Searching for a Rigorous Geometry Book

AI Thread Summary
A user is seeking a rigorous geometry book, specifically one that is advanced yet focuses on elementary issues, expressing dissatisfaction with Moise's and Downs's offerings. The discussion includes suggestions for Euclidean geometry resources, such as Euclid's Elements and Hartshorne's "Geometry, Euclid and Beyond." Participants emphasize the importance of modern approaches to geometry, noting that advancements have occurred since Euclid's time. Recommendations also include more advanced texts, although the user is cautioned that they may be too mathematical. Overall, the conversation highlights the need for a balance between rigor and accessibility in geometry literature.
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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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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.
 
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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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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