Kiselev vs Euclid? High school Geometry

Question

I wish to study High School Geometry from scratch. My goal is to be able to study College Level Physics, i.e. Mechanics, Optics, Electricity and Magnetism. I want some opinions on which book to use Kiselev's Geometry or Euclid's Elements with the supplementary text Geometry: Euclid and Beyond. Can you please give me some thoughts on the matter?

Answer 1

Hartshorne's book Geometry:Euclid and Beyond isn't really intended to teach geometry from scratch. Instead, it's a detailed investigation of various issues related to the foundations of Euclidean geometry.

I wouldn't recommend reading the Elements directly. Later if you're interested in the foundations of geometry, you can read them along with Hartshorne's book.

Using Kiselev's book is an entirely reasonable choice, but you'll need to learn analytic geometry (with vectors) somewhere else later. In fact, you'll find that that's even more important for physics.

If you want to learn high school geometry in an easier book than Kiselev's, you could try Basic Geometry by Birkhoff and Beatley, although it doesn't discuss solid geometry. You could also consider Geometry by Lang and Murrow.

Answer 2

I would avoid Euclid's Elements, opting instead for a more modern treatment. Also, based on your stated future goals, what you want is strong geometric computation and visualization skills, with only a minimal focus on things like straight-edge-and-compass constructions, or the axiomatic stuff.

Here are some texts that I would recommend:

Gibson -- Elementary Euclidean Geometry - An Undergraduate Introduction (2003)

Aarts -- Plane and Solid Geometry (2008)

Those books appear to assume some knowledge of Linear Algebra, so if you haven't had any of that, I would hold off on the above books.

I'll keep looking.

Update: After reflecting a little more, I can't find any Geometry text that fits well with your stated future goals.

Instead, I would review Precalculus and Calculus -- that material should be regarded as your base, and you should aim for mastery not just competence.

Then head towards Vector Analysis, Linear Algebra, and Differential Equations.

Along the way, you'll pick up the neeeded Geometry, without the parts that are extraneous to your goals.