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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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470 files in 35 albums with 0 comments viewed 468,893 times
Mathematical Concepts Illustrated by Hamid Naderi Yeganeh


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One of my goals is to create very beautiful images by using mathematical concepts such as trigonometric functions, exponential function, regular polygons, line segments, etc. I create images by running my program on a Linux operating system. --- Hamid Naderi Yeganeh

4 files, last one added on Oct 01, 2014
Album viewed 508 times

Simon Beck's Snow and Sand Patterns


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I create geometric patterns in the snow, walking along the frozen lakes of Savoie, France in snowshoes. On average the works take about 10 hours to really do it properly, some are a little unfinished, if my feet get cold or hurt too much. The setting out is done using handheld orienteering compass and distance determination using pace counting or measuring tape. Curves are either judged or arcs of circles are made using a clothesline attached to an anchor at the centre. Designs are chosen from the world of geometry. The Koch curve and Sierpinski triangle in this album are among my favorites. The works are very large (the size of several soccer fields), and many of the mathematical patterns appear 3D, especially when viewed from above. more recently I've also created patterns in the sand. --- Simon Beck

9 files, last one added on Aug 19, 2014
Album viewed 3140 times

2014 Mathematical Art Exhibition


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The 2014 Mathematical Art Exhibition was held at the Joint Mathematical Meetings held in Baltimore, MD. Here on Mathematical Imagery is a selection of the works in various media. Mathematical Art Exhibition Awards were given: "Enigmatic Plan of Inclusion I & II," by Conan Chadbourne was awarded Best photograph, painting, or print; "Three-Fold Development," by Robert Fathauer was awarded Best textile, sculpture, or other medium; and "Blue Torus," by Faye E. Goldman received Honorable Mention. The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name.

16 files, last one added on May 05, 2014
Album viewed 2213 times

Daina Taimina's Hyperbolic Crochet


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Inspired by William Thurston's paper creations back in the 1960s, I thought if something can be made out of paper, it can also be crocheted, so I made my first crocheted hyperbolic planes in June 1997 by increasing stitches in constant ratio---after every two stitches I did an increase by one stitch. The number of stitches in each row grew exponentially, so after finishing my first small, very ruffled one I realized that to explore the hyperbolic plane I have to change the ratio of increase. For classroom use the best is to use the ratio 12:13---it means to increase one stitch after every 12 single crochet stitches. See more crochet examples on my blog, Daina Taimina Fiber Sculptures, at http://dainataimina.blogspot.com/. --- Daina Taimina (Cornell University, Ithaca, NY)

6 files, last one added on Jun 21, 2013
Album viewed 2296 times

Frank Farris :: Seeing Mathematics


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I'm particularly interested in visualizing mathematics and giving talks on mathematics and art. Many of my digital works, some of which are made into fabric and wallpaper, are based on photographs of everyday scenes and objects. --- Frank A. Farris, Santa Clara University

4 files, last one added on Sep 18, 2013
Album viewed 1204 times

Robert J. Lang :: Origami


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The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. We can group these intersections into roughly three categories: Origami mathematics, which includes the mathematics that describes the underlying laws of origami; Computational origami, which comprises algorithms and theory devoted to the solution of origami problems by mathematical means; Origami technology, which is the application of origami (and folding in general) to the solution of problems arising in engineering, industrial design, and technology in general. One genre blends into another. Origami math defines the "ground rules" for computational origami's goal of solving origami design problems (and quantifying their difficulty). The results of computational origami, in turn, can be (and have been) pressed into service to solve technological problems ranging from consumer products to the space program. Origami, like music, also permits both composition and performance as expressions of the art. Over the past 40 years, I have developed nearly 600 original origami compositions. About a quarter of these have been published with folding instructions, which, in origami, serve the same purpose that a musical score does: it provides a guide to the performer (in origami, the folder) while allowing the performer to express his or her own personality website includes galleries of my designs, crease patterns, schedule of my lectures, appearances and exhibitions, commissioned works, and more on the science of origami.

