Geometric inequalities / by Nicholas D. Kazarinoff.

Format:

Book

Author/Creator:

Kazarinoff, Nicholas D.

Series:

Anneli Lax New Mathematical Library ; no. 4

Language:

English

Subjects (All):

Geometry, Plane.

Inequalities (Mathematics).

Physical Description:

1 online resource (132 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington, DC : Mathematical Association of America, 1961.

Language Note:

English

Summary:

Anybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students.

Contents:

Front Cover

Geometric Inequalities

Copyright Page

CONTENTS

Preface

Chapter 1. Arithmetic and Geometric Means

1.1 Fundamentals

1.2 The Theorem of Arithmetic and Geometric Means

Chapter 2. Isoperimetric Theorems

2.1 Maxima and minima

2.2 Isoperimetric theorems for triangles

2.3 Isoperimetric theorems for polygons

2.4 Steiner's attempt

Chapter 3. The Reflection Principle

3.1 Symmetry

3.2 Dido's problem

3.3 Steiner symmetrization

3.4 Conic sections

3.5 Triangles

Chapter 4. Hints and Solutions

Index of Numhered Theorems

Back Cover.

Notes:

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

Description based on print version record.

ISBN:

0-88385-922-X

OCLC:

929120472