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Home > Mathematical Concepts Illustrated by Hamid Naderi Yeganeh
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"8,000 Ellipses," by Hamid Naderi Yeganeh

This 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

Butterfly_3.jpg Heart.jpg 8000_Ellipses_1~0.jpg Ring.jpg A_Bird_in_Flight.jpg

American Mathematical Society