On the Number of Ordinary Lines Determined by n Points

1958/01/01 by L. M. Kelly, W. O. J. Moser · 5 citations
Engineering · Computer Science · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Mathematics and Applications

paper · pdf · doi:10.4153/cjm-1958-024-6

Abstract

More than sixty years ago, Sylvester (13) proposed the following problem: Let n given points have the property that the straight line joining any two of them passes through a third point of the set. Must the n points all lie on one line? An alleged solution (not by Sylvester) advanced at the time proved to be fallacious and the problem remained unsolved until about 1933 when it was revived by Erdös (7) and others.

Citations

• The lines and planes connecting the points of a finite set

Cited by

• Note on the Number of Almost Ordinary Triangles
• Combinatorics of free and simplicial line arrangements
• Bichromatic lines in the plane
• Spanned lines and Langer's inequality
• On sets defining few ordinary lines

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