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Boris Pritsker - Geometrical Kaleidoscope

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Boris Pritsker Geometrical Kaleidoscope
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    Geometrical Kaleidoscope
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Geometrical Kaleidoscope: summary, description and annotation

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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 thinkingwhat 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, Eulers line and circle properties, Fagnanos problem, and Napoleons 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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GEOMETRICAL
KALEIDOSCOPE
GEOMETRICAL
KALEIDOSCOPE
BORIS PRITSKER
DOVER PUBLICATIONS, INC.
MINEOLA, NEW YORK

Copyright

Copyright 2017 by Boris Pritsker

All rights reserved.

Bibliographical Note

Geometrical Kaleidoscopeis a new work, first published by Dover Publications, Inc., in 2017.

International Standard Book Number

ISBN-13 :978 -0 -486 -81241 -0

ISBN-10 :0 -486 -81241 -3

Manufactured in the United States by LSC Communications

81241301 2017

www.doverpublications.com

Contents
Preface

I cant do it anymore! My oldest son Alex put aside his geometry homework. And please dont tell me I would ever use this nightmare somewhere, somehow in my life! My heroic attempts to explain to him the solution of the problem involving the properties of the bisector of a triangle failed miserably. You should be ashamed of yourself. I recently published an article about the properties of the bisector (see ) and you dont have the patience even to listen to me. I made this final argument trying to get him to pay attention to the subject. All of a sudden there was a spark in his eyes and he looked at me with definite expression of interest on his face.

May I see it?

Sure, here it is. I was very proud of myself.

He looked at the article, read a few paragraphs, and then patiently let me finish the explanation of the solution to his homework problem.

Could you please make a copy of this article for me? he asked when we finished working on the homework. It was a real pleasure to hear something like this from him. Obviously the kid wanted to show the copy to his friends at school and gain some popularity because of his fathers math skills.

In a few days he got back from school and told me about getting an A on his most recent geometry test. My efforts had finally paid off, and I was very happy for a few days. Then I met his school friend. He told me the true story about how the A was earned.

Alex is a very good tennis player. His interests have always been in sports and he has never been a great math student. He has compensated for his lack of knowledge and desire to learn the subject by making jokes and telling funny stories during the classes. Teachers always had a tough time trying to keep him quiet. By the way, he never mentioned in a classroom that his dad used to be a professional mathematician.

That day he was more annoying to the teacher than usual. At the end of the session Alex announced that he did not have to do the assigned homework, because he had just studied those properties with his dad, while reading his published article in a math magazine. It was obviously hard to imagine that he was telling the truth.

I am sick and tired of your fantasies. Ill teach you a lesson this time. If you bring that article into class tomorrow, youll get an A on the next test without even taking it. But if you dont have it, your homework assignment will be tripled and you will need to hand in every single problem to me, the teacher said.

The teachers desire to make fun of this annoying kid was quite understandable.

You know the end of the story. The teacher kept his word.

That was my sons only experience of using geometry in real life so far. I have to admit, that even though he did not succeed in geometry class, he did apply the methods I was teaching him.

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