Searching for a Rigorous Geometry Book

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Discussion Overview

The discussion revolves around the search for a rigorous geometry book, with a focus on elementary issues while seeking advanced content. Participants explore various types of geometry, including Euclidean geometry, and share recommendations based on their experiences.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks a rigorous geometry book that balances advanced content with elementary issues.
  • Another participant asks for clarification on the type of geometry being sought, mentioning categories like Euclidean, Differential, and Projective geometry.
  • Some participants recommend specific books, including two that are described as "more advanced," though their mathematical rigor is questioned.
  • One participant suggests Euclid's Elements, augmented by Hartshorne's Geometry, Euclid and Beyond, citing personal experience and learning from these texts.
  • Another participant expresses unfamiliarity with the suggested books and emphasizes the importance of understanding the purpose of the book, suggesting that a modern approach might be more beneficial given developments since Euclid.

Areas of Agreement / Disagreement

Participants have differing views on the type of geometry and the suitability of various books. There is no consensus on a single recommended text, and the discussion remains unresolved regarding the best choice for a rigorous geometry book.

Contextual Notes

Some limitations include the lack of clarity on the specific needs of the original poster and the varying definitions of what constitutes a "rigorous" geometry book.

zalook
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Hello, I am searching for a geometry book, a rigorous one. I have taken a look at Moise's and Downs's book but it looked too short, I want something more advanced but keeping the focus on elemtary issues at the same time.

Thanks.
 
Last edited:
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What kind of geometry?

You can have Euclidean, Differential, Projective...
 
Well, the kind of geometry showed in the book I mentioned: Euclidian mainly. By the way, have you used those books? Could you tell me your experience with them?.

Thanks.
 
Last edited:
Try Euclid's Elements, from the green lion press, augmented by Hartshorne: Geometry, Euclid and beyond. I cannot think of a better source. I used those last time I taught it and I learned a lot, even after a 30 year career as a professional mathematician.
 
I am not familiar with the book you mention, if you could explain what you want the book for it would be easier to help. There has been a lot of development since Euclid, so for many purposes I would advise a book that includes a more modern approach.
 

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