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...Basics of hyperbolic geometry rich schwartz october thepurpose this handout is to explain some the i ll talk entirely about plane model let c denote complex numbers as a set consists x iy with y denoted by h another name for number form in other words just real line geodesics are either circles that meet at right angles vertical rays count see figure b d and points exercise prove any two distinct point determine unique geodesic contains these be p not on there innitely many through do contain failure parallel postulete angle between intersection de ned usual curves it tangent lines segment circular arc contained three naturally triangle you can connect each segments sum interior triangles less than degrees distance formula given we nd such endpoints joining if same then dene log lie one or case assuming have only how equation limiting put way continuous function locations symmetries amobius transformation map f az ad bc cz talked maps general when here want take r will call mobius tran...