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Home > Mathematical Concepts Illustrated by Hamid Naderi Yeganeh

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
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
 
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