Quote:
Originally Posted by Robh
But did I discover spherical geometry or create it- I can certainly confirm it in U2? But the mathematics for a hyperbolic Universe exists even though it seems such a Universe does not. Is it a creation or a discovery? It is not a physical discovery of the world we live in.
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To take a leaf out of the book of relativity, an observer makes a measurement in his own frame of reference. The frame of reference doesn't have to be the Universe itself.
Mathematicians refer to objects being embedded in higher dimensional space. A triangle drawn on a sheet of paper is an example of a two dimensional object embedded in three dimensional space.
If I measure the dimensions of this triangle, my frame of reference is the surface the of paper not the Universe.
Therefore even if a hyperbolic Universe doesn't exist I can still construct a triangle on a hyperbolic surface (much like a horse saddle).
So I believe the hyperbolic geometry is a discovery.
Regards
Steven