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Title: A New Window into Hyperbolic Space Franz Rothe Publishes Volume V of A Course in Old and New Geometry

United States, 14th May 2025 — Renowned mathematician and emeritus professor Franz Rothe continues his acclaimed exploration of geometric theory with the release of A Course in Old and New Geometry: Volume V – Hyperbolic Geometry, now available on Amazon at https://www.amazon.com/dp/B0DRW6LX19.This fifth volume in Rothe’s foundational series provides a rigorous and enlightening journey into hyperbolic geometry, one of the most fascinating and non-intuitive branches of mathematics. Carefully structured to blend classical principles with modern insights, this volume brings clarity to a field often reserved for advanced specialists. Through the use of both the Poincaré and Klein disk models, Rothe offers a compelling and accessible approach to hyperbolic constructions using traditional Euclidean tools such as the straightedge and compass.Returning to Hilbert’s original axioms from his seminal Foundations of Geometry, Rothe reconstructs the logical architecture that underpins non-Euclidean geometry. He offers students and scholars a precise framework for understanding the nature of hyperbolic space through asymptotic rays and ultimately guides the reader toward a reconstruction of the Poincaré disk model using Hilbert’s axiomatic approach. The final section of the book transitions into Gauss’ differential geometry, offering a natural progression toward the concept of the pseudosphere—a surface of constant negative curvature—giving readers a tangible representation of hyperbolic space.Franz Rothe, whose academic journey began at the University of Tuebingen in Germany, brings decades of scholarly and teaching experience to this work. After receiving his doctorate, he earned his Habilitation and venia legendi from both the University of Tuebingen and the Ludwig Maximilian...

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