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.
- R. Courant and H.E. Robbins, What is Mathematics? Oxford Univ. Pr., New York, 1953.
- H.S.M. Coxeter, Introduction to Geometry, Wiley, New York, 1961.
- Euclid, Elements,
- D. Pedoe, Circles, Dover, New York, 1957.
April, 1998; March, 2002.
David E. Joyce
Department of Mathematics and Computer Science
Worcester, MA 01610