Excursions in Geometry
Published on 28. March 2003
Book
Paperback/Softback
192 pages
978-0-486-26530-8 (ISBN)
Description
Topics including harmonic division and Apollonian circles, inversive geometry, the hexlet, conic sections, projective geometry, the Golden Section and angle trisection are addressed in a way that brings out the true intellectual excitement inherent in each. Also included: some unsolved problems of modern geometry. Notes. References. 132 line illustrations.
More details
Language
English
Place of publication
United States
Dimensions
Height: 219 mm
Width: 138 mm
Thickness: 10 mm
Weight
204 gr
ISBN-13
978-0-486-26530-8 (9780486265308)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
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
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