Geometry What are the best books to explore hyperbolic trigonometry?

[ciubba]

My calc. 2 book more or less only mentioned the hyperbolic functions to make integration easier, so, now that I have some free time, I'd like to explore the area further. Could someone recommend a good book on the subject or do I need to take more math first?

A quick google search revealed "Hyperbolic Functions: With Configuration Theorems and Equivalent and Equidecomposable Figures," which sounds about what I'm looking for, but I can't find a preview of the book.

 

[verty]

This one would work: Van Brummelen - Introduction to Non-Euclidean Geometry. But I don't like this subject myself and wouldn't bother (I find it uninteresting, is all).

Why not learn spherical trig instead? Van Brummelen - Heavenly Matter, The Forgotten Art of Spherical Trigonometry.

 

[micromass]

This one would work: Van Brummelen - Introduction to Non-Euclidean Geometry. But I don't like this subject myself and wouldn't bother (I find it uninteresting, is all).

Why not learn spherical trig instead? Van Brummelen - Heavenly Matter, The Forgotten Art of Spherical Trigonometry.

Is that really what the OP wants? It was my impression he was only interested in learning a bit more about the cosh and sinh functions. I don't think it was his purpose to really do trigonometry on the hyperbolic plane. Nevertheless, if it was his purpose to learn this anyway, then I recommend Brannan: http://www.cambridge.org/be/academic/subjects/mathematics/geometry-and-topology/geometry-2nd-edition The chapter on hyperbolic geometry is mostly self-contained.

The book "Visual complex analysis" by Needhamhttp://[URL='https://www.amazon.com...omplex-Analysis-Tristan-Needham/dp/0198534469[/URL] gives the deep connections between the usual trig functions and the hyperbolic trig functions by using complex numbers.

 

[verty]

Is that really what the OP wants? It was my impression he was only interested in learning a bit more about the cosh and sinh functions. I don't think it was his purpose to really do trigonometry on the hyperbolic plane. Nevertheless, if it was his purpose to learn this anyway, then I recommend Brannan: http://www.cambridge.org/be/academic/subjects/mathematics/geometry-and-topology/geometry-2nd-edition The chapter on hyperbolic geometry is mostly self-contained.

When he said "the area", I thought he meant hyperbolic geometry. I thought it piqued his interest that there might be a hyperbolic geometry and he wanted to know more about that. Because when I first saw sinh and cosh, what sprang to mind is, wow, there must be hyperbolic triangles, I want to know more. I did warn him off it as well, pointing out that I didn't think it was worth looking into.

The book "Visual complex analysis" by Needhamhttp://[URL='https://www.amazon.com...omplex-Analysis-Tristan-Needham/dp/0198534469[/URL] gives the deep connections between the usual trig functions and the hyperbolic trig functions by using complex numbers.

Hmm, I thought the connection was the formula cosh^2 - sinh^2 = 1 which is superficially very similar to cos^2 + sin^2 = 1 (this is honestly hand on my heart what I concluded when I first researched them some years ago), and that they are therefore useful for integration for the same reasons that the trig functions are useful. And perhaps this connection is enough for him in this direction as well, if he doesn't want to learn a whole lot of extra stuff.