# Analytic geometry - textbook

1. May 3, 2012

Hello! I'm looking for a good analytic geometry textbook. I'm studying circumferences and sphere and I'm using the book Analytic Geometry: A vector approach from Wexler but I find this book quite bad. I want some suggestions!

Thank you.

2. May 3, 2012

### mathwonk

i am puzzled how to answer this because has ever asked me for a book of analytic geometry before. maybe a good old calculus book back when it was called calculus and analytic geometry, maybe an old version of george b thomas' Calculus and analytic geometry.

gee, its still called that recently,

https://www.amazon.com/Calculus-Analytic-Geometry-9th-Edition/dp/0201531747

or maybe the last part of the excellent book, Principles of Mathematics, by Allendoerfer and Oakley.

https://www.amazon.com/Principles-M...=sr_1_1?s=books&ie=UTF8&qid=1336083669&sr=1-1

3. May 3, 2012

Here, in Brazil, we have analytic geometry in college (I'm studying physics). Well, I'll try to find this book. Thank you for your help.

4. May 4, 2012

5. May 4, 2012

### mathwonk

Since this topic has almost disappeared from the US math curriculum, I really didn't know what it consisted of. Nonetheless it seem the books I suggested do cover it.

It seems to be a study of elementary Euclidean geometry from the standpoint advocated by Descartes, namely coordinate geometry. So one introduces coordinates and then studies the same objects that could have been studied without them, namely circles and ellipses, parabolas, and hyperbolas, as well as their presentation as conic sections.

One also studies to some degree changes of coordinates, e.g. polar coordinates, and representations of the same basic quadratic curves via polar coordinates.

As described in the introduction to the chapter in Allendoerfer and Oakley: analytic geometry consists of taking equations and finding the graphs of those equations in the coordinate plane, and conversely, taking curves in the plane and writing equations to describe them. Oh of course one also discusses lines and line segments.

Almost the only book i found on amazon devoted exclusively to this topic was the one below from 1918, but it is a topic that would probably benefit students today. It just gets left out as part of the general, but unfortunate, move away from geometry in the US.

https://www.amazon.com/Analytic-Geo...=sr_1_3?s=books&ie=UTF8&qid=1336154468&sr=1-3

6. May 4, 2012

7. May 4, 2012

### alissca123

At my university, the Analytic Geometry is kind of an "Intro to linear algebra" course... What mathwonk said is covered but with a linear algebra approach, so that when the student gets to the "real" Linear Algebra course (based on Friedberg or Hoffman), he has some familiarity with the concepts...

8. May 4, 2012

9. May 4, 2012

### phinds

About 50 years ago, I studied Analytic Geometry using a Schaum's Outline book on exactly (and exclusively) that topic. It was terrific, and even this much later, you can still find it on-line (it's the 1958 edition, as I recall). More recent editions, I'm not so sure about.

10. May 4, 2012

### Petek

I also taught myself Analytic Geometry from the Schaum's book about 50 years ago. I still have it! The copyright is 1950.

11. May 4, 2012

### mathwonk

alissca123, are you at UNAM? I am interested in whether one cvan still buy copies of the monografias del instituto de matematicas? I can't find them on the web anymore.

12. May 4, 2012

Yes! I've found the Analytic Geometry (Schaum's Outline) pdf! Thanks for all the answers!

13. May 4, 2012

### alissca123

14. May 4, 2012

### mathwonk

yes. number #13 (1983), abelian integrals, by my friend george kempf, is a great treatment of the topic of jacobians and the riemann singularities theorem that cannot be beat.

I have two copies actually myself, but it is a shame it is not available more widely. there are other nice titles as well. did you know my friend sevin recillas? or xavier and carlos gomez mont?

i apologize for diverting the thread.

15. May 5, 2012

mathwonk, it's ok don't worry! Unfortunately the book Analytic Geometry (Schaum's Outline) is too simple, it won't help at all :(

16. May 5, 2012

### qspeechc

I thought I found a book that pretty closely matches what you want:

In fact, here are some others:
https://www.amazon.com/Elementary-V...=sr_1_1?s=books&ie=UTF8&qid=1336245819&sr=1-1
https://www.amazon.com/Vector-Geome...=sr_1_2?s=books&ie=UTF8&qid=1336245819&sr=1-2

17. May 5, 2012

qspeechc, is it possible to find these books online? If yes, can you send me the download link?

18. May 5, 2012

### alissca123

Only by name, they are pretty famous around here (except Carlos, i've never heard of him)...
I think they replaced the Monografías with these ones... Aportaciones Matemáticas... http://texedores.matem.unam.mx/publ...ion=com_remository&Itemid=57&func=select&id=9

19. May 6, 2012

### qspeechc

For Hausner and Schuster there are used copies on amazon.com for less than $5, and Robinson for less than$8.