Geometry of Curves: 1st Edition (Paperback) book cover

Geometry of Curves

1st Edition

By J.W. Rutter

Chapman and Hall/CRC

384 pages

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Description

Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving.

Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness.

The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations.

The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.

Reviews

"The examples, richly illustrated, make the book."

-D. V. Feldman, University of New Hampshire, in CHOICE, March 2001

Table of Contents

Preliminaries

Lines, Circles and Conics

Conics: General Position

Some Higher Algebraic and Transcendental Curves

Parameters, Tangents, Normals. Contact, Inflexions

Undulations

Cusps, Non-Regular Points

Curvature

Curvature Applications

Circle of Curvature

Limacons

Evolutes

Parallels, Involutes

Roulettes

Envelopes

Singular Points of Algebraic Curves

Projective Curves

About the Series

Chapman Hall/CRC Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT012000
MATHEMATICS / Geometry / General
MAT022000
MATHEMATICS / Number Theory