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.
Sprache
Verlagsort
Maße
Höhe: 216 mm
Breite: 137 mm
Dicke: 10 mm
Gewicht
ISBN-13
978-0-486-26530-8 (9780486265308)
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Schweitzer Klassifikation
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
