The last method mentioned at that wolfram.com link should work for any dimension (i.e. choosing random Cartesian coordinates with a normal distribution, then no

The last method mentioned at that wolfram.com link should work for any dimension (i.e. choosing random Cartesian coordinates with a normal distribution, then normalizing the vector obtained thus to get a point on the sphere). The method presented in the parent article is derived exactly from this method of Marsaglia, and it should also work for any dimension.