Hyperbolic Geometry: The All in One Textbook (Haneul Choi Mathematics Textbooks)

By Haneul Choi

Step into a universe where straight lines bend, angles shrink, and infinite parallels redefine common sense. This definitive textbook on nonEuclidean 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 Escherlike tessellations. What Sets This Book Apart * Complete Model Coverage - Poincaré disk, upper halfplane, and Klein projective models explained sidebyside with crystalclear mappings. * ProofDriven Approach - From the independence of Euclid's fifth postulate to Möbius transformation matrices, every theorem is demonstrated stepbystep. * Hyperbolic Trigonometry Toolkit - Laws of sines, cosines, and righttriangle 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 selfcontained reference for graduate study or independent exploration. Who Will Benefit * Mathematicians seeking a rigorous yet accessible foundation. * Physicists and cosmologists modeling negatively curved spacetime. * 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 nonEuclidean perspective. Equip yourself with the knowledge to navigate curved space, calculate precise distances, and design extraordinary tilings that only hyperbolic geometry makes possible.

• Format: Hardcover
• Language: English
• ISBN: B0F6597Z8J
• ISBN13: 9798281110143
• Release Date: April 2025
• Publisher: Independently published
• Length: 370 Pages
• Dimensions: 9.2" x 1.0" x 6.2"