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Mathematical Concepts Illustrated by Hamid Naderi Yeganeh

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Hamid Naderi Yeganeh, "1,000 Line Segments (1)" (August 2014)This 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, "1,000 Line Segments (2)" (August 2014)This 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 (3)" (August 2014)This 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

Hamid Naderi Yeganeh, "1,000 Line Segments (4)" (August 2014)This 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

Hamid Naderi Yeganeh, "Heart" (November 2014)This 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

Hamid Naderi Yeganeh, "A Bird in Flight" (November 2014)This 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

"10,000 Circles," by Hamid Naderi YeganehThis 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

"A Bird in Flight (2015)," by Hamid Naderi Yeganeh This 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

"Boat," by Hamid Naderi YeganehThis 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

"Fish," by Hamid Naderi YeganehThis 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

"Olive Branch," by Hamid Naderi YeganehThis image shows 4,000 circles. For k=1,2,3,...,4000 the center of the k-th circle is (X(k), Y(k)) and the radius of the k-th circle is R(k), where

"Butterfly (1)," by Hamid Naderi YeganehThis 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

"Butterfly (3)," by Hamid Naderi YeganehThis 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

"Heart," by Hamid Naderi YeganehThis 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),

"8,000 Ellipses," by Hamid Naderi YeganehThis 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),