This comprehensive guide to advanced geometric principles offers a deep exploration of both Euclidean and non-Euclidean approaches to geometry. Written by renowned Polish mathematician Prof. Marek Krawczyk, this book bridges the gap between theoretical concepts and practical applications.
Advanced Geometry Principles is designed for undergraduate and graduate students of mathematics, as well as teachers and enthusiasts who wish to deepen their understanding of geometric concepts. The book takes a rigorous yet accessible approach to advanced geometry, connecting classical principles with modern applications.
Beginning with a review of fundamental Euclidean concepts, the book gradually introduces non-Euclidean geometries, exploring their axioms, models, and implications. Readers will discover how different geometric systems relate to one another and how they can be applied to solve real-world problems.
What sets this book apart is its emphasis on visualization and intuition. Complex concepts are illustrated through clear diagrams, and each theoretical development is accompanied by concrete examples. The inclusion of historical context provides insight into the evolution of geometric thinking throughout the centuries.
The problem sets at the end of each chapter progress from standard applications to challenging extensions that encourage deeper exploration. Complete solutions are provided for odd-numbered problems, with hints for the even-numbered ones.
This edition includes a new appendix on computational geometry and its applications in computer graphics, reflecting the growing importance of geometry in technological fields.
| Language | English |
|---|---|
| Hardcover | 612 pages |
| Publisher | Warsaw Academic Press |
| Edition | 3rd Edition (2023) |
| ISBN | 978-83-7456-823-5 |
| Dimensions | 18.5 × 24 cm |
As a mathematics professor, I've found this book to be an invaluable resource both for my research and for teaching advanced courses. The balance of rigor and intuition is perfect, and the historical context adds depth to the material. I particularly appreciate the extensive problem sets and the new section on computational geometry.
I'm a graduate student in mathematics, and this book has completely transformed my understanding of geometry. The illustrations are exceptionally clear, and the progression from basic to advanced concepts is logical and well-paced. I've been recommending it to everyone in my program!
The theoretical foundation presented in this book is superb, and Krawczyk's insights are brilliant. My only critique is that some sections, particularly those on differential geometry, could benefit from additional worked examples. Nevertheless, it remains one of the best advanced geometry texts available.
