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...Non euclidean geometry rick roesler i can think of three ways to talk about m pretty sure they are all equivalent but t prove it the parallel postulate is called because greek mathematician euclid developed a number postulates one these was given line l and point p not on there exactly through that s for really long time years people tried could be derived from other in fact independent you invent has different geometries flat space like this piece paper or computer screen plane newtonian two archetypal spherical hyperbolic ll mostly easier picture found some good graphics web no lines even so what lineon surface sphere when we have way measure distances between points define segment curve minimum length isn curved straight satisfies distance principle april version page math curves geodesics get ball whose string mark stretch tightly along find part great circle intersection with passing center ve stretched as possible defines must shortest if didn tighter path geodesic figure example...