 31 cm, 2015
Best photograph, painting, or print, 2016 Mathematical Art Exhibition

This image is a classification of all closed paths, on a 6x6 grid, with the following properties: First, each path must proceed around the center of the grid and be orthogonal in the sense that every turn is 90 degrees. Also, the path must use each row and column exactly once. Finally, we require that each path be asymmetrical, and we do not distinguish between paths which differ by a rotation or flip. Each center square is colored black, and the shades of red are dictated by the winding number of each region. Acknowledgements: Craig Kaplan (Waterloo), for helpful notation and the coloring scheme idea, and artists Kate Hawkes and Misha Bolstad (UW-La Crosse) for the poppies idea. --- Karl Kattchee
Mar 09, 2016
"Waves - Offering to the Moon," by Veronika Irvine & Lenka Suchanek (University of Victoria, British Columbia, Canada) Stainless steel wire, shell, driftwood cedar frame, 40 x 36 x 9 cm, 2015

"Waves" was designed and created by lenka using a tessellation pattern generated algorythmically by Veronica. Bobbin lace, a 500-year-old art form, features delicate patterns formed by alternating braids. Lenka: "I had a beautiful frame made from old growth, driftwood red cedar and I needed a pattern that would look like the waves of the Pacific Ocean... The model is an incredible source of designs--every graph has so many variations for working the stitches and each combination results in a different pattern. I love the experimental nature of the work. --- Veronika Irvine & Lenka Suchanek
Mar 09, 2016
"Sword Dancing," by George Hart (Stony Brook University, Stony Brook, NY USAWood (dyed) and cable ties, 32 x 45 x 45 cm, 2015
Best textile, sculpture, or other medium, 2016 Mathematical Art Exhibition

As a sculptor of constructive geometric forms, my work deals with patterns and relationships derived from classical ideals of balance and symmetry. Mathematical yet organic, these abstract forms invite the viewer to partake of the geometric aesthetic. This is a model for a large wood sculpture consisting of two congruent but mirror-image orbs of this design, each two meters in diameter. The sixty components of the design are "affine equivalent," meaning they can be stretched linearly to become congruent to each other. They lie in groups of three in twenty planes--the planes of a regular icosahedron which had been compressed by a factor of 1/2 along a five-fold axis. --- George Hart
Mar 09, 2016
"Ammann Cushion," by Maggi Harriss (Great Malvern, UK)Cotton cross-stitch, 38 x 38 x 5 cm, 2009

I am fascinated by mathematical patterns and enjoy using them to make something useful. Cushion with each tile shape for the Ammann-Beenker tiling in a different colour. --- Maggi Harriss
Mar 09, 2016
"Woven Dodec," by Edmund Harriss (University of Arkansas, Fayetteville) Laser cut paper, 20 x 20 x 20 cm, 2014

I like to play with the ways that the arts can reveal the often hidden beauty of mathematics and that mathematics can be used to produce interesting or beautiful art. 32 pieces of paper cut into two shapes connect and weave together to form a ball mixing the dodecahedron and icosahedron. Inspired by Quintron by Bathsheba Grossman. --- Edmund Harriss
Mar 09, 2016
"Fibonacci Downpour," by Susan Goldstine (St. Mary's College of Maryland, St. Mary's City, MD)Merino yarn, cotton thread, embroidery hoop, 21 x 26 x 26 cm, 2015

For me, the most exciting part of mathematics is communicating it to others. I am especially interested in models that make mathematical concepts tactile or visual. In Fibonacci Downpour, the vertical stitch lines branch and form drops following a physical version of the Fibonacci recursion. The number of drops and branchings in each row are consecutive Fibonacci numbers. As the Fibonacci numbers are asymptotically exponential, the fabric falls into a more or less pseudospherical form. --- Susan Goldstine
Mar 09, 2016
"Brown and Green Egg -163," by Faye Goldman (Ardmore, PA)Strips of polypropylene ribbon, 13 x 10 x 10 cm, 2013

Loosely defined, a 'Buckyball' is a polyhedron made of pentagons and hexagons with every vertex of degree three (three edges meeting). Buckyballs must have exactly twelve pentagons. I enjoy creating Buckyballs and their duals. I discovered that if you rearranged the twelve pentagons in a semi-regular pattern you could get interesting shapes. Thus began my series of eggs. --- Faye Goldman
Mar 09, 2016
"Dragony Curve," by Robert Fathauer (Tessellations Company)Ceramics, 60 x 45 x 3 cm, 2014

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 a particular stage in the development of a fractal curve known as the ternary dragon. This ceramic piece has been mounted on a board, with standoffs, partly to make it easier to handle without breaking. The resulting construct could be viewed as either a two-dimensional or three-dimensional artwork, which echoes the manner in which fractal curves can be considered as one-dimensional (a line), two-dimensional (a plane-filling object), or something in between. --- Robert Fathauer
Mar 09, 2016
"An Iris Spiral," by Frank A. Farris (Santa Clara University, San Jose, CA)Aluminum print, 51 x 61 cm, 2015

My artistic impulse is to let the beauty of the real world shine into the realm of mathematical patterns. My method combines photographs with complex-valued functions in the plane to create images with all possible types of symmetry. I photographed the irises and used complex wave functions to turn the image into a pattern with four-fold rotational symmetry. Then I applied a complex exponential mapping to wind the wallpaper around the complex plane, choosing just the right scaling to make the pattern match, while also creating five-fold symmetry. I bleached an outer ring to bring focus to the center of the spiral and to allow the original photograph of the iris to stand out. Details about wallpaper waves appear in my book, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. --- Frank A. Farris
Mar 09, 2016
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American Mathematical Society