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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 FILE 14/17

# "Heart," by Hamid Naderi Yeganeh

## This image shows 2,500 ellipses. For each k=1,2,3,...,2500 the foci of the k-th ellipse are: A(k)+iB(k)+C(k)e^(68πik/2500) and A(k)+iB(k)-C(k)e^(68πik/2500) and the eccentricity of the k-th ellipse is D(k), where A(k)=(-3/2)((sin(2πk/2500))^3)+(3/10)((sin(2πk/2500))^7), B(k)=sin((2πk/1875)+(π/6))+(1/4)(sin((2πk/1875)+(π/6)))^3, C(k)=(2/15)-(1/8)cos(πk/625), D(k)=(49/50)-(1/7)(sin(4πk/2500))^4. --- Hamid Naderi Yeganeh

 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