Read about the 2018 Mathematical Art Exhibition . . .

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by Nedeljko and Milka Ad?ić (Novi Sad, Serbia)

40 x 40 x 10 cm, plastic, 2017

I was inspired by the Leonardo da Vinci codex, and I realized the polyhedra illustrated by Leonardo da Vinci. The polyhedra represent both Renaissance elements of surprise and modern sculpture, highlighting the relevance of Leonardo and his artistic-intellectual context in the present time. Filippo Brunelleschi invented perspective during the Renaissance period, when the use of polyhedrons and other geometric forms became more frequent, and Mazzocchio, the popular Florentine headwear of the time, also became an icon of perspective. -- Nedeljko and Milka Adić

40 x 45 cm, inkjet print on canvas, 2017

Twenty colored spheres are surrounded by ten greenish, slinky-like toroidal helices. The helices also follow paths traced out by linear combinations of the normal and binormal vectors to the curve joining the centers of the spheres. This makes a kind of a symbiotic-geometric relationship between the solid objects and the surrounding safety net. Do you see a pattern for the colors of the spheres? –Dan Bach

50 x 70 cm, digital print, custom software, 2017

This piece derives from work I did to generalize the so-called chaos game, which yields a Sierpinski gasket, to any regular polygon. It is a montage of fractal and near-fractal images that are the natural product of such a generalization, especially when that is cast into code. The stained-glass-like background, an "off-resonance" hexagonal analog to the stochastically produced Sierpinski gasket, is behind an "inverse" pentagonal analog, and a flare from the paths taken between chosen points of an inverse and off-resonance heptagonal analog. – Tom Bates

24 x 12 x 12 cm, copper mesh, paper mâché, 2016

This Seifert Surface is an orientable surface whose boundary is the trefoil knot. The sculpture is based on a copper mesh frame with paper mâché and acrylic paint. Contrasting black and blue colors are used to highlight the distinct sides of this orientable surface. In creating a physical model, I found a deeper appreciation for the particular character of the trefoil knot. – Elliott A. Best

61 x 51 cm, ink on paper, 2017

I enjoy seeking out interesting intersections between mathematics, computer science, and art. This image is an embedding of natural imagery video of flowers and a butterfly, using Locally Linear Embedding (LLE) a nonlinear dimensionality reduction technique, introduced by Saul & Roweis in 2000. LLE, an unsupervised machine learning algorithm, was applied to five frames of creative commons video of a butterfly flapping it wings surrounded by flowers utilizing open source software. – Linda Beverly

50 x 50 cm, acrylics on canvas, 2017

This artwork mixes three math problems: It is a Simple Imperfect Squared Square of order 21, colored using the Four-Color Map Theorem and design and painted with Symmetry; the 21 squares are not of different sizes which makes it imperfect, and simple because no subset of the squares forms a rectangle or a square; and the Four-Color Map Theorem states that any map in a plane can be painted using four colors, so that regions sharing a common boundary do not share the same color. The main square has rotational Symmetry of order 4, since the tiling is invariant when rotated by 90 degrees. – Regina Bittencourt

44 x 44 x 44 cm, wood and brass, 2017

Counting suggests that the complete bipartite graph K(5,5) might be rigid even though it has no triangles. Ben Roth and I proved that in "When is a bipartite graph a rigid framework?" (Pacific Journal of Mathematics, 90, 1981). The graph has one more edge than the number of degrees of freedom, so can be built as a tensegrity structure. In this realization four of the five vertices from each set form a tetrahedron with the fifth vertex near its center. The tetrahedra overlap so that the center vertex of each is inside the other. Eight struts join each center vertex to the four vertices of the other tetrahedron. The remaining 17 edges are cables. – Ethan Bolker