Searching for a Rigorous Geometry Book

In summary, the conversation is about the search for a geometry book that is advanced but still focuses on elementary issues. The person suggests two books but the other person is looking for something more specifically related to Euclidean geometry. The first person then recommends Euclid's Elements, augmented by Hartshorne's Geometry, Euclid and beyond as a comprehensive and helpful resource.
  • #1
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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.
 
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  • #2
What kind of geometry?

You can have Euclidean, Differential, Projective...
 
  • #4
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.
 
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  • #5
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.
 
  • #6
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.
 

1. What makes a geometry book considered "rigorous"?

A rigorous geometry book is one that is thorough, logically organized, and presents material in a precise and rigorous manner. It should also include challenging exercises and proofs to strengthen the understanding of geometric concepts.

2. How do you determine the level of rigor in a geometry book?

The level of rigor in a geometry book can be determined by examining the depth and breadth of topics covered, the complexity of exercises and proofs, and the level of detail and precision in explanations. Additionally, reviews and recommendations from reputable sources can also help gauge the level of rigor.

3. Are there any specific criteria to look for when evaluating a geometry book for rigor?

Yes, there are several criteria to consider when evaluating a geometry book for rigor. These include the clarity and coherence of the book's structure, the accuracy and completeness of explanations and proofs, the variety and difficulty of exercises, and the overall quality of the writing and presentation.

4. Are there any commonly recommended geometry books known for their rigor?

Yes, there are several commonly recommended geometry books known for their rigor, such as "Euclidean Geometry in Mathematical Olympiads" by Evan Chen, "Geometry: A Comprehensive Course" by Dan Pedoe, and "The Art and Craft of Problem Solving" by Paul Zeitz.

5. Does the level of rigor in a geometry book affect its usefulness for real-world applications?

While the level of rigor in a geometry book may not directly impact its usefulness for real-world applications, a more rigorous book may provide a stronger foundation and deeper understanding of geometric concepts that can be applied in various contexts. However, it is important to note that some geometry books may focus more on theory and proofs rather than practical applications.

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