the arithmetics of the hyperbolic plane talk 1 hyperbolic geometry valentino delle rose introduction these notes are a short introduction to the geometry of the hyperbolic plane we will start ...
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...The arithmetics of hyperbolic plane talk geometry valentino delle rose introduction these notes are a short to we will start by building upper half model here and in continuation certain is simply space including notions point straight line which axioms that hold then describe isometries i e class trasfor mations preserving distance geodesics shortest paths connecting two after brief poincar disk about geodesictriangleandwewillgiveaclassicationofthehyperbolicisome tries end explain why an example non euclidean for more details missing proofs see r schartz mostly surfaces m s student library series volume https www mathbrown edu res papers surfacebook pdf westart dening as set points with metric denition call u z c im let v be real vector inner product on map h such hav w xi ahv hw x hx yi hy y figure iy at introduce hv wi where usual dot mean apply this vectors based now can dene norm induced iz p kvk vi dierentiable curve length b t l k dt consider dened ie portion given et note image...