Geodesic
Extensions of Sylvester's Theorem
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 1-14

Voir la notice de l'article provenant de la source Cambridge University Press

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? 
Balomenos, Richard H.; Bonnice, William E.; Silverman, Robert J. Extensions of Sylvester's Theorem. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 1-14. doi: 10.4153/CMB-1966-001-6
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[1] 1. Coxeter, H. S. M., Introduction to Geometry, John Wiley and Sons, Inc., 1961, 65. Google Scholar

[2] 2. Dirac, G. A., Collinearity Properties of Sets of Points, Quart. J. Math. Oxford Ser. 2(1951), 221-227. Google Scholar

[3] 3. Erdös, P., Problem No. 4065, Amer. Math. Monthly, 50 (1943), 65. Google Scholar

[4] 4. Amer. Math. Monthly, 51 (1944) 169-171. Google Scholar

[5] 5. Kelly, L. M. and Moser, W.O.J., On the Number of Ordinary Lines Determined by n Points, Canad. J. Math. 10 (1958), 210-219. Google Scholar

[6] 6. Motzkin, Th., The Lines and Planes Connecting the Points of a Finite Set, Trans. Amer. Math. Soc. 70 (1951), 451-464. Google Scholar

[7] 7. Sylvester, J.J., Mathematical Question 11851, Educational Times, 59 (1893) 98. Google Scholar

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