Consider the plane in coordinates related to polar coordinates (r. o) by u=a \ln (r / a), \quad v=\phi, where a is a constant. We've just transformed the usual radial

coordinate in a funny way. ) Write the line element in the new coordinates. (b) A line segment from u = -o to u = 0 at fixed v has infinite coordinate length inthe u-coordinate. What is its proper length? (c) Write the area element in the new coordinates and check it by integrating the area of a circle of radius r = a.