Geometry Revisited

Geometry Revisited is a mathematical text that presents classical geometry topics through a modern lens. The book was written by renowned mathematician H.S.M. Coxeter in collaboration with Samuel L. Greitzer. The work systematically covers fundamental concepts including triangles, circles, collinearity, and geometric transformations. Each chapter builds upon previous material while introducing increasingly complex theorems and their proofs. Through diagrams, examples, and clear explanations, the text demonstrates connections between different geometric principles. The progression moves from basic Euclidean geometry through projective geometry and inversive geometry. This text represents both a return to foundational mathematical concepts and an advancement of geometric understanding through modern perspectives. Its enduring influence stems from its ability to bridge classical and contemporary approaches to the subject.

Readers describe this as a clear and rigorous presentation of classical geometry theorems and their proofs. Math students and teachers appreciate how it connects introductory topics to more advanced concepts. Liked: - Compact but thorough coverage of key theorems - Historical notes provide context - Well-chosen exercises reinforce concepts - Bridges high school and college-level geometry Disliked: - Some proofs move too quickly for beginners - Several readers note it requires strong math foundation - Limited illustrations compared to modern texts Ratings: Goodreads: 4.29/5 (56 ratings) Amazon: 4.6/5 (31 ratings) From reviews: "Perfect companion to high school geometry" - Amazon reviewer "Dense but rewarding for serious math students" - Goodreads review "Would have benefited from more diagrams" - Math forum comment "Not for casual reading, requires work with pencil and paper" - Math teacher review

Introduction to Geometry by H.S.M. Coxeter A deeper exploration into geometric principles with emphasis on transformations, projective geometry, and non-Euclidean concepts.

Journey Through Genius: The Great Theorems of Mathematics by William Dunham The historical development of geometric proofs and theorems unfolds through detailed mathematical derivations and original sources.

Regular Polytopes by H.S.M. Coxeter The mathematical structures of regular geometric figures in multiple dimensions receive systematic treatment through group theory and combinatorial methods.

The Real Projective Plane by H.S.M. Coxeter The fundamental concepts of projective geometry build from basic principles to advanced theorems with rigorous mathematical development.

Ruler and Compass by Andrew Sutton Classical geometric constructions connect to modern algebraic concepts through step-by-step mathematical demonstrations.

🔷 H.S.M. Coxeter was known as "The King of Geometry" and mentored young John Conway, who later became famous for Conway's Game of Life and numerous mathematical discoveries. 🔷 Geometry Revisited was co-authored with Samuel L. Greitzer and published in 1967, making complex geometric concepts accessible to high school students and teachers alike. 🔷 The book revived interest in classical Euclidean geometry at a time when "New Math" was pushing more abstract approaches in mathematics education. 🔷 Coxeter was a pacifist who spent World War II teaching at the University of Toronto, where he remained for his entire career, despite having been born and educated in England. 🔷 Many of the geometric principles discussed in the book have practical applications in modern fields like computer graphics, crystallography, and architectural design.