3
$\begingroup$

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?

$\endgroup$

1 Answer 1

5
$\begingroup$

You can pack at most $d+1$ pairwise obtuse vectors in $\mathbb{R}^d$. Several proofs of this fact can be found here.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.