Let's say we have a closed ball $B(x,r)\subset\mathcal{R}^n$ centered at $x$ with radius $r$.
The question I want to ask is: how many distinct points in $\mathcal{R}^n$, in which the distance between any two points is larger than or equal to $r$, can fall in $B(x,r)$?
When $n=2$, the question is easy to visualise. But to imagine the case generally when $n$ is large is not so easy.
I think the points must be located on the boundary of $B(x,r)$ to maximise the number. Therefore it is possible to derive an upper bound by estimating the area each point would occupy on the boundary of $B(x,r)$. But the computation gets complicated because the area occupied by several points depends on the location of these points.
Thanks!
