Geometrical Kaleidoscope (Second Edition)

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The goal of the book is to provide insight into many enjoyable and fascinating aspects of geometry, and to reveal interesting geometrical properties. The chapters cover the myriad of little-known material not covered well in high school courses along with well-known classic topics 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.In the 2nd edition of the book there are many new ideas and additional explanations provided to easier understand the solutions of problems and better relate many seemingly unrelated topics. New chapter 'Alternative views at 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 missing in the first edition of the book.