| | [SOLVED] 5 points on a sphere |  |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: [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. 
Last edited by Bruno on Sat Dec 19, 2009 2:32 pm; edited 1 time in total | |
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vincent
Pythagoras
Posts : 2
Join date : 2009-09-17
| | Subject: 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
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: Re: [SOLVED] 5 points on a sphere Sat Dec 19, 2009 1:33 pm | |
| Hell yeah! Bienvenue sur le forum. T'as donc ben une belle face? | |
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vincent
Pythagoras
Posts : 2
Join date : 2009-09-17
| | Subject: 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!  | |
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: Re: [SOLVED] 5 points on a sphere Sat Dec 19, 2009 2:32 pm | |
| C'est un grand honneur!  | |
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Mohammad
Descartes
Posts : 100
Join date : 2009-11-05
Age : 40
Location : Right behind you
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Bruno
Admin
Posts : 184
Join date : 2009-09-15
Age : 36
Location : the infinite, frictionless plane of uniform density
| | Subject: 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!"  | |
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Mohammad
Descartes
Posts : 100
Join date : 2009-11-05
Age : 40
Location : Right behind you
| | Subject: 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  | |
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| | [SOLVED] 5 points on a sphere | |
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