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reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.
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Home > 2011 Mathematical Art Exhibition

2011 Mathematical Art Exhibition
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"Magic Square 25 Study," by Margaret Kepner (Washington, DC)First Place Award, 2011 Mathematical Art Exhibition
Archival inkjet print, 12.5" x 12.5", 2010
Magic squares are numerical arrays that have substructures with constant sums. This design is based on a magic square of order 25, containing the numbers from 0 to 624. Each row, column, and main diagonal sums to the â€śmagic constantâ€ť of 7800. The numbers in the magic square are represented by a visual base5 system: four concentric squares serve as the 1, 5, 25, and 125 places, while shades of grey stand for the numerals 0 to 4. Coding the numbers into their base5 versions yields a pattern of 625 unique, nestedsquares in shades of grey. This particular magic square also has a substructure of 25 minisquares of size 5. Each of these minisquares is â€śmagicâ€ť (although the numbers are not consecutive), with rows, columns, and diagonals summing to 1560. In addition, certain other groups of 5 squares add up to 1560. Examples are the quincunx and the plussign shapes (when fully contained in a minisquare). The colored accents are used to indicate a few of these â€śmagicâ€ť substructures.  Margaret Kepner


"Unknown," by Ghee Beom Kim (Sydney, Australia)Print, 300 x 250 mm, 2007
Hexagonal fractal creates this terracelike surface that imitates exotic terrain, which has architectural implication. The triangular fractal formations occasionally occur amongst rather random surface.  Ghee Beom Kim (http://sites.google.com/site/geometricarts/)


"Whirled Heart," by Matjuska Teja Krasek (Ljubljana, Slovenia)Digital print, 170 x 230 mm, 2010
In the mysterious world of chaos and strange attractors a seeker can find very heartful things.  Matjuska Teja Krasek (http://tejakrasek.tripod.com)


"The Fibonacci Project," by Lindsay Lindsey (University of Alabama, Tuscaloosa)Cast aluminium, 18" x 18" x 16", 2010
The sculpture is based off the mathematical concept of the Fibonacci sequence and the spiral found in the Nautilus shell. In order to accurately construct a threedimensional spiral that has the specifications of the Fibonacci sequence, special attention had to be paid to the size of the sculpture. At specific intervals along the sculpture, the diameter of the sculpture accurately increased with respect to the Fibonacci sequence. The intervals along the sculpture were also planned out using the sequence as a guide to the everincreasing segments. The turns of the spiral were calculated using the Nautilus shell as a guide. Their increasing diameters are directly proportional to the diameter of the shell. Throughout the construction process, various checks were made to insure that the sequence was being preserved. The sculpture has truly become an accurate threedimensional representation of both the sequence and the spiral.  Lindsay Lindsey


"Equal Areas," by Susan McBurney (Western Springs, IL)Digital print, 12" x 12", 2010
This artwork was inspired by two pages from Leonardo DaVinci's notebooks. While these magnificent books are legendary for their beauty of illustration and depth of subject matter, his purely geometric diagrams have been dismissed by some as intellectual doodling. Closer inspection reveals that at least some of them highlight the equality of differentshaped areas. "Equal Areas" builds upon that concept to also include relative areas of similar figures. In particular, those areas of a certain color in the border design are equal to the samecolored areas in the central figure. All light yellow areas in the borders add up to the all the yellow areas in the center, etc. Note that in some cases the shapes of the same colors are different, yet they are still equal in area.  Susan McBurney


"Infinite Journey," by Frank Mingrone Poster (scan of hand ink drawing on paper), 32â€ť x 24â€ť (original 45â€ť x 42â€ť), 1985
There were no computers used in the creation of this drawing. It was completely hand drawn using a pen and ruler and consists of straight, unbroken, parallel lines that extend to the outermost perimeter. If the perimeter expanded and the lines repeated and extended, the symmetrical pattern would continue infinitely.â€¨The use and placement of straight lines are not a random guess but must conform to a mathematical framework for their representation. Each group of lines is analogous to a group of integers, and it is the exact arrangement of the lines arising from balanced proportions that create the intricate patterns. The lines can flow in a successive order, or, with varied intricate combinations. The singularity of straight lines unites a complex system of multiple interrelated sections creating the illusion of curvature. The various parts relate to the whole and the patterns grasped and visualized as a whole.  Frank Mingrone (http://www.supersymmetryart.com/)


"Paper stars," by Velichka Minkova (Bulgaria, Sofia) Digital C, 18 "x 18", 2010
Law is offered at a symmetry in proper square network and her use at making abstract constitution by a volumetricplastic forms.  Velichka Minkova


"Woman flower," by Marcel Morales (Institut Fourier, UniversitĂ© de Grenoble I, France) Digital print on canvas, 300 x 450 mm, 2010
I use hyperbolic geometry, in fact the idea of tiling the hyperbolic plane, to produce a tile such that by repeating hyperbolic rotations we can fill the plane. In this artwork a difficult point is to find the tile. My idea is to use a woman to fulfill a flower, and this flower fulfills the moon and the earth, changing colors and getting maturity.  Marcel Morales (http://marcel.morales.perso.sfr.fr/)


