# if there are 5 points on a sphere then 4 of them belong to a half-sphere.

If there are 5 points on the surface of a sphere, then there is a closed half sphere, containing at least 4 of them.

It's in a pigeonhole list of problems. But, I think I have to use rotations in more than 1 dimension.

Regards

• An answer is given by Calvin Lin here. This is a duplicate in a way, but the topic of that other question is vastly different (a call for trick questions), so I am a bit reluctant to call it a duplicate. Feb 13 '14 at 22:50
• So if you ever see a headline like "80% of Olympic Sites In The Last 20 Years Have Been In The ___ Hemisphere," it means bupkis. Feb 14 '14 at 16:36
• @Bob Stein What is the maning of "bupkis" ? I never met this term... Jun 22 '20 at 6:57
• @JeanMarie "bupkis" means "nothing at all". According to yourdictionary it comes from Yiddish. I think it's especially funny when used in a string of synonyms. Jun 22 '20 at 10:15
• @Bob Stein Thanks. Set apart the meaning, I hadn't any idea about the origin of this word. Yiddish is a very interesting language ; I had once the opportunity to listen to old people speaking a language that I thought at first regional german. I asked them the area of Germany they were from, but in fact they were coming from Ukraine... Jun 22 '20 at 18:36

• @zinking: Take 5 points on $\mathbb S^1$ such that the angle of any two neighboring points is $2\pi/5$. Then in every closed hemisphere there lie at most 3 of the points. Feb 14 '14 at 14:54