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.