
#1
May1313, 10:39 PM

P: 1,572

A polygon with nonnegative area cannot be formed with fewer than 3 points.
A polyhedra with nonnegative volume cannot be formed with fewer than 4 points. A hyperspace with nonnegative measure cannot be formed with fewer than n points. What I mean by "3 points" is that the cardinality of the set of vertices is 3. 



#2
May1313, 10:50 PM

Mentor
P: 4,499

When you say "prove this statement in geometry" are you saying "prove this statement, which has to do with geometry" (because a proof using linear algebra is pretty easy) or are you asking "prove this statement using geometry" which I think would be significantly harder 



#3
May2013, 12:44 PM

P: 1

I hope you mentioned the word "cardinality" for no reason, because in an infinitedimensional space volume as we're used to it (Lebesgue measure) doesn't exist. 


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