Geometric Transformations II

✍ Scribed by Yaglom, Isaak Moiseevich

• Publisher: Mathematical Association of America (MAA)
• Year: 1968
• Tongue: English
• Leaves: 202
• Series: New Mathematical Library
• Category: Library

✦ Synopsis

This book is the sequel to Geometric Transformations I which appeared in this series in 1962. Part I treas length-preserving transformations, this volume treats shape-preserving transformations; and Part III treats affine and protective transformations. These classes of transformations play a fundamental role in the group-theoretic approach to geometry.As in the previous volume, the treatment is direct and simple. The introduction of each new idea is supplemented by problems whose solutions employ the idea just presented, and whose detailed solutions are given in the second half of the book.

✦ Table of Contents

Front Cover......Page 1
Title page......Page 4
Copyright Page......Page 5
Note to the Reader......Page 8
Contents......Page 12
Translator’s Preface......Page 14
From the Author’s Preface......Page 15
Introduction. What is Geometry?......Page 17
1. Central similarity (homothety)......Page 22
2. Spiral similarity and dilative reflection. Directly similar and oppositely similar figures......Page 49
1. Systems of mutually similar figures......Page 76
2. Applications of isometries and of similarities to the solution of maximum-minimum problems......Page 97
Chapter One. Classification of similarities......Page 100
Chapter Two. Further applications of isometries and similarities......Page 154

✦ Subjects

Science;Mathematics;Geometry