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The 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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 "Capsule," by David Reimann (Albion College Albion, MI) 316 views18 x 45 x 18 cm, paper backed cherry veneer, metal fasteners, 2016 This is a capped cylinder was created using 75 squares that are 5 cm on a side and connected at their corners using split-pin fasteners. The end-caps are based on dodecahedral hemispheres and the cylinder is based on a planar hexagonal tessellation, which results in a polyhedral form in which every vertex has order 3. The edges in the underlying form have been replaced by squares, resulting in an open lattice form. Every opening is either triangular (throughout), pentagonal (on the endcaps), or hexagonal (on the cylinder). --- David Reimann
 "4-Wheel Decomposition," by Ally Stacey (Oregon State University, Corvallis)316 views45 x 60 cm, Crayola crayon and Sharpie, 2015 Learning math inspires me to make art which in turn helps me better understand the math. This work is essentially a change-of-basis calculation going from the space of Closed Jacobi diagrams (trivalent graphs with an outer circle) to the space of Chord Diagrams, which are trivalent graphs with all vertices on the outer circle. These algebras are important to the field of Vassiliev Knot Invariants. This is done via what's the called the STU relation which is a way of resolving internal vertices. All algebraic steps are shown in the foreground. Making these helps me keep track of calculations in my research in an aesthetically pleasing way. --- Ally Stacey
 "Being Dis-Functional 00_01e1a / 00_01d1a," by Robert Krawczyk (Illinois Institute of Technology, Chicago, IL)314 views19 x 8 x 12 cm, sandstone, 2016 Lemniscate of Bernoulli, included angle of 90 and 290 degrees with a 225 degree twist; 90 and 270 degrees with a 180 degree twist. This series investigates a simple form based on approximately one-half of a Lemniscate of Bernoulli curve, developed about 1694. It is very similar to a common eight curve, except the loops are more elliptical. For the enclosure a simple solid surface was incorporated. Custom software has been developed to generate these containers. These containers are computationally generated by custom developed software, a method which can express a consistency of a developing concept and enable a variety of designs that focus on the idea and its variations. Then the digital model is 3D printed in sandstone. More information.--- Robert Krawczyk
 "Towards Infinite Smallness - 2," by Irene Rousseau (www.irenerousseau.com)314 views47 x 47 x 8 cm, Venetian glass on wood hand cut by artist, 2016 This mosaic wall sculpture consists of tessellated (tightly fitted together) patterns and each sculpture is a 3D disc with 18.5" diameter. The hyperbolic sculpture is composed of planes, each suggests negative curvature and represents the concept of infinite smallness contained within the bounding edge. Hyperbolic geometry can be represented as the points in a circular disc with hyperbolic distance defined. A hyperbolic plane has infinite structures within boundaries.In my hyperbolic sculpture repeating patterns which decrease in size at the bounding edge metaphorically represent infinity. Symmetry is a transformation that preserves the distance as shown on the surface tiling patterns of the sculpture. --- Irene Rousseau
 "Borromean racks," by Saul Schleimer (University of Warwick, Coventry, UK) and Henry Segerman (Oklahoma State University, Stillwater, OK)314 views10 x 10 x 10 cm, 3D printed nylon plastic, 2013 This sculpture consists of three identical pieces. Each has two identical rods; each rod is a rectangular prism with racks on three of its four sides. These racks mesh with one or two racks on the other pieces, for a total of 12 meshings. The pieces interlink in the fashion of the Borromean rings; their long axes form a standard orthogonal frame. When we take the directions of the racks into account, the sculpture has a handedness. At its middle position it realizes its maximal symmetry, a dihedral group of order six. Curiously, the Borromean Racks give an example of a triple of gears that mesh pairwise, but are not frozen. Challenge: Does this pattern of racks extend to tile three-space? If so, how many degrees of freedom does it have? --- Saul Schleimer and Henry Segerman
 "Linked Tetra Frames," by Carlo Séquin (University of California, Berkeley)313 views48 x 40 x 30 cm, pvc-pipes, painted, 2016 With Walt van Ballegooijen we have studied the number of topologically different ways in which two identical tetrahedral wire-frames could be interlinked. Not counting mirror images separately, we have found eleven different configurations. For each topological configuration there is a maximal clearance between the infinitely thin mathematical wire frames. If the edges are expanded to a diameter identical to this clearance, then a rigid structure results. This particular configuration has been scaled up to accommodate fattened edges of 22mm diameter, the size of the PVC pipes employed. --- Carlo Séquin