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Suppose that  \(d\)  points are selected on the surface of a sphere.

 

Each point "induces" a hemisphere of the sphere. That is, it defines a hemisphere "centered" at that point (i.e. the "top" / "pole" of the hemisphere is at that point).

 

Prove that all \(d\)  points are located within one same hemisphere \(\iff\) the \(d\)  induced hemispheres all overlap somewhere.

 

Have fun!

 Jan 1, 2022
 #1
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HELP PLEASE URGENT!!!

 Jan 1, 2022

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