Titlebook: Classical Geometries in Modern Contexts; Geometry of Real Inn Walter Benz Book 20072nd edition Birkh?user Basel 2007 Classical geometry.Fin

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Dawdle

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Book 20072nd edition(general) translations and general distances of X, euclidean and hyperbolic geometries are characterized. For these spaces X also the sphere geometries of M?bius and Lie are studied (besides euclidean and hyperbolic geometry), as well as geometries where Lorentz transformations play the key role. Th

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Translation Groups,hers we shall use later on, see the section . of this book. Instead of . (.) we will write . or, occasionally, .. The laws above are then the following: . for all . ∈ ., λ ∈ ?, and .:= . > 0 for all . ∈ .{0}. Instead of (.) we mostly will speak of ., hence tacitly assuming that . is equipped with a

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-Projective Mappings, Isomorphism Theorems, we do not exclude the case that there exist infinite linearly independent subsets of . or .. One of the important results of this chapter is that the hyperbolic geometries (.(.)), (.(.)) over . = (.), . = (.), respectively, . the group of hyperbolic motions, are isomorphic (see p. 16f) if, and only

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