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Science & Technology

April 25, 2025

Foundations of Geometry: A Comprehensive Guide to Classical Constructions

by Franz Rothe

Reviewed by Alexa Berdin

Book Browse Reflection

The book provides an in-depth examination of essential constructions in Euclidean geometry, trigonometry, the Pythagorean theorem, algebra, and related topics, utilizing traditional instruments like a straightedge and compass. It is organized as a collection of problems and solutions, each focusing on a particular mathematical construction or property.

It is well-structured, beginning with definitions and progressing to specific problems along with their solutions. Each problem is presented clearly, followed by a detailed, step-by-step solution, making it accessible for readers who have a basic understanding of geometry. It encompasses a broad array of fundamental constructions, such as angle bisection, perpendiculars, reflections, equilateral triangles, perpendicular bisectors, and parallels. Additionally, it offers various methods for constructing parallels, highlighting the adaptability of Euclidean tools.

This book thoroughly investigates the foundational principles of planar Euclidean geometry, trigonometry, the Pythagorean theorem, and circle measurements. It begins with Euclid's ancient viewpoint and transitions into a comprehensive introduction to the modern axiomatic framework established by Hilbert, which is now widely accepted in the contemporary mathematics community. The material is presented with an emphasis on modern interpretations, ensuring it remains relevant and clear for today's audience.

The book also makes a concerted effort to enhance explanations visually. Annotations and additional checks bolster the reliability of the methods and provide deeper insights into the concepts discussed.

In summary, this educational book serves as a thorough and well-organized guide to fundamental mathematical constructions and formulas. It is ideal for readers with a solid foundation in geometry and trigonometry. Its strengths lie in its detailed explanations, extensive coverage, and mathematical rigor, making it an excellent resource for both students and educators in mathematics.

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