Let with the following properties:

1. For any line :

or or

2. For any plane :

or or

Prove that is a sphere.

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- Aug 30th 2013, 12:33 AMAlso sprach ZarathustraProving that a shape S is a sphere.
Let with the following properties:

1. For any line :

or or

2. For any plane :

or or

Prove that is a sphere. - Sep 9th 2013, 06:46 AMSkalkazRe: 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.