Geometry Revisited

Geometry Revisited presents classical Euclidean geometry through a systematic exploration of key theorems and relationships. The authors build from fundamental concepts to advanced geometric principles, including extensive coverage of triangle centers, circles, collinearity, and more. The text incorporates historical context and biographical details about mathematicians who made crucial contributions to geometric understanding. Problems and exercises follow each section, allowing readers to test their grasp of the material through practical application. Written for high school and undergraduate students, the book serves as both a rigorous introduction to geometry and a bridge to more advanced mathematical concepts. The clear progression and precise mathematical language make complex ideas accessible while maintaining mathematical rigor. At its core, this text demonstrates the elegance and interconnectedness of geometric principles while highlighting the foundational role of classical geometry in mathematical thinking. The work stands as a testament to geometry's enduring relevance in mathematics education.

Readers describe this as a challenging but rewarding text for those with a strong mathematical foundation. Many note it works best as a supplement rather than a primary textbook. Likes: - Clear explanations of advanced concepts - Historical context and elegant proofs - Excellent problems that build understanding - Concise presentation without unnecessary material Dislikes: - Requires significant prior knowledge - Some proofs skip steps that frustrate beginners - Small font size and dense layout - Limited illustrations One reader noted: "Not for the faint of heart - assumes comfort with mathematical thinking and notation. But the insights are worth the effort." Ratings: Goodreads: 4.26/5 (50 ratings) Amazon: 4.5/5 (28 ratings) Multiple reviewers recommend reading alongside other geometry texts to fill in foundational gaps. Several mention successfully using it for competition math preparation and advanced high school study.

Mathematical Discovery by George Pólya This book develops geometric intuition through problem-solving methods and mathematical reasoning techniques.

Proofs Without Words by Roger B. Nelsen This collection presents geometric theorems through visual proofs that reveal mathematical relationships without formal algebraic arguments.

Journey Through Genius by William Dunham The book examines great geometric theorems through history, connecting mathematical concepts to their original discoverers and historical context.

The Elements by Euclid This foundational text presents geometric principles in a systematic, axiomatic approach that influences mathematical thinking to this day.

What Is Mathematics? by Richard Courant The text explores geometric concepts alongside other mathematical fields, emphasizing connections and fundamental principles.

🔷 H.S.M. Coxeter was nicknamed "The King of Geometry" and continued publishing mathematical papers well into his 90s, with his last paper appearing when he was 96 years old. 🔷 The book revives classical Euclidean geometry at a time when "New Math" was becoming prominent, showing how traditional geometric methods remain powerful and elegant. 🔷 Many of the problems and theorems discussed in the book have connections to the International Mathematical Olympiad (IMO), making it a valuable resource for competitive mathematics students. 🔷 Co-author Samuel L. Greitzer was the founder of the USA Mathematical Olympiad and helped establish many of the mathematical competitions that are still running today. 🔷 The book explores nine distinct geometric topics, including the famous "Nine-Point Circle" theorem, which states that for any triangle, the feet of the altitudes, the midpoints of the sides, and the midpoints of the segments from the orthocenter to the vertices all lie on a single circle.