ITOT 42 Spring 2021 - THPT A - additive practice Question 7

Let $n>2$ be an integer. Peter wants to draw $n$ pairwise disjoint arcs of length $\alpha$ on great circles of the unit sphere. Prove: (a) this is possible for every $\alpha\lt \pi+2\pi/n$; (6 points) (b) this is impossible for every $\alpha>\pi+2\pi/n$. (7 points) Arc lengths are positive; endpoints count as part of an arc.



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