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Geometrical kaleidoscope

Author: Boris Pritsker
Publisher: Mineola : Dover Publications, 2017. ©2017
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Geometrical Kaleidoscope.
Dover Pubns 2017
(OCoLC)962232295
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Boris Pritsker
ISBN: 9780486824819 0486824810
OCLC Number: 1002468922
Description: 1 online resource (xi, 124 pages)
Contents: Medians, centroid, and center of gravity of a system of points --
Altitudes and the orthocenter of a triangle and some of its properties --
The orthic triangle and some of its properties --
The angle bisector of a triangle and its properties --
The area of a quadrilateral --
The theorem of ratios of the areas of similar polygons --
A pivotal approach: applying rotation in problem solving --
Auxiliary elements in problem solving --
Constructions siblings --
Session of one interesting construction problem --
Morley's theorem.
Responsibility: Boris Pritsker.

Abstract:

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, inclusing 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.

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