$5$ points on a sphere

Question

Diffuse $5$ points on a sphere. Prove there is a closed half-sphere that has at least $4$ points on it.

score 5 · Accepted Answer · answered Apr 19 '15 at 08:58

5

Connect two of the points on a great circle. By the pigeonhole principle, at least $2$ of the remaining $3$ points lie on the same side - giving a closed hemisphere with at least $4$ of the $5$ points.

answered Apr 19 '15 at 08:58

Peter Woolfitt

21,476

$5$ points on a sphere

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