@xpil@fosstodon.org this is due to the fact that the map (x, y) -> (x cos y, x sin y). Does not preserve volumes. In fact it scales them proportional to x! You can see this is you calculate the Jacobean determinant and getting y, or if you notice that that it maps a square [0,r]x [0, 2pi] to an annulus of area 2pir^2. The firs area scales linearly while the second scales quadraticly. Changing the map to (x,y) -> ( sqrt x cos y, sqrt x sin y) changes the Jacobean determinant to 1/2, so the volumes scale proportional to each other.