Elementary Geometry from an Advanced Standpoint

Elementary Geometry from an Advanced Standpoint presents geometric principles through the lens of modern mathematics. The book bridges the gap between basic high school geometry and advanced mathematical concepts taught at the college level. The text examines fundamental geometric ideas including congruence, similarity, area, and the parallel postulate. Moise structures the material to show how these concepts connect to abstract algebra, real numbers, and formal mathematical systems. The book includes detailed proofs and emphasizes the logical foundations that underpin geometric theorems. Each chapter contains practice problems that reinforce key concepts through hands-on application. This work serves as both a teaching text and a deeper exploration of how basic geometric principles form the basis for more complex mathematics. The approach demonstrates the evolution from concrete spatial reasoning to abstract mathematical thinking.

Readers consistently note this book serves math teachers preparing to teach geometry rather than students learning geometry for the first time. Many reviewers highlight the rigorous treatment of axioms and proofs. Likes: - Clear explanations of why geometric principles work, not just how - Thorough coverage of transformational geometry - Effective bridge between high school and college-level geometry - Strong focus on pedagogical approaches for teachers Dislikes: - Dense writing style requires multiple careful readings - Some find the level of abstraction excessive for practical teaching - Limited exercises and examples - Print quality issues in newer editions Ratings: Goodreads: 4.13/5 (15 ratings) Amazon: 4.3/5 (12 reviews) Notable comment from math teacher on Amazon: "The chapter on area is worth the price alone - it finally helped me understand how to properly explain area calculations to students using first principles."

Introduction to Geometry by H.S.M. Coxeter A rigorous treatment of classical Euclidean geometry that connects elementary concepts to advanced geometric theory and transformations.

Geometry: A Comprehensive Course by Dan Pedoe The text bridges the gap between basic high school geometry and university-level geometry through detailed proofs and historical development of geometric concepts.

Geometry Revisited by H.S.M. Coxeter, Samuel L. Greitzer The work presents classical geometry theorems and problems with connections to modern mathematical concepts and techniques.

College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle by Nathan Altshiller-Court The book develops Euclidean geometry from first principles while incorporating modern geometric methods and advanced triangle properties.

Roads to Geometry by Edward C. Wallace and Stephen F. West The text examines geometry through multiple approaches including synthetic, analytic, and transformational methods while maintaining connections to elementary concepts.

🔷 Edwin Moise co-authored several influential mathematics textbooks with Floyd L. Downs Jr., including "Geometry" (1964), which became a standard text in American high schools for decades. 🔷 The book bridges the gap between high school geometry and college-level mathematics by exploring the foundations and deeper meanings behind familiar geometric concepts taught in secondary education. 🔷 Moise served as president of the Mathematical Association of America (1967-1968) and was known for his contributions to mathematics education reform during the "New Math" movement of the 1960s. 🔷 The text presents both synthetic geometry (based on axioms and proofs) and analytic geometry (using coordinates), showing how these approaches complement each other in understanding geometric concepts. 🔷 The book's treatment of non-Euclidean geometry helps readers understand why certain axioms, like the parallel postulate, are necessary in Euclidean geometry – a topic rarely covered in standard high school texts.