Geometrical Kaleidoscope

A high school course in geometry and some curiosity and enthusiasm for the subject are the only prerequisites for tackling this original exploration into the field, long a favorite for readers whose interest in math is not only practical and educational, but also recreational. The book centers on geometric thinking—what it means, how to develop it, and how to recognize it. Readers will discover fascinating insights into many aspects of geometry and geometrical properties and theorems, including such classic examples as Archimedes' law of the lever, Euler's line and circle properties, Fagnano's problem, and Napoleon's theorem.
The volume is divided into sections on individual topics such as "Medians of a Triangle," and "Area of a Quadrilateral." Chapters typically begin with some interesting geometrical history, some relevant theorems, and some worked examples of problems followed by problems for readers to figure out for themselves (solutions are provided at the end of the book). The result is a many-faceted exploration, rather like a kaleidoscope, focusing on the mysteries and the pleasures of geometry.

Kiev native Boris Pritsker worked as a math teacher and in a special school for gifted and talented high school students with advanced programs in algebra, geometry, trigonometry, and calculus. His teaching experience led to his publication of numerous articles and problems in mathematical magazines in the former Soviet Union, United States, Australia, and Singapore.

Preface1. Median of a Triangle2. Altitudes and Orthocenter of a Triangle3. Orthic Triangle and Its Properties4. Bisector of a Triangle and It Properties5. Area of a Quadrilateral6. Theorem of Ratios of the Area of Similar Polygons7, Applying Rotation in Problem Solving8.Auxiliary Elements in Problem Solving9. Constructions-Siblings10. Session of One Interesting Construction Problem11. Morley's Theorem.Solutions and Answers to the Chapter Problems.References