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 University of Munich. He is the author of approximately 40 peer-reviewed articles and the influential monograph Global Solutions of Reaction-Diffusion Systems (Lecture Notes in Mathematics 1072), published in 1984.
For nearly three decades, Dr. Rothe inspired undergraduate and graduate students at the University of North Carolina at Charlotte, teaching a wide range of mathematical disciplines including calculus, differential equations, geometry, graph theory, number theory, and abstract algebra. Though retired due to health reasons, Rothe continues his intellectual pursuits as an emeritus professor and author, committed to making complex mathematical theories comprehensible to a broader audience.
Mike Miller of Top Three Solutions, LLC, the publishing and distribution partner for Rothe’s work, emphasizes the significance of this volume: “This is not just a textbook. It’s an invitation to see space and structure from a completely different lens. Whether you’re a student, educator, or mathematical enthusiast, this book gives you the tools to visualize and understand hyperbolic geometry in a hands-on, logical way.”
With its combination of theoretical rigor and practical application, A Course in Old and New Geometry: Volume V serves as an essential resource for university mathematics departments, libraries, and self-motivated learners around the world. Rothe’s work bridges the gap between historical mathematical foundations and contemporary educational approaches, reaffirming the enduring relevance of geometric thinking in the 21st century.
To explore the book and begin your journey into hyperbolic geometry, visit the Amazon listing here: https://www.amazon.com/dp/B0DRW6LX19
For additional information, interview requests, or academic inquiries, please contact:
Mike Miller
Top Three Solutions, LLC
Email: info@topthreesolutions.com
About Top Three Solutions, LLC:
Top Three Solutions, LLC is a U.S.-based publishing and digital solutions company committed to promoting thought leadership and scholarly excellence across academic, technical, and professional domains. With a passion for education and innovation, the company partners with authors, researchers, and educators to bring complex ideas to market through expertly produced digital publications, print editions, and media outreach. Top Three Solutions helps amplify voices that contribute to scientific understanding, educational development, and public enrichment.
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