A Mathematical Artwork for Pi Day

Pi is an international number. This number can be a symbol of peace between nations. The following image is a public domain artwork that I have created in honor of Pi day. Here I would like to mention some of the mathematicians who played a significant role in the history of Pi: Archimedes, Liu Hui, Aryabhata, Jamshid Kashani, William Jones, Johann Heinrich Lambert, Ferdinand von Lindemann.

Pi (2,000 Circles)


2016-03-13-1457868767-7909315-Pi.jpg

This image shows 2,000 circles. For k=1,2,3,...,2000 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)=(19k/30000)+(cos((πk/1000)+(3π/10)))10(cos((3πk/1000)+(9π/10)))10sin((πk/21000)-(17π/140)),

Y(k)=-(cos((πk/1000)+(3π/10)))10(cos((3πk/1000)+(9π/10)))10-(1/6)(cos(πk/6000))14(cos(πk/2000))14,

R(k)=(1/20)(cos((πk/1000)+(3π/10)))14(cos((3πk/1000)+(9π/10)))14+(1/14)(1-(cos(πk/6000))8(cos(πk/2000))8).