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 [SOLVED] 5 points on a sphere

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Bruno
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PostSubject: [SOLVED] 5 points on a sphere   Sat Nov 28, 2009 1:48 pm

This one is from Putnam a few years back. It's quite easy if you pay attention to the wording of the problem...

There are 5 points on a sphere. Show that you can find a closed hemisphere containing 4 of the points. Basketball


Last edited by Bruno on Sat Dec 19, 2009 2:32 pm; edited 1 time in total
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vincent
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 12:59 pm

from two points on the sphere you have a great circle, the 3 other points are either on one of the two hemispheres created or on the same great circle, in all cases there is at most one point not on one of the two hemispheres.

QED!
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Bruno
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 1:33 pm

Hell yeah! Basketball

Bienvenue sur le forum. T'as donc ben une belle face?
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vincent
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 1:49 pm

merci je dois dire que nos deux faces semblent être apparentés! afro
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Bruno
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 2:32 pm

C'est un grand honneur! What a Face
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Mohammad
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 4:26 pm

What!! you are writing in French Very Happy bounce
OK! Peyman and I will be writing in Farsi then after Very Happy
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Bruno
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 4:47 pm

Haha okay sorry. Translation :

Me : "Welcome to the forum, you have a pretty nice face!"
Vincent : "Thank you, and I must say that it seems our faces are related!" albino
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Mohammad
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PostSubject: Re: [SOLVED] 5 points on a sphere   Sat Dec 19, 2009 4:52 pm

I know what you were saying, I have a translator on my Laptop hehe Very Happy
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