Log-polar Coordinates

$$\begin{array}{rl}(\rho ,\theta )& \to (\ln r,\theta )\\ & \to \left(\ln \left(\sqrt{x^2+y^2},{\tan }^{-1}\left(\frac{y}{x}\right)\right)\right)\end{array}$$

• Definition of log-polar coordinates in terms of polar coordinates and cartesian coordinates