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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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A_Bird_in_Flight_1-epostcard.jpg
Hamid Naderi Yeganeh, "A Bird in Flight" (November 2014)This image is like a bird in flight. It shows 2000 line segments. For each i=1, 2, 3, ... , 2000 the endpoints of the i-th line segment are:
(3(sin(2πi/2000)^3), -cos(8πi/2000))
and
((3/2)(sin(2πi/2000)^3), (-1/2)cos(6πi/2000)).

I created this image by running my program. --- Hamid Naderi Yeganeh
Dec 18, 2014
Heart_1-epostcard.jpg
Hamid Naderi Yeganeh, "Heart" (November 2014)This image contains a heart-like figure. It shows 601 line segments. For each i=1, 2, 3, .... , 601 the endpoints of the i-th line segment are:
(sin(10π(i+699)/2000), cos(8π(i+699)/2000))
and
(sin(12π(i+699)/2000), cos(10π(i+699)/2000)).

I created this image by running my program. --- Hamid Naderi Yeganeh
Dec 18, 2014
math-img-4-285.jpg
Hamid Naderi Yeganeh, "1,000 Line Segments (4)" (August 2014)This image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(10πi/1000), -cos(2πi/1000)) and ((-1/2)sin(12πi/1000), (-1/2)cos(2πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi YeganehOct 01, 2014
math-img-3-231.jpg
Hamid Naderi Yeganeh, "1,000 Line Segments (3)" (August 2014)This image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(8πi/1000), -cos(2πi/1000)) and ((-1/2)sin(6πi/1000), (-1/2)cos(2πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi YeganehOct 01, 2014
math-img-2-166.jpg
Hamid Naderi Yeganeh, "1,000 Line Segments (2)" (August 2014)This image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(4πi/1000), -cos(2πi/1000)) and ((-1/2)sin(8πi/1000), (-1/2)cos(4πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi YeganehOct 01, 2014
math-img-1-134.jpg
Hamid Naderi Yeganeh, "1,000 Line Segments (1)" (August 2014)This image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(2πi/1000), -cos(2πi/1000)) and ((-1/2)sin(8πi/1000), (-1/2)cos(12πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi YeganehOct 01, 2014
beck-sand-brean-down.jpg
"Sierpinski Tringle at Brean Down," by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down, UK. -- Simon Beck (https://www.facebook.com/snowart8848/Aug 19, 2014
beck-snow-peisey-vallandry.jpg
"Serpinski Triangle at Peisey-Vallandry," by Simon Beck (https://www.facebook.com/snowart8848/)Pattern made in snow with snowshoes at Peisey-Vallandry. --- --- Simon Beck (https://www.facebook.com/snowart8848/)Aug 08, 2014
beck-sand-brean-down3.jpg
"Mandelbrot set in the sand, view two" by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down in the U.K. Find a time lapse video of the creation at http://youtu.be/MVzGyAAtHiU --- Simon Beck (https://www.facebook.com/snowart8848/) Aug 08, 2014
beck-sand-brean-down2.jpg
"Mandelbrot set in the sand," by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down in the U.K. Find a time lapse video of the creation at http://youtu.be/MVzGyAAtHiU --- Simon Beck (https://www.facebook.com/snowart8848/) Aug 08, 2014
sittner14-hopfknott.jpg
"Hopf Knott, " by Peter Sittner (Kensington, MD)13.5" x 13.5" x 13.5", red oak, 2013

Hopf Knott is the offspring of two forms that have intrigued me for some time, the Hopf Link and the Borromean Rings. While the sculpture may appear to be a series of connected Hopf Links, it is actually two sets of Borromean Rings, an inner set and an outer set. Of course, the "rings" are stretched to make the crossings possible and shaped to resemble Hopf Links. The 6 outermost points correspond to the vertices of a regular octahedron. --- Peter Sittner
May 05, 2014
sarhangi14-dancestars.jpg
"Dance of Stars I, " by Reza Sarhangi (Towson University, Towson, MD)12" X 12" X 12", heavy paper, 2013

"I am interested in Persian geometric art and its historical methods of construction. "

Dance of Stars I is one of the Kepler-Poinsot polyhedra, the Small Stellated Dodecahedron, with Schläfli Symbol (5/2, 5). It has been ornamented by the sâzeh modular tiles, that are used in a majority of tiling that conform to local fivefold symmetries. In an article that appeared in Science, the authors proposed the possibility of the use of a set of tiles, girih tiles, by the medieval craftsmen, for the composition of the underlying pattern. Ink outlines for these girih tiles appear in panel 28 of the Topkapi scroll. I used girih tiles and left the dashed outlines in the final tessellation. I also included rectilinear patterns that appear as an additional small-brick pattern in the decagonal Gunbad-i Kabud tomb tower in Maragha, Iran. --- Reza Sarhangi

May 05, 2014
nau14-creasej.jpg
"Longest Crease J, " by Sharol Nau (Northfield, MN)10" x 10" x 10", book sculpture, 2013

"A classical calculus problem, the so-called Paper Creasing Problem, deals with extremizing the length of the crease formed when a rectangular sheet of paper is altered by folding one corner, say the lower right-hand corner, to the opposite edge. The length of the crease depends on the distance the active corner is from the upper left-hand corner."

This sculpture formed by folding individual pages is an example of the variety of the three-dimensional forms which can be obtained by incremental changes in the length of the crease from page to page and by extending the points that can be used. --- Sharol Nau (http://www.sharolnau.com)
May 05, 2014
lym14-jose~0.jpg
"Jose, " by So Yoon Lym (Paterson, NJ)22" x 30", acrylic on paper, archival pigment print, 2009

"The Dreamtime is inspired by the Aboriginal stories and visions of creation. Each braided pattern, carried by the students, is a map of the ancient universe, a topographical palimpsest of the world in pattern: valleys, mountains, forests, oceans, rivers, streams. "

The link to Dr. Ron Eglash's website on cornrow hair-braiding best details the mathematic content behind my hair and braid paintings. Professor Eglash's website called "Transformational geometry and iteration in cornrow hairstyles" outlines one aspect of his research in ethno-mathematics and cybernetics. Ethnomathematics "aims to study the diverse relationship between math and culture." More information: --- So Yoon (http://www.soyoonlym.com/works/dreamtime/)
May 05, 2014
love14-platonic.jpg
"Untitled, " by Jack Love (graduate student, George Mason University, Fairfax, VA)Spherical, 18" in diameter, medium-density fiberboard, 2013

"The Platonic solids have been the inspiration for the pieces I have created thus far. My work explores the structure of these objects and their relationships to one another, and attempts to express this structure in a way that is aesthetically appealing. "

Take either the icosahedron or dodecahedron and center it at the origin. Project its vertices outward from the origin onto the surface of a sphere surrounding it, giving a collection of points on a sphere. Draw a great circle through two points if they are images of two adjacent vertices in the original polytope. Each of these great circles is partitioned into arcs by its intersection with the other great circles thus produced. The arcs come in three lengths and are projections of the edges of, respectively, an icosahedron, a dodecahedron, and a third polytope whose facets are rhombic. This model exhibits this construction. The convex arcs correspond to the icosa, the concave to the dodeca, and the straight to the rhombic. --- Jack Love
May 05, 2014
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