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I always liked geometry at school, so by the side of my normal studies I've been going through the Khan academy videos. Could anyone suggest some good books that takes these geometry topics further? I'm not sure which subject area to look into now. Is the next thing manifolds?

I should say that I've just finished my first year of calculus (economics), but as I'm not taking a maths degree, I won't be studying things like analysis or abstract algebra, etc, and I don't know if there are any prerequisites that I need to look into first, or really even what the next subject is, I just kinda like shapes and stuff! ;)

Anyway thanks for the help.

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  • $\begingroup$ Have you ever taken math courses where exercises were mainly proofs? I don't know if one would want to jump into something at the level of manifolds without being comfortable with proofs first. $\endgroup$ – rschwieb Apr 23 '14 at 11:27
  • $\begingroup$ None of my maths classes, even the calculus one, dealt with proofs. I was thinking of getting Proofs Demystified to get me started. $\endgroup$ – Tim H UK Apr 24 '14 at 8:21
  • $\begingroup$ Sounds like a plan, although you'll probably need humans to give feedback on your proofs too. Luckily we do that here. Being comfortable with proofs is a great investment. $\endgroup$ – rschwieb Apr 24 '14 at 9:56
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There are a lot of choices, but I could safely recommend Hartshorne's Geometry: Euclid and beyond.

Based on my experiences with it, it seems like a great bridge from high school geometry to geometry taught in universities.

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There are good resources online with far more than you can buy in books... Here are just two of them:

http://www.cut-the-knot.org/geometry.shtml

http://gogeometry.com/

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