| 41. | Other useful models of hyperbolic geometry exist in Euclidean space, in which the metric is not preserved.
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| 42. | These forms, based on non-Euclidean hyperbolic geometry, are known today as hyperboloids of revolution.
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| 43. | The geometry on rapidity space is inherited from the hyperbolic geometry on velocity space via the map stated.
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| 44. | Interactive geometry and analysis takes place in the realm of euclidean geometry, spherical geometry or hyperbolic geometry.
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| 45. | Several authors still consider " non-Euclidean geometry " and " hyperbolic geometry " to be synonyms.
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| 46. | The characteristic postulate of hyperbolic geometry says that there are at least two lines of the latter type.
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| 47. | In the late 1970s, William Thurston introduced hyperbolic geometry into the study of knots with the hyperbolization theorem.
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| 48. | These together with the subspace hyperplanes separating hemispheres are the hypersurfaces of the Poincar?disc model of hyperbolic geometry.
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| 49. | M�bius transformations are also isometries of the hyperbolic plane, so in hyperbolic geometry all Apollonian gaskets are congruent.
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| 50. | However, in spherical geometry and hyperbolic geometry, there are infinitely many different shapes of right isosceles triangles.
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