Excursions in Geometry

Häftad, Engelska, 2003

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2003-03-28
Mått:135 x 215 x 11 mm
Vikt:180 g
Format:Häftad
Språk:Engelska
Serie:Dover Books on MaTHEMA 1.4tics
Antal sidor:192
Förlag:Dover Publications Inc.
ISBN:9780486265308

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Innehållsförteckning

Introduction1 A bit of backgroundA practical problemA basic theoremMeans2 Harmonic division and Apollonian circlesHarmonic conjugatesThe circle of ApolloniusCoaxial families3 Inversive geometryTransformationsInversionInvariantsCross-ratio4 Application for inversive geometryTwo easy problemsPeaucellier's linkageApollonius' problemSteiner chainsThe arbelos5 The hexletThe conics definedA property of chainsSoddy's hexletSome new hexlets6 The conic sectionsThe reflection propertyConfocal conicsPlan sections of a coneA characteristic of parabolas7 Projective geometryProjective transformations The foundationsCross-ratioThe complete quadranglePascal's TheoremDuality8 Some Euclidean topicsA navigation problemA three-circle problemThe Euler lineThe nine-point circleA triangle problem9 The golden sectionThe pentagramSimilarities and spiralsThe regular polyhedraThe continued fraction for ø10 Angle trisectionThe unsolved problems of antiquityOther kinds of trisection11 Some unsolved problems of modern geometryConvex sets and geometric inequalitiesMalfatti's problemThe Kakeya problemNotesIndex