Compass Geometry

David E. Joyce
Clark University

Table of contents

  1. Euclidean constructions
  2. Reduction to circular constructions
  3. Summary of inversion
  4. Stereographic projection
  5. Construction PC to invert a point in a circle
  6. Construction C to find the center of a circle
  7. Inversive geometry and involutory quandles


    With compasses alone, all the points that can be constructed with straightedges and compasses can be constructed. That means that straightedges are only necessary for the actual drawing of lines. One would not want to dispense with straightedges, however, since the constructions with compasses alone are much more complicated.

    The geometry of compasses was developed independently by G. Mohr in Denmark in 1672, and by L. Mascheroni in Italy in 1797. The easiest way, however, to show that compasses are sufficient depends on circle inversion which wasn't invented until 1828 by Jacob Steiner.


    1. R. Courant and H.E. Robbins, What is Mathematics? Oxford Univ. Pr., New York, 1953.
    2. H.S.M. Coxeter, Introduction to Geometry, Wiley, New York, 1961.
    3. Euclid, Elements,
    4. D. Pedoe, Circles, Dover, New York, 1957.

    April, 1998; March, 2002.
    David E. Joyce
    Department of Mathematics and Computer Science
    Clark University
    Worcester, MA 01610

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