Extensions of Sylvester's Theorem

Author:

Balomenos Richard H.,Bonnice William E.,Silverman Robert J.

Abstract

Sylvester [7] proposed the following question in 1893. If a finite set of points in a plane is such that on the line determined by any two points of the set there is always a third point of the set, is the set collinear? Equivalently, given a finite planar set of non-collinear points, does there exist a line containing exactly two of the points?

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Topological Characterization of Hamming and Dragonfly Networks and Its Implications on Routing;ACM Transactions on Architecture and Code Optimization;2015-01-09

2. A survey of Sylvester's problem and its generalizations;Aequationes Mathematicae;1990-12

3. A lower bound on the number of cells in arrangements of hyperplanes;Journal of Combinatorial Theory, Series A;1976-05

4. On the number of ordinary planes;Journal of Combinatorial Theory, Series A;1971-07

5. Generalizations of the Sylvester Problem;Mathematics Magazine;1970-11

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