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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Most viewed - Mathematical Concepts Illustrated by Hamid Naderi Yeganeh
 Hamid Naderi Yeganeh, "1,000 Line Segments (2)" (August 2014)2169 viewsThis image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(4πi/1000), -cos(2πi/1000)) and ((-1/2)sin(8πi/1000), (-1/2)cos(4πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi Yeganeh
 Hamid Naderi Yeganeh, "1,000 Line Segments (1)" (August 2014)2152 viewsThis image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(2πi/1000), -cos(2πi/1000)) and ((-1/2)sin(8πi/1000), (-1/2)cos(12πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi Yeganeh
 Hamid Naderi Yeganeh, "A Bird in Flight" (November 2014)2062 viewsThis image is like a bird in flight. It shows 2000 line segments. For each i=1, 2, 3, ... , 2000 the endpoints of the i-th line segment are: (3(sin(2πi/2000)^3), -cos(8πi/2000)) and ((3/2)(sin(2πi/2000)^3), (-1/2)cos(6πi/2000)). I created this image by running my program. --- Hamid Naderi Yeganeh
 Hamid Naderi Yeganeh, "Heart" (November 2014)1934 viewsThis image contains a heart-like figure. It shows 601 line segments. For each i=1, 2, 3, .... , 601 the endpoints of the i-th line segment are: (sin(10π(i+699)/2000), cos(8π(i+699)/2000)) and (sin(12π(i+699)/2000), cos(10π(i+699)/2000)). I created this image by running my program. --- Hamid Naderi Yeganeh
 "A Bird in Flight (2015)," by Hamid Naderi Yeganeh 1708 viewsThis image is like a bird in flight. It shows 500 line segments. For each i=1,2,3,...,500 the endpoints of the i-th line segment are: ((3/2)(sin((2πi/500)+(π/3)))^7, (1/4)(cos(6πi/500))^2) and ((1/5)sin((6πi/500)+(π/5)), (-2/3)(sin((2πi/500)-(π/3)))^2). --- Hamid Naderi Yeganeh
 Hamid Naderi Yeganeh, "1,000 Line Segments (3)" (August 2014)1593 viewsThis image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(8πi/1000), -cos(2πi/1000)) and ((-1/2)sin(6πi/1000), (-1/2)cos(2πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi Yeganeh
 "Fish," by Hamid Naderi Yeganeh1481 viewsThis image is like a fish. It shows 1,000 line segments. For i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-2cos(4πi/1000), (1/2)(cos(6πi/1000))^3) and (-(2/15)sin(6πi/1000), (4/5)sin(2πi/1000)). --- Hamid Naderi Yeganeh
 "Boat," by Hamid Naderi Yeganeh1429 viewsThis image is like a sailing boat. It shows 2,000 line segments. For each k=1,2,3,...,2000 the endpoints of the k-th line segment are: (cos(6πk/2000)-i cos(12πk/2000))e^(3πi/4) and (sin((4πk/2000)+(π/8))+i sin((2πk/2000)+(π/3)))e^(3πi/4). --- Hamid Naderi Yeganeh
 Hamid Naderi Yeganeh, "1,000 Line Segments (4)" (August 2014)1422 viewsThis image shows 1,000 line segments. For each i=1,2,3,...,1000 the endpoints of the i-th line segment are: (-sin(10πi/1000), -cos(2πi/1000)) and ((-1/2)sin(12πi/1000), (-1/2)cos(2πi/1000)). I created this image by running my program on a Linux operating system. --- Hamid Naderi Yeganeh
