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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# "4-Wheel Decomposition," by Ally Stacey (Oregon State University, Corvallis)

## 45 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

 Art & Music, MathArchives Geometry in Art & Architecture, by Paul Calter (Dartmouth College) Harmony and Proportion, by John Boyd-Brent International Society of the Arts, Mathematics and Architecture Journal of Mathematics and the Arts Mathematics and Art, the April 2003 Feature Column by Joe Malkevitch Maths and Art: the whistlestop tour, by Lewis Dartnell Mathematics and Art, (The theme for Mathematics Awareness Month in 2003) MoSAIC - Mathematics of Science, Art, Industry, Culture Viewpoints: Mathematics and Art, by Annalisa Crannell (Franklin & Marshall College) and Marc Frantz (Indiana University) Visual Insight, blog by John Baez