Before revision:  Moreover, we show that the lower bound for the gap ratio of placing up to three points is approximately 1.618. The uniform distribution of points on a sphere also corresponds to uniform distribution of unit quaternions which represent rotations in 3D space and has numerous applications in many areas .
After revision:  Moreover, we show that the lower bound for the gap ratio of placing up to three points is the golden ratio, approx. 1.618, and for at least four points is no less than 1.726 .