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Hardly anyone would maintain that it is better to begin to learn geography from at maps than from a globe. But almost all introductions to hyperbolic non-Euclidean geometry, except [6], present plane models, such as the projective and conformal disk models, without even mentioning that there exists a model that has the same relation to plane models that a globe has to at maps. This model, which is ... read moreon one sheet of a hyperboloid of two sheets in Minkowski 3-space and which I shall call H2, is over a hundred years old; Killing and Poincare both described it in the 1880's (see Section 14) It is used by differential geometers [29, p. 4] and physicists (see [21, pp. 724-725] and [23, p. 113]) Nevertheless it is not nearly so well known as it should be, probably because, like a globe, it requires three dimensions.read less
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