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So while not actually a specific problem I'm struggling with, I was hoping for some of your insight! For a course, I'm currently reading Stillwell's Four Pillars of Geometry. While it does a nice job of motivating the theory, I find it a little sparse with regard to challenging/engaging problems. Any suggestions as to where I can turn to find a nice supplementary text on projective/hyperbolic geometry?

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There are several relatively recent textbooks on projective geometry and a host of pre-1950 texts. The most well known of the more recent ones is the probably the one by Coexeter. A little known book I consider a gem is Pierre Samuel's book.It's almost impossible to find now, but well worth tracking down for it's algebraic flavor. And of course, the major general axiomatic geometry texts-like Greenberg's classic and the more recent book by Hartshorne- have chapters on projective geometry.

Hyperbolic geometry is a lot harder to find a book on. I know there's a pretty good chapter in Greenberg, but other then that,I can't think of one off the top of my head.

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There is a book by Hartshorne on the Foundations of projective geometry. I'm not sure that's what you're looking for, having skimmed it a long time ago.

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That's a really good book,but it may be a bit too advanced for his purposes. But if you have a strong background in abstract algebra, it's a great read. –  Mathemagician1234 Sep 30 '11 at 3:31
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Whoa, Mathemagician, I'm right here... –  AsinglePANCAKE Oct 1 '11 at 0:54
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Ok,my bad,chill.You STILL need a good background in algebra to read it.........LOL –  Mathemagician1234 Oct 2 '11 at 0:05
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I taught a math undergrad course from Henle's book "Modern Geometries." I recall liking the book, and I think the problems were pretty good. However, it's been awhile, so I can't be more specific. In any event, he does cover both projective and hyperbolic geometry.

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If you, or anybody else, needs the theoretical background behind projective geometry for Computer Vision, I found these two books to be great: (1) Multiple View Geometry in Computer Vision by Richard Hartley et al., and (2) An Invitation to 3-D Vision by Yi Ma et al.

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