Editing Polar coordinate system (section)

===Quadratrix===
[[File:Quadratrix animation.gif|thumb]]
{{Main|Quadratrix of Hippias}}

A quadratrix in the first quadrant (''x, y'') is a curve with ''y'' = &rho; sin &theta; equal to the fraction of the quarter circle with radius ''r'' determined by the radius through the curve point. Since this fraction is <math>\frac{2 r \theta}{\pi}</math>, the curve is given by <math>\rho (\theta) = \frac{2 r \theta}{\pi \sin \theta}</math>.<ref>N.H. Lucas, P.J. Bunt & J.D Bedient (1976) ''Historical Roots of Elementary Mathematics'', page 113</ref>