Excursions in Geometry
Dover Publications Inc. (Verlag)
9780486265308 (ISBN)
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.
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 ø
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
| Erscheint lt. Verlag | 28.3.2003 |
|---|---|
| Sprache | englisch |
| Maße | 137 x 216 mm |
| Gewicht | 205 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-13 | 9780486265308 / 9780486265308 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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