Angles, Areas, and Axioms: A Journey Through Euclidean Geometry

California, LA —  Franz Rothe's A Course in Old and New Geometry II: Basic Euclidean Geometry offers a meticulously crafted journey through the fundamental principles of Euclidean geometry, seamlessly blending classical concepts with modern axiomatic perspectives. This second volume, as the author describes, adopts a more pedagogical and elementary approach, making it an accessible yet rigorous exploration for students and enthusiasts alike.

The book embarks on its exploration with foundational theorems, starting with the elegant simplicity of Thales' theorem concerning angles inscribed in a semicircle. From this cornerstone, Rothe skillfully guides the reader through Euclid's related theorems on angles within circles, laying a solid groundwork in basic geometric relationships. The text progresses systematically, delving into the intricacies of similarity, a concept crucial for understanding scaling and proportion in geometric figures.

“The book offers a detailed exploration of fundamental mathematical constructions, employing classic tools like the straightedge, structures, and compass. Organized as a series of problems and solutions, it systematically addresses specific constructions and concepts. The content is presented with clear headings and subheadings, guiding the reader through each topic. Each problem follows a structured format, presenting a step-by-step solution.” — Stephen Munich, Global Literary Journey Book Review.

“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.” — Alexa Berdin, Book Browse Reflection Book Review.

“Rothe's writing is clear and engaging, making complex ideas accessible to a wide audience. His explanations are thorough, yet concise, allowing readers to grasp intricate concepts without feeling overwhelmed. It includes diagrams and illustrations throughout the book that significantly enhances the learning experience, and provides visual aids that complement the text and clarify geometric, trigonometry, and other math relationships.” — Patrick Timms, The Reader’s Forum Book Review.

In essence, "A Course in Old and New Geometry II: Basic Euclidean Geometry" serves as a comprehensive and insightful guide to the fundamental principles of Euclidean geometry. By carefully weaving together classical theorems with modern axiomatic treatments, Franz Rothe has created a text that is both educationally sound and intellectually stimulating, offering a rich and nuanced understanding of this foundational area of mathematics.

You can check and read the full book reviews at their websites: Global Literary Journey Book Review, Book Browse Reflection, and The Reader’s Forum Book Review.

Grab a copy of A Course in Old and New Geometry II: Basic Euclidean Geometry in bookstores and other online outlets like Barnes & Noble, and more bookstores.

A Course in Old and New Geometry II: Basic Euclidean Geometry

Written by Franz Rothe

Paperback |

Hardcover |

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