A great lot.
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You cant, stuff like geometry is supposed to be learned just for getting a good grade in school :P
in ancient egypt, pharoes were placed in great pyramids, which served as a tumb. these pyramids were magnifacent, and there were no mistakes made on them. the archatects eventually learned geometry to have the right proportions for the pyramids, and other mathimatical needs. also, they learned some in science.
4, some say 8, some say 16 or 24 but I am certain it is 4. I learned this in geometry.
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
Yes that is correct I'm in Geometry myself and we just learned this, it is called the Centroid because it divides each median in a 2:1 ratio