I'm a last year high school student, I'm looking for a "short" (by short I mean, not over 250 pages) Euclidean geometry book that covers topics linked to euclidean geometry of math contests, I have a decent knowledge in the topic thus I'm looking for a book to tackle a bit more advanced stuff. By searching a bit on the internet I found this one book: "Geometry revisited by Coxeter & Greitzer", I've read through the content and it seemed what I was looking for, is the book good for my purpose? any better suggestion?
Euclidean geometry book for math contests
book-recommendationcontest-mathgeometry
Related Solutions
Tristan Needham,
Visual Complex Analysis, Oxford Univ. Press.
"One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. ... to replace our rich visual intuition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's Visual Complex Analysis with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices—but his are interesting." —Ian Stewart
Here's one figure from the book, p.135:
You can almost guess the theorem from the figure: The two spheres $S_1$ and $S_2$ are
orthogonal iff the two circles $C_1$ and $C_2$ are orthogonal.
I am telling my favourites-
- Introduction to Set Theory- Karel Hrbacek, Thomas Jech
- Real analysis- Howie and Understanding analysis- Abbott Complex analysis- Zill & Shanahan and Complex analysis - Lang
Abstract algebra- Dummit & Foote and Contemporary Abstract algebra- Gallian
Linear Algebra- Friedberg, Insel and Spence & Linear Algebra- Hoffman & Kunze
- Differential equations- Sheldon Ross No idea about PDE, but you can check out Simmons book
- Topology- Munkres or Topology- Dugundji. Dont know about algebraic topology but see
- An Introduction to Manifolds- Loring Tu
- Undergraduate Commutative Algebra- Miles reid (for beginner/self study) Commutative algebra - Atiyah (Classic) Steps in Commutative Algebra-R.Y.Sharp. (I like it)
Hartshorne's Algebraic Geometry
A Classical Introduction to Modern Number Theory- Ireland & Rosen
- Introduction to Lie Algebras-Erdmann & Wildon
Best Answer
A great book is
Evan Chen, Euclidean Geometry in Mathematical Olympiads
While something a bit more elementary, but containing some hard problems is
Louridas & Rassias, Problem-Solving and Selected Topics in Euclidean Geometry
A great Dover edition with famous problems and less famous is
Aref & Wernick, Problems and Solutions in Euclidean Geometry