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Re: Euclidean, Hyperbolic and Elliptic Geometry
Posted:
Mar 12, 2009 9:24 PM


> Can someone tell me some universal rules that apply > all the time no matter what type of geometry?
Euclidean, hyperbolic and elliptic geometry have quite a lot in common. For example, the Euclidean criteria for congruent triangles also apply in the other two geometries, and from those you can prove many other things.
To give a more historical answer, Euclid I.115 apply to all three geometries. Euclid I.16 and various later propositions fail in the elliptic plane. Euclid I.29 and various later propositions fail in the hyperbolic plane.
> My friend Brian asks: Is there a specific ratio > between hyperbolic sines and euclidean sines?
Are you willing to use complex numbers? If so, then sinh(iz) = i.sin(z), cosh(iz) = cos(z).
Ken Pledger.



