Book recommendations

Question

I'm looking for two books:

1) a sophisticated, but high school level Euclidean Geometry book. I've got some bright younger students, and I'd like to get them thinking about more interesting geometry problems than are covered in typical modern American public high schools.

2) For myself, I'd like to find a book that presents dynamical systems (i.e. non-linear diff. eq.s) from a differential forms perspective, and with a fair degree of geometry, less abstract formal manipulations and more geometric intuition. Ideally it would also connect to, hint at, or even outright discuss, algebraic topology, i.e. cohomology...

Any ideas?

For the geometry book, see High School Geometry Text?. – Dave L. Renfro Oct 07 '15 at 18:30 — Dave L. Renfro, Oct 07 '15 at 18:30
This is two questions, not one question. – djechlin Jan 04 '16 at 23:08 — djechlin, Jan 04 '16 at 23:08
I highly recommend you split this into two questions. – Suganth Kannan Jul 07 '16 at 21:08 — Suganth Kannan, Jul 07 '16 at 21:08

score 1 · Answer 1 · answered Dec 29 '15 at 06:26

I don't think they qualify as textbooks, but I think books like "Flatterland", by Ian Stewart would be really great. It can ignite enthusiasm and interest for the subject. It would also make them aware that Euclidean geometry is really a small part of the overall landscape of the subject.

Another book which is good but I haven't made time to read yet is "Geometry and the Imagination" by David Hilbert. He was one of the best mathematicians of the last century, and this work is readable although it requires more attention and focus than the previous book.

For problems, I recommend "Geometry revisited" by Coxeter, who was probably one of the best geometers ever. It's not a traditional book which aims to take one through the entire subject, just provides interesting sprinkles from all kinds of interesting areas.

Hope this helps.

score 0 · Answer 2 · answered Jan 04 '16 at 23:00

0

This link might provide you with the book you are looking for and possibly others you might be interested in.

answered Jan 04 '16 at 23:00

Simply Beautiful Art

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