 "10,000 Circles," by Hamid Naderi Yeganeh1263 viewsThis image shows 10,000 circles. For each i=1,2,3,...,10000 the center of the i-th circle is: ((cos(38πi/10000))^3, sin(10πi/10000)) and the radius of the i-th circle is: (1/3)(sin(16πi/10000))^2. --- Hamid Naderi Yeganeh
 "Butterfly (1)," by Hamid Naderi Yeganeh1142 viewsThis image shows 40,000 circles. For k=1,2,3,...,40000 the center of the k-th circle is (X(k), Y(k)) and the radius of the k-th circle is R(k), where X(k)=(6/5)((cos(141πk/40000))^9)(1-(1/2)(sin(πk/40000))^3)(1-(1/4)((cos(2πk/40000))^30)(1+(2/3)(cos(30πk/40000))^20)-((sin(2πk/40000))^10)((sin(6πk/40000))^10)((1/5)+(4/5)(cos(24πk/40000))^20)), Y(k)=cos(2πk/40000)((cos(141πk/40000))^2)(1+(1/4)((cos(πk/40000))^24)((cos(3πk/40000))^24)(cos(19πk/40000))^24), R(k)=(1/100)+(1/40)(((cos(2820πk/40000))^6)+(sin(141πk/40000))^2)(1-((cos(πk/40000))^16)((cos(3πk/40000))^16)(cos(12πk/40000))^16). --- Hamid Naderi Yeganeh
 "Butterfly (3)," by Hamid Naderi Yeganeh1111 viewsThis image shows 40,000 circles. For k=1,2,3,...,40000 the center of the k-th circle is (X(k), Y(k)) and the radius of the k-th circle is R(k), where X(k)=(3/2)((cos(141πk/40000))^9)(1-(1/2)sin(πk/40000))(1-(1/4)((cos(2πk/40000))^30)(1+(cos(32πk/40000))^20))(1-(1/2)((sin(2πk/40000))^30)((sin(6πk/40000))^10)((1/2)+(1/2)(sin(18πk/40000))^20)), Y(k)=cos(2πk/40000)((cos(141πk/40000))^2)(1+(1/4)((cos(πk/40000))^24)((cos(3πk/40000))^24)(cos(21πk/40000))^24), R(k)=(1/100)+(1/40)(((cos(141πk/40000))^14)+(sin(141πk/40000))^6)(1-((cos(πk/40000))^16)((cos(3πk/40000))^16)(cos(12πk/40000))^16). --- Hamid Naderi Yeganeh
 "Heart," by Hamid Naderi Yeganeh1027 viewsThis 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
 "8,000 Ellipses," by Hamid Naderi Yeganeh1004 viewsThis image shows 8,000 ellipses. For each k=1,2,3,...,8000 the foci of the k-th ellipse are: A(k)+iB(k)+C(k)e^(300πik/8000) and A(k)+iB(k)-C(k)e^(300πik/8000) and the eccentricity of the k-th ellipse is D(k), where A(k)=(3/4)sin(2πk/8000)cos(6πk/8000)+(1/4)sin(28πk/8000), B(k)=(3/4)cos(2πk/8000)cos(8πk/8000)+(1/4)cos(28πk/8000), C(k)=(1/18)+(1/20)cos(24πk/8000), D(k)=(49/50)-(1/7)(sin(10πk/8000))^4. --- Hamid Naderi Yeganeh
 "A Bird in Flight (2016)," by Hamid Naderi Yeganeh932 viewsThis image shows all circles of the form: (x-A(k))^2+(y-B(k))^2=(R(k))^2, for k=-10000, -9999, ... , 9999, 10000, where A(k)=(3k/20000)+sin((π/2)(k/10000)^7)((cos(41πk/10000))^6)+(1/4)((cos(41πk/10000))^16)((cos(πk/20000))^12)sin(6πk/10000), B(k)=-cos((π/2)(k/10000)^7)(1+(3/2)(cos(πk/20000)cos(3πk/20000))^6)((cos(41πk/10000))^6)+(1/2)(cos(3πk/100000)cos(9πk/100000)cos(18πk/100000))^10, R(k)=(1/50)+(1/10)((sin(41πk/10000)sin(9πk/100000))^2)+(1/20)((cos(41πk/10000))^2)((cos(πk/20000))^10). --- Hamid Naderi Yeganeh
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 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