%0 PDF %T Hyperbolic Geometry on a Hyperboloid. %A Reynolds, William F. %D 2018-07-19T09:44:23.953-04:00 %8 2018-07-19 %I Tufts University. Tisch Library. %R http://localhost/files/bk128p14r %X 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 on 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. %[ 2018-10-10 %9 Text %~ Tufts Digital Library %W Institution