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Author:   C. Stanley Ogilvy
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Edition:   New edition
Dimensions:   Width: 13.70cm , Height: 1.00cm , Length: 21.60cm
Weight:   0.205kg
ISBN:  

9780486265308

ISBN 10:   0486265307
Pages:   192
Publication Date:   28 March 2003
Audience:   General/trade ,  General
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Introduction 1 A bit of background A practical problem A basic theorem Means 2 Harmonic division and Apollonian circles Harmonic conjugates The circle of Apollonius Coaxial families 3 Inversive geometry Transformations Inversion Invariants Cross-ratio 4 Application for inversive geometry Two easy problems Peaucellier's linkage Apollonius' problem Steiner chains The arbelos 5 The hexlet The conics defined A property of chains Soddy's hexlet Some new hexlets 6 The conic sections The reflection property Confocal conics Plan sections of a cone A characteristic of parabolas 7 Projective geometry Projective transformations The foundations Cross-ratio The complete quadrangle Pascal's Theorem Duality 8 Some Euclidean topics A navigation problem A three-circle problem The Euler line The nine-point circle A triangle problem 9 The golden section The pentagram Similarities and spirals The regular polyhedra The continued fraction for o 10 Angle trisection The unsolved problems of antiquity Other kinds of trisection 11 Some unsolved problems of modern geometry Convex sets and geometric inequalities Malfatti's problem The Kakeya problem Notes Index

Reviews

A follow-up to his Excursions in Number Theory, this book is intended to demonstrate that geometry is really not so dull as you may have thought it. It actually requires a considerable prior interest in and inclination for mathematical recreation, since it takes one beyond the trivial theorems proved within the framework of the usual geometry course to the startlingly good ones just around the corner. The excursion progresses through Harmonic division, Apollonian circles, inversion geometry, the hexlet, conic sections, projective geometry, the Golden Section, and angle trisection, with side jaunts to some of geometry's classic unsolved problems. The few practical applications provided are not exactly the sort of problems you'd run into every day. Though the material does not require extensive new definitions and abstractions, and the tools are the familiar straightedge and compass, it is definitely not mathematics for the millions. (Kirkus Reviews)

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