2

I need some information about Hyperbolic Geometry. For example, Spherical Geometry is a subsection of Hyperbolic Geometry or no?

Can you suggest to me a book or some other reference to help me better understand these notions?

Thanks a lot!

amWhy
  • 210,739
Iuli
  • 6,870

2 Answers2

10

You might want to start with this very nice ~$60$ page pdf: Hyperbolic Geometry - from Flavors of Geometry by Cannon, Floyd, Kenyon, and Parry. (MSRI Publications Volume 31, 1997.)

See also references and external links available in the Wikipedia entry for Hyperbolic Geometry. The entry itself is informative, and you'll quickly see that there is not a hyperbolic geometry, but rather, four or five models of hyperbolic geometries that share some fundamental characteristics. Compare and contrast with the Wikipedia entry for Spherical Geometry, which is not a proper "subsection" of hyperbolic geometries, though it is a non-Euclidean Geometry.

You can't go wrong, of course, with Euclidean and Non-Euclidean Geometries: Development and History by Marvin J. Greenberg.

amWhy
  • 210,739
  • 1
    Nice recommendations and pointers +1 – Amzoti Jun 06 '13 at 00:49
  • Not sure what you mean by "our or five models of hyperbolic geometries that share some fundamental characteristics". Poincaré, Klein, Gans, etc. models are planar representations of the same mathematical object (just as there is just one Earth and dozens of different projections used in cartography to represent the surface of Earth on the map). – Zeno Rogue Mar 28 '18 at 20:45
3

I don't know your background, but I recommend Marcel Berger's two-volume book Geometry. Pedoe's Geometry: A Comprehensive Course is also a gem.

Ted Shifrin
  • 125,228