"Longest and Shortest CreaseB," by Sharol Nau (Northfield, MN)Folded book, 12.5â€ť x 9â€ť x 6â€ť, 2010
For this booksculpture of several hundred pages, the shortest crease was obtained by folding the pages without separating them from the binding. Also the folding process began in the middle in an effort to achieve a symmetrical design.  Sharol Nau (http://www.sharolnau.snakedance.org)


"DART," by Jo Niemeyer (Schluchsee, Germany)Archival inkjet print, 20" x 20", 2010
DART â€¨... as a very simple game by Jo Niemeyer 2010â€¨â€¨. Two dart players, A and B, are facing this "image", whose area is split 1 : 0.618.. into white and black. This two basic elements are rotated in 90Â° increments. The winner is, who aims first a black part.â€¨ Since we have two equal partners and an uneven distribution of the "target", one would think, that this is not a fair game. But it is! Because A as the "majority", and consequently B as the "minority", transferred their inequality onto the "court". The ratio of the two playing partners is 1:1.â€¨With this harmonious proportionality there is exactly the same chance to win for both players A and B! The Swiss mathematician Hans Walser mentions for the justice condition, the formula p = 1/2*(3sqrt(5)). And with sqrt(5), we have the golden section in this game, which ensures equity between different partners. â€¨This is also a very fair game! â€¨Or a piece of art, which ensures harmony and balance.  Jo Niemeyer (http://www.jo.niemeyer.com)


"Sierpinski Theme and Variations," by Larry Riddle (Agnes Scott College, Decatur, GA)Counted cross stitch on fabric (25 count per inch), 13.5" x 13.5", 2009
The Sierpinski Triangle is a fractal that can be generated by dividing a square into four equal subsquares, removing the upper right subsquare, and then iterating the construction on each of the three remaining subsquares. That is our â€śThemeâ€ť, shown in the upper left. The â€śVariationsâ€ť arise by exploiting symmetries of the square. The three variations in this piece were generated by rotating the upper left and lower right subsquares at each iteration by 90 or 180 degrees, either clockwise or counterclockwise. The selfsimilarity of the fractals, illustrated by the use of three colors, means that you can read off which rotations were used from the final image. Each design shows the construction through seven iterations, the limit that could be obtained for the size of canvas used.  Larry Riddle (http://ecademy.agnesscott.edu/~lriddle/)


"Traveling Ribbons," by Irene Rousseau (Irene Rousseau Art Studio, Summit, NJ)Painted wood and paper collage with gestural expression, 17"x17"x5", 2010
The sculpture "Traveling Ribbons"Â© 2010 is composed of geometric symmetry and interweaving patterns. The alternating overpasses and underpasses at crossings result in graceful curves and transitions between straight and curved sections. The repeating ribbon patterns are arranged in a threedimensional lattice form and can be viewed from many different directions. The voids between the ribbons become a part of the form and also create a symmetrical pattern. The ribbons are painted in complementary colors of orange and purple with markings, which lead the eye on a continuous path.  Irene Rousseau (http://www.irenerousseau.com)


"Sierpinski's Doughnut," by Ian Sammis (Holy Names University, Oakland, CA)Digital print on canvas, 15" x 12", 2010
A Sierpinksi curve is a spacefilling curve that fills a triangle. Sierpinski curves may be chained together to construct a continuous path from triangle to triangle. The correct arrangement of triangles allow the construction of a single path that fills the unit square while following an Eulerian path along a graph with the topology of a torus. Mapping the square onto the torus in the usual way gives us a spacefilling closed circuit on the surface of a torus. The image is a render of a tube following such a circuit.  Ian Sammis


"Calm," by Reza Sarhangi (Towson University, Towson, MD)Digital print, 16" x 20", 2008
"Calm" is an artwork based on the â€śModularityâ€ť concept presented in an article â€śModules and Modularity in Mosaic Patternsâ€ť (Reza Sarhangi, Journal of the Symmetrion, Volume 19, Numbers 23, 2008/. Another article in this regard is â€śModularity in Medieval Persian Mosaics: Textual, Empirical, Analytical, and Theoretical Considerationsâ€ť (Sarhangi, R., S. Jablan, and R. Sazdanovic, Bridges Conference Proceedings, 2004). The set of modules with extra cuts used to create this artwork is presented in this figure: http://gallery.bridgesmathart.org/sites/gallery.bridgesmathart.org/files/Reza/Calm_figure.jpg.  Reza Sarhangi (http://pages.towson.edu/gsarhang/)


"Tryptique," by Radmila Sazdanovic (University of Pennsylvania) and Aftermoon studio (Paris, France)Ink/brush, 24" x 8", 2010
Tryptique is a drawing of three different kinds of diagrams used in categorifications of the onevariable polynomial ring with integer coefficients. These diagrams are elements of three distinct algebras: on the level of Grothendieck rings, projective modules spanned by these diagrams correspond to Chebyshev polynomials, integer powers of x and (x1), and Hermite polynomials. Asgar Jorn's comment about Pierre Alechinsky's work could as well apply to the signs Aftermoon studio created based on our diagrams.â€¨â€¨
"L'image est Ă©crite et l'Ă©criture forme des images... on peut dire qu'il y a une Ă©criture, une graphologie dans toute image de mĂŞme que dans toute Ă©criture se trouve une image."  Radmila Sazdanovic (http://www.math.upenn.edu/~radmilas/)


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