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Excursions in Geometry

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Overview

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.

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Overview

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.

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Product Details

  • ISBN-13: 9780486265308
  • Publisher: Dover Publications
  • Publication date: 12/1/1990
  • Edition description: Reprint
  • Pages: 192
  • Sales rank: 746,074
  • Product dimensions: 5.44 (w) x 8.64 (h) x 0.38 (d)

Table of Contents

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 ΓΈ
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
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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted April 9, 2000

    Let's invert it out of there!

    This guide is ambiguous and provides very little information about obscure topics such as inversive geometry. The text is difficult to comprehend not because of its vocabulary, but because it tend to veer off course. Although the subject matter is interesting, it is very difficult to expose when confronted to diagrams that are basically not explained. This could not be used as a classroom guide because it tends to confound even gifted math students. An interesting remark was made, which was, 'I think he's going to start talking about his dog right now.' This book would only be reccomended to the top 2% of math students, because it is not accesible to the general public. I should hope that someone who reads this book writes a revision of it.

    0 out of 1 people found this review helpful.

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