Deriving a Metric: Show that the metric for a 3-sphere (i.e. a three- dimensional "sphere" embedded in 4-dimensional space) of radius Reis de= dr + R sin (r/Re) (d0 + sin 0 do). Hint: The 3-sphere can be written as the surface w+x + y + z = R in 4-dimensional Cartesian space. This surface can be parameterized with a generalization of spherical coordinates: W = Z = X = Y = Recos X Resin x cos X Resin x sin Resin x sin cos o sin o Begin with the distance relation in four dimensions, change coordinates to the above, and then change variables once more, setting r = Rex. Show your work, or you will not receive full credit for the problem.