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Hyperbolic Geometry: The All in One Textbook by Haneul Choi

Hyperbolic Geometry: The All in One Textbook

by Haneul Choi
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₹3,352.00
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Book cover type: Paperback
  • ISBN13: 9798281099899
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 372
  • Original Price: GBP 29.64
  • Language: English
  • Edition: N/A
  • Item Weight: 495 grams
  • BISAC Subject(s): Geometry / Non-Euclidean

Step into a universe where straight lines bend, angles shrink, and infinite parallels redefine common sense. This definitive textbook on non-Euclidean space delivers everything you need to see, measure, and command the geometry of negative curvature-whether you are a mathematics major, a graduate researcher, a theoretical physicist, or an artist chasing Escher-like tessellations.

What Sets This Book Apart

- Complete Model Coverage - Poincar? disk, upper half-plane, and Klein projective models explained side-by-side with crystal-clear mappings.
- Proof-Driven Approach - From the independence of Euclid's fifth postulate to M?bius transformation matrices, every theorem is demonstrated step-by-step.
- Hyperbolic Trigonometry Toolkit - Laws of sines, cosines, and right-triangle identities ready for direct calculation.
- Geodesics & Isometries - Master reflections, translations, rotations, and the elliptic-parabolic-hyperbolic classification that powers modern geometric group theory.
- Tessellations & Tilings - Build regular {p, q} mosaics, explore fundamental domains, and unlock the symmetry groups that tile the plane forever.
- Curvature & Metrics - Understand Gaussian curvature, metric tensors, and why circles and areas explode exponentially with radius.
- Classroom to Research Ready - Ideal for advanced undergraduates as a second course in geometry and a self-contained reference for graduate study or independent exploration.

Who Will Benefit

- Mathematicians seeking a rigorous yet accessible foundation.
- Physicists and cosmologists modeling negatively curved space-time.
- Computer scientists working on visualization, graphics, and network theory.
- Educators needing a structured curriculum packed with proofs, diagrams, and problem sets.
- Artists and designers inspired by hyperbolic tessellations and non-Euclidean perspective.

Equip yourself with the knowledge to navigate curved space, calculate precise distances, and design extraordinary tilings that only hyperbolic geometry makes possible.

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