Advanced Euclidean Geometry
Description
Advanced Euclidean Geometry is a definitive textbook that takes students and enthusiasts beyond the basics of classical geometry into a deeper understanding of Euclidean principles and their applications.
This acclaimed work by Professor Marian Kowalski, one of Poland's leading geometers, builds systematically from foundational concepts to sophisticated theorems. The book's strength lies in its meticulous approach to proofs, its rich variety of problems, and its emphasis on geometric intuition.
Key Features:
- Comprehensive coverage of advanced topics including triangle centers, power of a point, harmonic ranges, and projective methods in Euclidean geometry
- Over 500 carefully selected problems ranging from straightforward applications to challenging Olympiad-level questions
- Historical notes highlighting the development of geometric concepts and the contributions of Polish mathematicians
- Detailed illustrations and diagrams that clarify complex spatial relationships
- Extensive bibliography for further reading and exploration
This English translation preserves the clarity and precision of Professor Kowalski's original work while making it accessible to an international audience. The book is suitable for advanced high school students, undergraduates, mathematics teachers, and anyone seeking to deepen their understanding of Euclidean geometry.
Table of Contents
- Fundamentals of Euclidean Geometry
- Axiom Systems
- Basic Constructions
- Congruence and Similarity
- Triangles: Advanced Properties
- Centers of Triangles
- The Euler Line
- The Nine-Point Circle
- Ceva's and Menelaus' Theorems
- Circles and Power
- Power of a Point
- Radical Axis and Radical Center
- Coaxial Circles
- Transformational Geometry
- Isometries
- Similarities
- Inversions
- Projective Methods in Euclidean Geometry
- Cross-Ratio
- Harmonic Ranges and Pencils
- Pole and Polar
- Advanced Problems and Applications
- Olympiad-Level Problems
- Applications to Physics and Engineering
- Computational Geometry
- Appendices
- Historical Notes
- Further Reading
- Solutions to Selected Problems
About the Author
Professor Marian Kowalski is a renowned mathematician and educator who has dedicated his career to the study and teaching of geometry. Born in Kraków, Poland in 1956, he received his doctorate from the University of Warsaw with a thesis on classical geometric problems.
For over thirty years, Prof. Kowalski has taught at the Warsaw University of Technology, where he developed the innovative teaching methods featured in this book. He has served as the coach for Poland's International Mathematical Olympiad team, contributing to their consistently strong performance in geometric problem solving.
His research focuses on the intersections between classical Euclidean geometry and modern approaches, particularly in applications to computational geometry and computer graphics. Prof. Kowalski has published over 60 papers in international journals and is the author of five textbooks widely used in Polish universities.
In 2018, he was awarded the Polish Mathematical Society's Medal for Outstanding Contributions to Mathematics Education. This book represents the culmination of his decades of experience in teaching advanced geometry to students at all levels.
