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GEOMETRICAL KALEIDOSCOPE (SECOND EDITION)
by 作者: Boris Pritsker (Author)
Publisher Finelybook 出版社: World Scientific Publishing Company
Publication Date 出版日期: 2024-04-22
Language 语言: English
pages 页数: : 180 pages
ISBN-10 书号: 9811285276
ISBN-13 书号: 9789811285271
Book Description
The goal of the book is to provide insight into many enjoyable and fascinating aspects of geometry, and to reveal interesting geometrical properties. The emphasis is on the practical applications of theory in the problem-solving process. The chapters cover a myriad of topics among which are the classic theorems and formulas such as Archimedes' Law of the Lever, the Pythagorean Theorem, Heron's formula, Brahmagupta's formula, Appollonius's Theorem, Euler's line properties, the Nine-Point Circle, Fagnano's Problem, the Steiner-Lehmus Theorem, Napoleon's Theorem, Ceva's Theorem, Menelaus's Theorem, Pompeiu's Theorem, and Morley's Miracle. The book focuses on geometric thinking ― what it means, how to develop it, and how to recognize it. "Geometrical Kaleidoscope" consists of a kaleidoscope of topics that seem to not be related at first glance. However, that perception disappears as you go from chapter to chapter and explore the multitude of surprising relationships, unexpected connections, and links. Readers solving a chain of problems will learn from them general techniques, rather than isolated instances of the application of a technique. In spite of the many problems' challenging character, their solutions require no more than a basic knowledge covered in a high school geometry curriculum. There are plenty of problems for readers to work out for themselves (solutions are provided at the end of the book).
In the 2nd edition of the book there are many new ideas and additional explanations that help the reader better understand the solutions of problems and connect the chapters to one another. A new chapter "Alternative proofs of the Pythagorean Theorem" is added. It covers seven different proofs of the famous theorem and discusses its generalizations and applications. There is also Appendix and Index added, which were missing in the first edition of the book.
About the Author
Pritkser is the author of the internationally acclaimed books Geometrical Kaleidoscope, (1st edition) Dover Publications, 2017, The Equations World, Dover Publications, 2019, Mathematical Labyrinths. Pathfinding, World Scientific, 2021 and Expanding Mathematical Toolbox: Interviewing Topics, Problems, and Solutions, Chapman and Hall/CRC; 2023.
