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Geometrical Kaleidoscope: 33 (Problem Solving in Mathematics and Beyond): 2nd Edition

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Book Details
Language
English
Publishers
World Scientific Publishing Co Pte Ltd; Second edition (22 April 2024)
Weight
0.26 KG
Publication Date
24/03/2024
ISBN-10
9811285608
Pages
180 pages
ISBN-13
9789811285608
Dimensions
15.24 x 1.02 x 22.86 cm
SKU
9789811285608
Author Name
Boris Pritsker (Author)
Boris Pritsker was born in Kiev, Ukraine. He studied mathematics at Kiev State Pedagogical University, which he graduated summa cum laude with US equivalent of B.S. degree in math/education. Pritsker worked as a math teacher in high schools including a special math-oriented school for gifted and talented students with advanced programs in algebra, geometry, trigonometry, and calculus. He developed educational seminars for studying classic math problems encouraging students to look for alternative solutions. He also trained school math teams for participation in math competitions; several students from these math teams won the prestigious local and regional math Olympiad contests. After immigrating to the United States, Pritsker earned an MBA degree magna cum laude from the Graduate school of Baruch College, City University of New York. Pritsker is a licensed CPA in New York State. For the past two decades he has been employed by CBIZ Marks Paneth LLC, New York City accounting and consulting firm, where he became a director. Never leaving behind his curiosity and devotion to mathematical education development and research, through the years Pritsker has been exploring various challenging and interesting topics in Euclidean geometry, algebra, and pre-calculus which he offered for publication in math educational journals. He has published problems and articles in the Soviet Union, USA, Singapore, and Australian magazines such as “Математика в школе” (in Russian), (Mathematics in School), NY State Mathematics Teachers’ Journal, Quantum, New England Mathematics Journal, Mathematics and Informatics, Journal of Recreational Mathematics, Mathematics Teacher, Mathematics Competitions (journal of the World Federation of National Mathematics Competitions).Pritsker authored four internationally acclaimed mathematics books “Geometrical Kaleidoscope”, Dover Publications, 2017, “The Equations World”, Dover Publications, 2019, “Mathematical Labyrinths. Pathfinding”, World Scientific, 2021, and "Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions", CRC Press, Taylor & Francis Group, 2023. The books have been featured with positive reviews in the Mathematical Association of America web-site. “Geometrical Kaleidoscope” was assigned a BLL rating and the MAA Basic Library List Committee suggested that undergraduate mathematics libraries consider the book for acquisition. "The Equations World" made it to List of Top Ten Best Dover Math Books (https://nicic.org/best-dover-math-book/) and “Mathematical Labyrinths. Pathfinding” made it to Book Authority's Best New Problems Solving e-books list and Best Logic Mathematics books of all time list (https://bookauthority.org/award/Mathematical-Labyrinths-Pathfinding/9811230072/best-logic-mathematics-books).Read more about this authorRead less about this author
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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 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. .

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