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by C. Stanley Ogilvy
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ISBN: 0486265307 Dover Publications Price: $9.95 |
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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.
Table of Contents for Excursions in Geometry
| 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 |