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Home > Mathematical Concepts Illustrated by Hamid Naderi Yeganeh

Last additions - Mathematical Concepts Illustrated by Hamid Naderi Yeganeh
A_Bird_in_Flight.jpg
"A Bird in Flight (2016)," by Hamid Naderi YeganehThis 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
Mar 23, 2016
Ring.jpg
"Ring," by Hamid Naderi YeganehThis image shows 5,600 ellipses. For each k=1,2,3,...,5600 the foci of the k-th ellipse are:
A(k)+iB(k)+C(k)e^(44πik/5600)
and
A(k)+iB(k)-C(k)e^(44πik/5600)
and the eccentricity of the k-th ellipse is D(k), where
A(k)=(cos(28πk/5600))^3,

B(k)=sin(28πk/5600)+(1/4)(cos((14πk/5600)-(7π/4)))^18,

C(k)=(1/70)+(1/6)+(1/6)sin(28πk/5600),

D(k)=(399/400)-(1/6)(sin(28πk/5600))^8.
--- Hamid Naderi Yeganeh
Mar 23, 2016
8000_Ellipses_1~0.jpg
"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),

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
Mar 23, 2016
Heart.jpg
"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),

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
Mar 23, 2016
Butterfly_3.jpg
"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

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
Mar 23, 2016
Butterfly_1.jpg
"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

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
Mar 23, 2016
Olive_Branch.jpg
"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

X(k)=(2k/4000)+(1/28)sin(42πk/4000)+(1/9)((sin(21πk/4000))^8)+(1/4)((sin(21πk/4000))^6)sin((2π/5)(k/4000)^12),

Y(k)=(1/4)(k/4000)^2+(1/4)(((sin(21πk/4000))^5)+(1/28)sin(42πk/4000))(cos((π/2)(k/4000)^12)),

R(k)=(1/170)+(1/67)((sin(42πk/4000))^2)(1-((cos(21πk/4000))^4)).
--- Hamid Naderi Yeganeh
Mar 23, 2016
Yeganeh-fish.jpg
"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 YeganehSep 16, 2015
Yeganeh-boat.jpg
"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
Sep 16, 2015
Yeganeh-Bird-in-Flight.jpg
"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
Sep 16, 2015
Yeganeh-10000-Circles.jpg
"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
Sep 16, 2015
A_Bird_in_Flight_1-epostcard.jpg
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
Dec 18, 2014
Heart_1-epostcard.jpg
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
Dec 18, 2014
math-img-4-285.jpg
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 YeganehOct 01, 2014
math-img-3-231.jpg
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 YeganehOct 01, 2014
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