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Top rated non-euclidean geometries books

Here are some top-rated books on non-Euclidean geometries:

  1. "Non-Euclidean Geometry" by H. S. M. Coxeter - A classic textbook on the subject, covering hyperbolic, elliptic, and Euclidean geometries.
  2. "Geometry: Euclid and Beyond" by Robin Hartshorne - This book provides a comprehensive introduction to Euclidean and non-Euclidean geometries, including hyperbolic and elliptic geometries.
  3. "Hyperbolic Geometry" by James W. Anderson - A thorough introduction to hyperbolic geometry, covering its history, foundations, and applications.
  4. "Elliptic Geometry" by William J. McClelland - A detailed exploration of elliptic geometry, including its axioms, theorems, and relationships to other geometries.
  5. "Non-Euclidean Geometry: A Critical and Historical Study" by Roberto Bonola - A historical and critical analysis of non-Euclidean geometries, covering the work of key figures like Gauss, Bolyai, and Lobachevsky.
  6. "The Geometry of Space" by Henry Parker Manning - A classic book that introduces non-Euclidean geometries through a series of problems and exercises.
  7. "Introduction to Non-Euclidean Geometry" by Harold R. Jacobs - A gentle introduction to non-Euclidean geometries, suitable for undergraduate students or those new to the subject.
  8. "Non-Euclidean Geometries: Theories and Problems" by Miloš Komma - A problem-based book that covers hyperbolic, elliptic, and Euclidean geometries, with an emphasis on theoretical and practical applications.
  9. "Differential Geometry, Lie Groups, and Symmetric Spaces" by Sigurdur Helgason - A graduate-level textbook that covers non-Euclidean geometries in the context of differential geometry and Lie groups.
  10. "Foundations of Hyperbolic Manifolds" by John G. Ratcliffe - A comprehensive introduction to hyperbolic geometry, covering its foundations, topology, and geometric properties.

These books are highly rated and well-regarded in the mathematical community, but keep in mind that some may be more advanced or specialized than others. It's essential to choose a book that aligns with your mathematical background and goals.

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Please note that the ratings can vary depending on the source and the audience. These books are generally well-regarded, but it's essential to read reviews and consult with experts to find the best fit for your needs.