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99 Points of Intersection

99 Points of Intersection
Examples-Pictures-Proofs

£29.99

Part of Spectrum

  • Date Published: September 2006
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Hardback
  • isbn: 9780883855539

£ 29.99
Hardback

This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
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About the Authors
  • The 99 points of intersection presented here were collected during a year-long search for surprising concurrence of lines. For each example we find compelling evidence for the sometimes startling fact that in a geometric figure three straight lines, or sometimes circles, pass through one and the same point. Of course, we are familiar with some examples of this from basic elementary geometry - the intersection of medians, altitudes, angle bisectors, and perpendicular bisectors of sides of a triangle. Here there are many more examples - some for figures other than triangles, some where even more than three straight lines pass through a common point. The main part of the book presents 99 points of intersection purely visually, developed in a sequence of figures. In addition the book contains general thoughts on and examples of the points of intersection, as well as some typical methods of proving their existence.

    • Translated from the original German
    • Readily accessible to students at the undergraduate level but will appeal to anyone interested in geometry
    • The examples given have both geometrical interest and an intriguing aesthetic aspect
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    Product details

    • Date Published: September 2006
    • format: Hardback
    • isbn: 9780883855539
    • length: 168 pages
    • dimensions: 236 x 156 x 13 mm
    • weight: 0.357kg
    • contains: 157 b/w illus.
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    Part I. What's It All About?:
    1. If three lines meet
    2. Flowers for Fourier
    3. Chebyshev and the Spirits
    4. Sheaves generate curves
    Part II. The 99 points of intersection: Part III. The Background:
    1. The four classical points of intersection
    2. Proof strategies
    3. Central projection
    4. Ceva's Theorem
    5. Jacobi's Theorem
    6. Remarks on selected points of intersection
    References.

  • Authors

    Hans Walser, ETH Zentrum, Switzerland
    Hans Walser is lecturer at the Swiss Federal Instititute of Technology and the University of Basel.

    Jean Pedersen

    Translator

    Peter Hilton

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