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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
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
| Erscheinungsjahr: | 1990 |
|---|---|
| Medium: | Taschenbuch |
| Reihe: | Dover Books on Mathematics |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9780486265308 |
| ISBN-10: | 0486265307 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Ogilvy, C. Stanley |
| Auflage: | Revised |
| Hersteller: | DOVER PUBN INC |
| Verantwortliche Person für die EU: | preigu, Ansas Meyer, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de |
| Abbildungen: | Illustrations, unspecified |
| Maße: | 219 x 138 x 10 mm |
| Von/Mit: | C. Stanley Ogilvy |
| Erscheinungsdatum: | 01.05.1991 |
| Gewicht: | 0,204 kg |
| Erscheinungsjahr: | 1990 |
|---|---|
| Medium: | Taschenbuch |
| Reihe: | Dover Books on Mathematics |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9780486265308 |
| ISBN-10: | 0486265307 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Ogilvy, C. Stanley |
| Auflage: | Revised |
| Hersteller: | DOVER PUBN INC |
| Verantwortliche Person für die EU: | preigu, Ansas Meyer, Lengericher Landstr. 19, D-49078 Osnabrück, mail@preigu.de |
| Abbildungen: | Illustrations, unspecified |
| Maße: | 219 x 138 x 10 mm |
| Von/Mit: | C. Stanley Ogilvy |
| Erscheinungsdatum: | 01.05.1991 |
| Gewicht: | 0,204 kg |
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