Geometric transformations III / by I.M. Yaglom ; translated from the Russian by A. Shenitzer.

Format:

Book

Author/Creator:

I︠A︡glom, I. M. (Isaak Moiseevich), 1921-1988.

Contributor:

Shenitzer, Abe.

Series:

Anneli Lax new mathematical library ; v. 24.

Anneli Lax new mathematical library ; 24

Standardized Title:

Geometricheskie prebrazovanii︠ì︡a, 3. English

Language:

English

Subjects (All):

Inversions (Geometry).

Geometry, Modern.

Physical Description:

1 online resource (viii, 237 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Geometric transformations 3

Place of Publication:

Washington, D.C. : Mathematical Association of America, 1973.

Language Note:

English

Summary:

This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in this series, but can be studies independently. It is devoted to the treatment of affine and projective transformations of the plane these transformations include the congruencies and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the principles of affine and projective geometry may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.

Contents:

Contents

Translator's Preface

From the Author's Preface

Introduction. What is Geometry? (Final Essay)

Chapter I. Affine and Projective Transformations (Affinities and Projectivities)

1. Parallel projection of a plane onto a plane : Affine transformations of the plane

2. Central projection of a plane onto a plane : Projective transformations of a plane

3. Central projections which carry a circle into a circle: Stereographic projections

4. Reciprocation (polarity) of the plane : Principle of duality

5. Projective transformation of a line and a circle : Straightedge construction

Supplement

Non-Euclidean Geometry of Lobachevsky-Bolyai (Hyperbolic Geometry)

Solutions

Chapter One. Affine and projective transformations

Supplement. Hyperbolic geometry.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Description based on print version record.

ISBN:

0-88385-939-4

OCLC:

923220176