In a space $\mathbb R^n$, how many vectors can you fit that are at least an angle $\theta$ apart, where $\theta>0$?
For example, in $\mathbb R^2$, the maximum number of vectors that are at least angle $\theta = 2/3$ radians apart is just $2\pi/\theta=2\pi/(2/3)=3\pi$ vectors (rounding down, that's $9$ vectors). How do I find the maximum number of vectors that are at least that angle apart in $n$ dimensions?