--- Robert J. Lang

17 files, last one added on May 22, 2013
Album viewed 4195 times

2013 Mathematical Art Exhibition


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The 2013 Mathematical Art Exhibition was held at the Joint Mathematical Meetings held in San Diego, CA. Here on Mathematical Imagery is a selection of the works in various media. Mathematical Art Exhibition Awards were given: "Bended Circle Limit III," by Vladimir Bulatov was awarded Best photograph, painting, or print; "Inlaid Wooden Boxes of Makoto Nakamura's Tessellations," by Kevin Lee was awarded Best textile, sculpture, or other medium; and "Tessellation Evolution," a beaded necklace by Susan Goldstine received Honorable Mention. The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name.

27 files, last one added on May 16, 2013
Album viewed 4799 times

Carlo Séquin :: Mathematical Images


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Since high school I have been fascinated by geometry. I enjoyed constructing the more complicated Platonic solids with ruler and compasses, as well as reading about the 4th dimension. While at Bell Labs in Murray Hill, I was introduced to the field of Computer Graphics, and later developed the Berkeley UniGrafix rendering system, so that I could depict objects more complex than I could build. Since then, the focus of my work has been on computer-aided design (CAD) tools -- for engineers, architects, and artists. When creating abstract sculptures I see myself as a composer in the realm of pure geometry. The artistic achievement then lies in finding a procedural formulation that can reflect the inherent symmetries and constructive elegance that seems to lie beneath many sculptural master pieces as well as at the foundations of the physical laws of our universe.

--- Carlo Séquin

16 files, last one added on Mar 18, 2013
Album viewed 2031 times

Fractal Pancakes


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I'm a math teacher, illustrator, and dad. Having begun entertaining my children with weekly pancakes earlier this year, I'm always looking for new themes; in this album you'll find some of the fractal pancakes I cooked up one morning. On my blog, www.10minutemath.com, you can find more about fractals and other topics that interest me as a teacher. --- Nathan Shields (www.10minutemath.com)

4 files, last one added on Jun 14, 2012
Album viewed 2030 times

2012 Mathematical Art Exhibition


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The 2012 Mathematical Art Exhibition, held at the Joint Mathematical Meetings held in Boston, MA, was the largest exhibition to date. Here on Mathematical Imagery is a selection of the works in various media. Mathematical Art Exhibition Awards were given: First Place to Sylvie Donmoyer for "Still Life with Magic Square"; Second Place to Thomas Hull, Robert Lang, and Ray Schamp for "Pleated Multi-sliced Cone"; and Third Place to Carlo H. Séquin for "Lawson's Minimum-Energy Klein Bottle. The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name.

40 files, last one added on May 14, 2012
Album viewed 5645 times

Erica Rollings Glass Works


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All my life I have vacillated between mathematics and art and find I am happiest when doing both. It's generally acknowledged that math and music are closely related in human developmental processes. I guess it boils down to basic communication. Math and music are languages, and art is a visual means of communication. My medium of choice is glass, and my favorite designs are mathematical and usually the ones that nature presents in both anatomical and botanical spheres of life. --- Erica Rollings Glass Works (www.ericarollings.net)

4 files, last one added on Apr 03, 2012
Album viewed 1489 times

Lipson's Lego Sculptures


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I love to make mathematical Lego® sculptures. They aren't constructed entirely without computer assistance; usually I write some C code to generate whatever the shape is and figure out which cells in a grid made up of 1x1x1 Lego® bricks should be filled in. The code outputs this as an LDraw .DAT file, separated into construction steps adding one complete layer of the structure in each step. Then I use MLCad to view the .DAT file. I play around with the parameters and repeat until I have something that looks nice and which will probably be able to balance. But that's the easy part. Now I have to try to construct it out of actual Lego® bricks so that it actually holds together. --- Andrew Lipson (http://www.andrewlipson.com/mathlego.htm)

5 files, last one added on Feb 06, 2012
Album viewed 3549 times

2011 Mathematical Art Exhibition


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The Mathematical Art Exhibition held at the 2011 Joint Mathematics Meetings in New Orleans, included juried works in various media. Robert Fathauer was the curator of the exhibition, and the exhibition website was prepared by Anne Burns. The 2011 Mathematical Art Exhibition Awards were awarded: First Place to Margaret Kepner, for her work, "Magic Square 25 Study"; Second Place to Carlo Sequin for "Torus Knot (5,3)"; and Third Place to Anne Burns for "Circles on Orthogonal Circles". The Award "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name.

