# Maximize the distance of pair points within a unit circle

given a unit circle and N points, how should I scatter these points inside the circle to obtain a maximum pairwise distance? i.e., the average distance (euclidean) between each pair of points will be maximal.

I guess that the answer is some uniform circular distribution, however, I can't generate one..

For 1D it's just np.arange(min_x, max_x, dx) But for 2D? What should be the dRadius and dTheta? Because with every increase in R I can place more points..

• Using the complex circle, it's just points of the form $$e^{\frac{ki\theta}n},\;k\in\mathbb Z$$ – Don Thousand Oct 20 at 16:00
• Instead of the average pairwise distance, you may want to maximize the minimum pairwise distance. This gives you something more similar to what one would intuitively consider a uniform scattering of points in a disk; in particular, the problem is equivalent to circle packing in a circle. – Rahul Oct 20 at 16:18
• K and N are uniformly distributed? – Jenia Golbstein Oct 20 at 16:34