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Math Help - Proving that a shape S is a sphere.

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Proving that a shape S is a sphere.

    Let S\subset {\mathbb{R}}^3 with the following properties:

    1. For any line l:

    |l\cap S|=2 or |l\cap S|=1 or |l\cap S|=0

    2. For any plane P:

    |P\cap S|=4 or |P\cap S|=1 or |P\cap S|=0

    Prove that S is a sphere.
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  2. #2
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    Re: Proving that a shape S is a sphere.

    What does the | | sign mean? First I thought it must be the number of elements of the set. But in that case |PS| = infinity, not 4.
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