Good intermediate introduction of geometry

[MidgetDwarf]

I am looking for a good intermediate introduction to Euclidean Geometry. I have knowledge of ordinary differential equations (first course), elementary linear algebra, and multivariable calculus. My geometry foundation is rather weak and I would like to improve it.

I purchased Kisselev Geometry which is a very good book. The problem is it is not very good because it lacks an answer key. In my opinion this is a better book used for when one has understanding of geometry and wants to improve what one knows. A bridge between euclidean geometry and non euclidean geometry.
I have worked half way through the book but I can not check my intuition. Often I am left wondering if I truly solved a problem and spend a lot of time thinking through it.

Any suggestions?

Currently not looking for the ELEMENTS (Later I will complete this book).

 

[jedishrfu]

One option is Schaums Outlines

https://www.amazon.com/dp/0071795405/?tag=pfamazon01-20

 

[MidgetDwarf]

One option is Schaums Outlines

https://www.amazon.com/dp/0071795405/?tag=pfamazon01-20

Thanks for replying Mr Jedi. I am looking for something a bit more "bookish". I have not seen the Schaum's geometry outline, but I have seen the LA/Cal and i thought it was extremely basic. Does the Schaum's Geometry outline also suffer from this? If so you any other recommendations. I would greatly appreciate it.

 

[jedishrfu]

I like Schaum's in general, although I do remember when I was in school then never quite lined up with my coursework and of course the other problem was we didn't have the internet and we didn't have calculators (adding machines yes, calculators). We did our physics with a slide rule and Shaum's.

The most useful Schaums for physics was the Mathematical Handbook of Formulas and Tables with a gazilion integrals, bessel functions..., and coordinate transforms for every kind of orthogonal coordinate system in use.

 

[MidgetDwarf]

Thanks Jedi. The librarian at the college ussually saves old books they are replacing ti make room in the library. There happened to be a Schaum's geometry and How to Solve it from Polya in there. She allowed me to take it home. Looking at the book it clear I would give it a 7 out 10. I also purchased a copy of jacobs geometry at the goodwill and I think this will be my primary and Schaum's my secondary.

Thanka

 

[merovingian12]

Hi MidgetDwarf,

There's "Challenging Problems in Geometry" by Posamentier and Salkind (a cheap Dover) and "Geometry Revisited" by Coxeter and Greitzer. If I'm not mistaken both of them have solutions for everything.

I certainly sympathize with you on the absense of answer keys! For some reason, while many "problem books" (with solutions) have been published in Russian over the years, the same cannot be said for English-language academic/pedagogical literature. While good books in English do exist (e.g. Purcell for E&M and Spivak for single-var. calculus,) one might be hard-pressed indeed to find a resource with a large number of good, challenging problems to work through and then be able to check one's work (but I have come across a few such books, e.g. the ones mentioned above.)

One other book you might consider is the collection of geometry problems by Prasolov. There is a translation from the original Russian here: http://students.imsa.edu/~tliu/Math/planegeo.pdf
(I hope I'm not violating any rules by posting this link! I don't think it's a problem since the Russian original is available on the MCCME website.)

That book has a LOT of problems, many of which are quite challenging (at the olympiad level.) I myself never got that far into it. I thought I'd mention it because there's a claim that the book is "complete" and "encyclopedic," and judging from the size it may very well be as close to "complete" as a book can be.

Oh, and you definitely need a good foundation on the theory before going through any of the above; Kiselev and/or Euclid should be fine for that.

 

[logan3]

https://www.amazon.com/dp/0764140698/?tag=pfamazon01-20 for the NY Regent's Exam is an excellent book. I recommend it over Schaum's.