A subset $A$ of a metric space is called $\varepsilon$-separated if
$$dist(x,y)> \varepsilon \mbox{ for all } x\ne y\in A.$$


(Notice that the inequality in my definition is strict.)


**What is the size of a maximal $\pi/2$-separated subset of the unit sphere $S^n$?**


**Where a proof can be found?**



Maximal $\pi/2$-separated subset of the sphere
You can pack at most $d+1$ pairwise obtuse vectors in $\mathbb{R}^d$. Several proofs of this fact can be found [here](https://mathoverflow.net/questions/208484/packing-obtuse-vectors-in-mathbbrd/).


