The geodesics on the plane are just straight lines. Such lines are parametrized as x (A) = a+xo, y (A) = bx+yo (1) Let us now consider the same plane in polar coordinates. The metric, as we know, is ds = dr + r do. (a) Write down the expressions for r(X) and (X) that describe the straight line (1) in polar coordinates. (b) Write down the geodesic equation in polar coordinates (the coefficients of the connection are I = r, F = For = 1/r, all the others vanish). Br (c) Verify that the expressions that you have found in question (a) are solutions of the geodesic equations found in (b).