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MARC 21

Geometry II: Spaces of Constant Curvature /
Tag	Description
020	$a9783662029015$9978-3-662-02901-5
082	$a516$223
099	$aOnline resource: Springer
245	$aGeometry II$h[EBook] :$bSpaces of Constant Curvature /$cedited by E. B. Vinberg.
260	$aBerlin, Heidelberg :$bSpringer Berlin Heidelberg :$bImprint: Springer,$c1993.
300	$aIX, 256 p. 10 illus.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aEncyclopaedia of Mathematical Sciences,$x0938-0396 ;$v29
505	$aI. Geometry of Spaces of Constant Curvature -- II. Discrete Groups of Motions of Spaces of Constant Curvature -- Author Index.
520	$aSpaces of constant curvature, i.e. Euclidean space, the sphere, and Loba chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space. Lobachevskij geometry, which in the first fifty years after its discovery had been regarded only as a logically feasible by-product appearing in the investigation of the foundations of geometry, has even now, despite the fact that it has found its use in numerous applications, preserved a kind of exotic and even romantic element. This may probably be explained by the permanent cultural and historical impact which the proof of the independence of the Fifth Postulate had on human thought.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aVinberg, E. B.$eeditor.
710	$aSpringerLink (Online service)
830	$aEncyclopaedia of Mathematical Sciences,$x0938-0396 ;$v29
856	$uhttp://dx.doi.org/10.1007/978-3-662-02901-5