A generalised Sylvester-Gallai Theorem

  • L. M. Pretorius Departement Wiskunde en Toegepaste Wiskunde, Universiteit van Pretoria, Pretoria 0002
  • K. J. Swanepoel Departement Wiskundige Wetenskappe, Universiteit van Suid-Afrika, Posbus 392, UNISA, Pretoria 0003

Abstract

We give an algorithmic proof for the contrapositive of the following theorem that has recently been proved by the authors:

Let S be a finite set of points in the plane, with each point coloured red, blue or with both colours. Suppose that for any two distinct points A and B in S sharing a colour k, there is a third point in S which has (inter alia) the colour different from k and is collinear with A and B. Then all the points in S are collinear.
This theorem is a generalization of both the Sylvester-Gallai Theorem and the Motzkin-Rabin Theorem.

Published
2007-09-21
How to Cite
Pretorius, L., & Swanepoel, K. (2007). A generalised Sylvester-Gallai Theorem. Suid-Afrikaans Tydskrif Vir Natuurwetenskap En Tegnologie / <i>South African Journal of Science and Technology</I&gt;, 26(1), 8-13. https://doi.org/10.4102/satnt.v26i1.118
Section
Oorspronklike Navorsing