Journal of Geometry

, Volume 38, Issue 1–2, pp 12–15

On strict strong constructibility with a compass alone

  • Arnon Avron
Article

Abstract

We show that every point in the plane which can be constructed by a compass and a ruler, given a setS of points, can be constructed using a compass alone so that the following restriction is met. LetO andK be two arbitrarily chosen distinct points ofS. Then every point is obtained as a proper intersection of two circles that are either completely symmetrical with respect to the lineOK or have both their centers on this line.

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References

  1. [1]
    AVRON, A.:Theorems on strong constructibility with a compass alone. Journal of Geometry, vol. 30 (1987), pp. 28–35.Google Scholar
  2. [2]
    MASCHERONI, L.:La Geometria del Compasso, Pavia V (1797).Google Scholar
  3. [3]
    MOHR, G.:Euclides Danicus, Amsterdam (1672).Google Scholar

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Arnon Avron
    • 1
  1. 1.School of Mathematical Science, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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