BOOK REVIEW
in
Science & Technology
February 12, 2025
A Problem-Driven Exploration of Euclidean and Hyperbolic Geometry: Franz Rothe's Rigorous Approach to Mathematical Constructions
by Franz Rothe
Reviewed by Debbie Chow
Book Browse Reflection
Franz Rothe's A Course in Old and New Geometry II: Basic Euclidean Geometry is a detailed mathematical exposition on various formulated math constructions and problems, primarily focused on Euclidean, hyperbolic geometry, mathematical formulas and concepts, trigonometry, and mathematical theories.
It is a comprehensive exploration structured around problems, claims, and constructions, with accompanying figures and explanations. The book demonstrates a strong mathematical rigor and is aimed at an audience with a solid foundation in geometry, such as advanced students, educators, or researchers in mathematics.
Further, it provides step-by-step instructions for constructions, such as constructing triangles, circles, and squares, with specific angles or solving problems involving altitudes and circumcircles. It uses classical mathematical principles, such as propositions, to justify claims and constructions, which adds depth and historical context to the explanations.
Then, it is problem-driven, encouraging readers to engage actively with the material. The use of precise mathematical language and references to mathematical propositions ensures that it adheres to a high standard of mathematical rigor.
Overall, it is a well-crafted and rigorous exploration of mathematical constructions, with a strong emphasis on problem-solving and theoretical understanding. It excels in mathematical depth and clarity for an advanced audience. With these learnings, the book could appeal to a wider range of readers while maintaining its academic rigor.