Math — Polar Coordinates

x = r\cos\theta, \quad y = r\sin\theta

r = \sqrt{x^2 + y^2}

A = \tfrac{1}{2}\int_\alpha^\beta r^2\,d\theta

L = \int_\alpha^\beta \sqrt{r^2 + \left(\tfrac{dr}{d\theta}\right)^2}\,d\theta