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Good book(s) on Geometry

by moe darklight
Tags: books, geometry
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moe darklight
Mar12-08, 08:44 PM
P: 411
I always have trouble when it comes down to all things geometry (angles and parabolas and ellipses, o my! <--- me frustrated).

I really think this is an area I could more than use some extra resources on.

For algebra, I turned to "dry" books without much explanations because I found that the other kind confused me more than anything else, and, just seeing the proofs and formulas as is, is better for me and cleared things up. With geometry I'm having the opposite problem; I need a book that will help me learn to think in terms of geometry and learn to approach problems involving geometry better.

This is a really weird problem, because I'm a very visual thinker in most other aspects, even when I listen to music I think of vivid shapes and textures and colors; it's as if I'm having trouble making my brain connect its logic parts and its visual parts.
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Mar12-08, 08:50 PM
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moe_darklight, you did not say what courses you have studied up to now. If you have been using just an intermediate Algebra book, either try a different one, or try a College Algebra, or PreCalculus book. You may find that some of the treatments of "conic sections" in College Algebra/PreCalculus books may be better than some of these treatments of Intermediate Algebra books.

If you have studied most of Intermediate Algebra already and have done well except for conic sections (ellipse, hyperbola, circle, parabola), then try a Larson & Hostetler book of PreCalculus or College Algebra. (or other college algebra book)
moe darklight
Mar12-08, 09:13 PM
P: 411
I'm not in a course, I didn't take precalculus in High School (or any math, for that matter), just this past year I bought a bunch of books, deciding to catch up with what I've missed.

So the geometry I've seen is all from precalculus books (basic trig, parabolas, angles, rotating axes, etc.). I do fine with all the algebra stuff, but the questions involving lots of geometry are really challenging when compared to those involving mostly equations and matrices.

I feel like I'm ready to move on to calculus as far as the algebra, but I also know that calculus and physics deals a lot with trig and geometry, and I don't want to start that feeling insecure about my understanding of those.

So maybe like a book or textbook that puts an extra emphasis on geometry (or even only on geometry) at the precalculus-->calculus level.

Mar14-08, 08:38 PM
rocomath's Avatar
P: 1,754
Good book(s) on Geometry

Have you ever heard of Math AoPS?

I'm working all their books simultaneously, and I love it! The geometry book is pretty good so far, it's not too expensive either.

If you want a book that is good enough for Calculus, Selby's book is cheaper and less detailed.
moe darklight
Mar15-08, 12:09 AM
P: 411
Never heard of it, thanks. Prices are pretty good compared with the $100+ textbooks I've seen elsewhere... I found this one cheap so I ordered it:

heard of it? any good?

I'm quite frustrated that I have such a hard time with triangles with their ... stupid... fouró i mean, three corners... they think they're sooo cool, and pointy

How did you get to get familiar with trigonometry and geometry? is it just that it takes time to memorize it? because algebra all kind of makes sense on its own. Trig is all so random and weird... to me at least. Maybe I'm just geometrically retarded .
Mar15-08, 12:41 AM
P: 705
Not for studying geometry itself, but rather for getting in the mindset of thinking about geometry, you might enjoy Edwin Abbot's Flatland: A Romance of Many Dimensions (1884; a quick read and well worth it; the link is to an online edition but you can find it in any library) and Martin Gardner's The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds.
moe darklight
Mar15-08, 01:10 AM
P: 411
Flatland! I heard about it, then completely forgot about it; thanks for reminding me!

yes, my problem is on an intuitive level. I can do simple exercises using the trig functions and all that, but I can't understand it the way I understand the rest of the stuff; I'm just regurgitating formulas. So on exercises that involve actually thinking about the concept I fail.
I'll see how it goes with the trig book.
May24-08, 01:18 PM
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the best elementary geometry book is "geometry", first edition, by harold jacobs. it was written for high school in the 60's or so, and the current third edition is dumbed down.

the best college geometry book is the one, euclid and beyond, by hartshorne.

neither of these deal with parabolas and ellipses, but in my opinion you need basic geometry, well treated, before going into analytic geometry. then a classical book on analytic geometry would help, even my old high school book, principles of mathematics, by allendoerfer and oakley.
moe darklight
May25-08, 01:44 AM
P: 411
Thanks, I'll look them up. Master Math: Trigonometry has really helped me get a feeling for the subject... I keep saying to myself "how didn't I understand that before."

The only problem with the book is that it has only one problem for every new concept she introduces, so I use the problems from the schaum's and the other textbook I have, but they're always about exactly what the lesson was talking about... so I've ordered , since from the reviews it seems to be a good book with LOTS of problems of all types.

Also, since the time I wrote that post, I've decided to sign up for more math in university and, if all goes well, do a double major (Literature/Physics). Since I didn't take math in highschool I signed up for a first year calculus course that goes over trig/pre-calc first (they add an extra lesson every week), and had to show them that I've caught up with most of what I've missed (i.e: everything ) since I left school... so I'm gonna have some guidance in that aspect and not be flying blind.

I think I'm ready... I can solve the examples in my textbook... but usually they go for the obvious, which kind of sucks, because I have no clue how I would do on a tricky question... I've never even seen what a math exam looks like I guess I'll find out soon enough.

So I have a few months now to get ready.

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