Book of Curves

by E. H. Lockwood

• ISBN13: 9780521044448
• ISBN10: 0521044448
• Format: Paperback
• Copyright: 2007-12-10
• Publisher: Cambridge University Press

Summary

This book opens up an important field of mathematics at an elementary level, one in which the element of aesthetic pleasure, both in the shapes of the curves and in their mathematical relationships, is dominant. This book describes methods of drawing plane curves, beginning with conic sections (parabola, ellipse and hyperbola), and going on to cycloidal curves, spirals, glissettes, pedal curves, strophoids and so on. In general, 'envelope methods' are used. There are twenty-five full-page plates and over ninety smaller diagrams in the text. The book can be used in schools, but will also be a reference for draughtsmen and mechanical engineers. As a text on advanced plane geometry it should appeal to pure mathematicians with an interest in geometry, and to students for whom Euclidean geometry is not a principal study.

Table of Contents

Frontispiece: section of the shell of a Pearly Nautilus fossil

Preface

Historical Introduction

Notation

Special Curves

The parabola

The ellipse

The hyperbola

The cardioid

The lima on

The astroid

The nephroid

The deltoid

The cycloid

The right strophoid

The equiangular spiral

The lemniscate of bernoulli

The tractrix and catenary

Ways of Finding New Curves

Conchoids

Cissoids

Strophoids

Roulettes

Pedal curves

Negative pedals

Glissettes

Evolutes and involutes

Spirals

Inversion

Caustic curves

Bipolar coordinates

Further reading

Glossary

Index of names

Index of subjects

Table of Contents provided by Publisher. All Rights Reserved.