>>13754218Sure! I'm going for lunch now¸ but since /sci/ is such a slow board I'll come back and post more later.
>BooksYou'll find no end of 1) Books full of challenging, Olympiad-style problems and 2) Books taking a modern, abstract approach to geometry. It's worth getting hold of a few of the best works in both these categories. You won't struggle in finding any.
Personally, however, I like books with a recreational angle that go deep into important, but forgotten aspects of geometry and are full of strongly intuitive explanations, both verbal and visual. As a starting point, I think everybody should have, in their mathematical library, the three books of Proofs Without Words, which should help you easily solve in your head many fundamental formulae in mathematics (strengthening your intuition of higher-level topics). I also like:
>Heavenly mathematics: The Forgotten Art of Spherical TrigonometryLearn the ancient maths of astronomers and explorers; instinctively and intuitively prove to anyone you meet that we do, in fact, live on a sphere.
>The Secrets of TrianglesYou won't struggle with basic geometry problems after you've gained a deep, intuitive grasp of exactly what you can and cannot do with triangles. Your gateway to understanding even deeper and more complex proofs.
>Keith Kendig's ConicsReally interesting and unusual book on conic sections. An essential, underappreciated area of mathematics full of interesting correspondences. The Greeks, for example, came close to discovering calculus when Archimedes computed the area under a parabola.
>A Book of CurvesLovely book that acts as a taxonomy of planar curves -- beautiful algebraic formulae which keep cropping up everywhere you look in mathematics.
>Sheratov's Hyperbolic FunctionsThis short book should serve as an intro to hyperbolic geometry, and it stays relatively grounded while other, university-level coursebooks on hyperbolic geometry very quickly blast off into the realm of abstract algebra.
