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Hello, I am looking for a source that discusses and teaches hyperbolic geometry from a synthetic approach (As opposed to the common analytinc approach in the poincare disk). I am looking for something more in spirit with eucld's elements or hilbert's geometry book.

Thank you

asked Oct 8 at 18:22

Blade

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This question should probably be community wiki. – Dan Petersen Oct 8 at 18:37

You are probably right, Fixed. – Blade Oct 9 at 11:25

Francois Ziegler · Answer 1 · 2012-10-09 17:40:38Z UTC

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I'd say your best bet is with works from the early 20th century, when this sort of thing was in fashion:

Julian Lowell Coolidge, The elements of non-Euclidean geometry (1909)
Horatio Scott Carslaw, The elements of non-Euclidean plane geometry and trigonometry (1916)
Duncan M'Laren Young Sommerville, The elements of non-Euclidean geometry (1919)

edited Oct 9 at 17:40

answered Oct 8 at 19:36

Francois Ziegler
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	I'll look into them all, but of those three, which would you recommend as the 'best'? – Blade Oct 10 at 0:42
	Depends for what. Carlslaw is the most illustrated and elementary, then Sommerville (which has exercises, and on p. 27 refers "the reader who wishes to study the development of non-euclidean geometry from a set of axioms" to Coolidge). Coolidge is more dry and more complete, with e.g. several chapters (IX, X, XVI) on line geometry in hyperbolic space: complexes, congruences, Malus-Dupin theorem, etc. – Francois Ziegler Oct 10 at 2:32

Dan Petersen · Answer 2 · 2012-10-08 18:36:44Z UTC

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Hartshorne's "Geometry: Euclid and Beyond" is very nice.

answered Oct 8 at 18:36

Dan Petersen

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Will Jagy · Answer 3 · 2012-10-08 21:14:33Z UTC

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Download the article at MARVIN and look at the references.

answered Oct 8 at 21:14

Will Jagy

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Richard Kent · Answer 4 · 2012-10-08 18:34:24Z UTC

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Cederberg's A Course in Modern Geometries does some of this.

answered Oct 8 at 18:34

Richard Kent
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Synthetic approach to hyperbolic geometry?

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