Yes, it is a really weird property of 2-spheres that that holds. One consequence is that yet another way to pick a point uniformly on the sphere is to choose z

Yes, it is a really weird property of 2-spheres that that holds. One consequence is that yet another way to pick a point uniformly on the sphere is to choose z ∈ [-1, 1] uniformly, then choose λ ∈ [-180°, 180°) uniformly and use the point (cos(λ)*sqrt(1-z*z), sin(λ)*sqrt(1-z*z), z)