# “A Bird in Flight”

Iranian artist Hamid Naderi Yeganeh makes art from math. The image above shows all circles of the form $(x-A(k))^2+(y-B(k))^2=(R(k))^2$, for k = -10000, -9999, … , 9999, 10000, where $A(k)=\left({\frac {3k}{20000}}\right)+\sin \left(\left({\frac {\pi }{2}}\right)\left({\frac {k}{10000}}\right)^{7}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{6}+\left({\frac {1}{4}}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{16}\left(\cos \left({\frac {\pi k}{20000}}\right)\right)^{12}\sin \left({\frac {6\pi k}{10000}}\right),}$ $B(k)=-\cos \left(\left({\frac {\pi }{2}}\right)\left({\frac {k}{10000}}\right)^{7}\right)\left(1+\left({\frac {3}{2}}\right)\left(\cos \left({\frac {\pi k}{20000}}\right)\cos \left({\frac {3\pi k}{20000}}\right)\right)^{6}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{6}+\left({\frac {1}{2}}\right)\left(\cos \left({\frac {3\pi k}{100000}}\right)\cos \left({\frac {9\pi k}{100000}}\right)\cos \left({\frac {18\pi k}{100000}}\right)\right)^{10},}$ $R(k)=\left({\frac {1}{50}}\right)+\left({\frac {1}{10}}\right)\left(\sin \left({\frac {41\pi k}{10000}}\right)\sin \left({\frac {9\pi k}{100000}}\right)\right)^{2}+\left({\frac {1}{20}}\right)\left(\cos \left({\frac {41\pi k}{10000}}\right)\right)^{2}\left(\cos \left({\frac {\pi k}{20000}}\right)\right)^{10}.}$