Over in the thread "Evenly distributing n points on a sphere" this topic is touched upon: https://stackoverflow.com/questions/9600801/evenly-distributing-n-points-on-a-sphere.

But what I would like to know is: "Is the Fibonacci lattice the very best way to evenly distribute N points on a sphere? So far it seems that it is the best. Does anyone know of a better method?"

I have a Ph.D. in physics and may have an application for some of this research in physics.

I came across this wonderful paper:

http://arxiv.org/pdf/0912.4540.pdf "Measurement of areas on a sphere using Fibonacci and latitude–longitude lattices"

The paper states, "The Fibonacci lattice is a particularly appealing alternative [15, 16, 17, 23, 65, 42, 66, 67, 68, 76, 52, 28, 56, 55]. Being easy to construct, it can have any odd number of points [68], and these are evenly distributed (Fig. 1) with each point representing almost the same area. For the numerical integration of continuous functions on a sphere, it has distinct advantages over other lattices [28, 56]."

It the Fibonacci lattice the very best way to distribute N points on a sphere so that they are evenly distributed? Is there any way that is better?

As seen above, the paper states, "with each point representing almost the same area. "

Is it impossible, in principle (except for special rare cases of N such as 4, etc.), to exactly evenly distribute N points on a sphere so that each point/region has the exact same are?

So far it seems to me that the Fibonacci lattice the very best way to distribute N points on a sphere so that they are evenly distributed. Do you feel this to be correct?

Thanks so much!