57 files, last one added on Mar 10, 2011
Album viewed 7176 times

Edmund Harriss:: Shapes and Tilings


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I am a mathematician and artist, fascinated by patterns, both theoretical and visual and their communication. My research is based on substitution tilings, tilings with a scaling symmetry like the Penrose Tiling. I write about ideas on maths, art and communication on my blog, Maxwell's Demon, at www.maxwelldemon.com. --- Edmund Harriss (University of Leicester).

6 files, last one added on Feb 09, 2010
Album viewed 2036 times

2010 Mathematical Art Exhibition


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The Mathematical Art Exhibition held at the 2010 Joint Mathematics Meetings in San Francisco, included works in various media by 64 artists. Robert Fathauer was the curator of the exhibition, and the exhibition website was prepared by Anne Burns. The exhibition was juried by Fathauer and Burns, along with Nat Friedman and Reza Sarhangi. The 2010 Mathematical Art Exhibition Prizes were awarded. Four judges, selected by the American Mathematical Society and the Mathematical Association of America, made the following awards: First Prize to Robert Bosch, for his work, "Embrace"; Second Prize to Harry Benke for "The Vase"; and Third Prize to Richard Werner for "Meditations". The Prize "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name.

63 files, last one added on May 10, 2010
Album viewed 6657 times

2009 Mathematical Art Exhibition


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The Mathematical Art Exhibition held at the 2009 Joint Mathematics Meetings in Washington, DC, included 49 works in various media by 36 artists. Robert Fathauer was the curator of the exhibition, and the exhibition website was prepared by Anne Burns. The exhibition was juried by Fathauer and Burns, along with Nat Friedman and Reza Sarhangi. The inaugural Mathematical Art Exhibition Prizes were awarded. Four judges, selected by the American Mathematical Society and the Mathematical Association of America, made the following awards: First Prize to Goran Konjevod, for his origami work, "Wave (32), 2006;" Second Prize to Carlo Séquin, for his sculpture, "Figure-8 Knot, 2007;" and Third Prize to Robert Fathauer, for "Twice Iterated Knot No. 1, 2008." The Prize "for aesthetically pleasing works that combine mathematics and art" was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The thumbnail images in the album are presented in alphabetical order by artist last name.

49 files, last one added on Apr 28, 2009
Album viewed 7572 times

Crocheted Lorenz Manifolds


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Dr. Hinke Osinga and Professor Bernd Krauskopf (Engineering Mathematics, University of Bristol) have turned the famous Lorenz equations into a beautiful real-life object, by crocheting computer-generated instructions of the Lorenz manifold.

3 files, last one added on May 05, 2009
Album viewed 1752 times

Gwen L. Fisher :: Woven Beads


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Weavers of beads use a needle and thread to sew beads together to make decorative objects including jewelry, wall hangings, sculptures, and baskets. Some bead weave designers weave beads into composite clusters, usually with at least one large hole, called beaded beads. Mathematically, many beaded beads can be viewed as polyhedra, with each bead (or, more precisely, the hole through the middle of each bead, which provides its orientation) corresponding to an edge of the polyhedron. Different weaving patterns will bring different numbers of these "edges" together to form the vertices of the polyhedron. So it is very natural to use various polyhedra as the inspiration for beaded bead designs. Mathematics, including geometry, symmetry, and topology, is an inspiration for the structure of these woven bead creations. Across cultures and continents, humans show a natural affinity towards the aesthetic of pattern and order, and this art form appeals to this aesthetic in a tactile, tangible form. --- Gwen L. Fisher, Ph.D., California Polytechnic State
University, San Luis Obispo, and beAd Infinitum (www.beadinfinitum.com)

9 files, last one added on Aug 26, 2011
Album viewed 1289 times

Simulated Snowflakes


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Mathematicians David Griffeath (University of Wisconsin-Madison) and Janko Gravner (University of California, Davis) have built a model that generates detailed 3D images of all types of nature's snowflakes.

13 files, last one added on May 11, 2009
Album viewed 2058 times

Mike Field :: Realizations


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An aspect of my art work that I particularly enjoy is that I write the software for all the programs I use and build the computers that run the software. In this sense, I like to feel that theory (mathematics), art (outcome), software (algorithms) and engineering (hardware) are integrated and interdependent and that no part survives without the others.

--- Mike Field

9 files, last one added on Aug 26, 2011
Album viewed 883 times

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