
- 144 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Geometrical Kaleidoscope
About this book
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 onlypracticaland 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 circleproperties, 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.
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Information
Table of contents
- Cover
- Title Page
- Copyright page
- Contents
- Preface
- 1. Medians, Centroid, and Center of Gravity of a System of Points
- 2. Altitudes and the Orthocenter of a Triangle and Some of its Properties
- 3. The Orthic Triangle and Some of its Properties
- 4. The Angle Bisector of a Triangle and its Properties
- 5. The Area of a Quadrilateral
- 6. The Theorem of Ratios of the Areas of Similar Polygons
- 7. A Pivotal Approach: Applying Rotation in Problem Solving
- 8. Auxiliary Elements in Problem Solving
- 9. Constructions Siblings
- 10. Session of One Interesting Construction Problem
- 11. Morley’s Theorem
- Solutions to the Problems and Exercises
- References