Can anyone recommend a good geometry book?

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Discussion Overview

The discussion revolves around recommendations for geometry books, with participants exploring various types of geometry and their suitability for different levels of understanding. The scope includes introductory texts and considerations for preparing for math contests.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant suggests "Algebraic Geometry" by Hartshorne but emphasizes the need for more specific information about the type of geometry desired.
  • Another participant expresses a lack of prior geometry experience and seeks foundational knowledge.
  • Recommendations include "Geometry" by Serge Lang as a suitable high school-level text, "Introduction to Geometry" by Coxeter as a rich but non-textbook introduction, and "Elements" by Euclid as a historically significant work, though noting its errors and omissions.
  • A later reply mentions the possibility of starting with Euclidean Geometry and suggests a book by Harold Jacobs as a good option.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single recommended book, indicating multiple competing views on what constitutes a good starting point in geometry.

Contextual Notes

Participants express varying levels of familiarity with geometry, which affects the recommendations provided. There are also mentions of specific needs related to math contests, which may influence the choice of texts.

Who May Find This Useful

Individuals seeking foundational knowledge in geometry, particularly those preparing for math contests or looking for introductory texts.

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Can anyone recommend a good geometry book?
 
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Algebraic geometry by Hartshorne.

If you want a better answer then you need to specify more. What kind of geometry?? Why do you need it?? What do you know already??
 


I have never taken a geometry class in my life so I would like to have some sort of knowledge about geometry, and I've heard that geometry is a good subject to have a good understanding in...
 


As far as "what type of geometry" I am not sure... can you suggest a good place to start?
 


OK, then I got three books for you

1) "Geometry" by Serge Lang. This is essentially a high school geometry book done right. It doesn't bother with two column proofs and other silly things. It treats geometry like it should be treated.

2) "Introduction to Geometry" by Coxeter. Maybe use this as a second book. It's very rich and offers an introduction to many different fields of geometry. It's not an actual textbook though, but more an introduction. Not suitable as first book.

3) "Elements" by Euclid. The very first geometry book and a standard for over 1000's of years. It is a recommended read to everybody: it develops geometry from scratch. However, you must be aware that there are some errors and omissions (for example coordinate geometry).
 


Thank you. I was also interested in taking my schools math contest next semester. I will be starting second semeste calculus. Do you know any good books that can prepare me for the types of questions math contests have?
 


Miike012 said:
As far as "what type of geometry" I am not sure... can you suggest a good place to start?

Probably with Euclidian Geometry? I've heard good things about the book by Harold Jacobs.
 

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