How to study Geometry?

Question

I've never been in High School, therefore never had a chance to take any geometry. Recently I passed GED then started taking the lowest tier math classes until I was able to take Differential Calculus. I really enjoyed the subject and even considering studying mathematics. What troubles me, however, is my lack of proficiency in geometry, sometimes it prevents me from solving an interesting problem in optimization or pretty much any geometrical construction on a plane. I'm looking for a source where I can study, perhaps a textbook that picks-up from essentials and moves on into challenging problems within perimeters of High School + curriculum. I'm not of faint of the heart, and open for suggestions.

Answer 1

Here are a couple of recommendations:

• Harold R. Jacobs. Geometry: Seeing, Doing, Understanding

• Kiselev's Geometry. Adapted from the Russian by Alexander Givental. (This used to be a standard geometry textbook in Russia/USSR. No doubt that Soviet engineers who sent Sputnik to space had studied geometry as school kids using this very textbook by A.P. Kiselev.)

Both are wonderful texts, each in its own way. As always with studying mathematics, you will need to solve many problems, not just read the textbook(s).

Once you master the above, try also

• H.S.M. Coxeter, Introduction to Geometry (This book is based, in part, on a series of lectures that the famous geometer Coxeter gave to audiences of high school math teachers.)

Answer 2

Textbook of Mechanical Drawing: Being an Explanation of the Principles of Geometry and Orthographic Projection, the Helix, and Toothed Gearing (1902) by John S. Rooke - Hardcover study this book carefully....