Bisecants of Finite Collections of Sets in Linear Spaces
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 375-380

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The question posed by Sylvester (6) concerning the collinearity of a finite set of points in E2 having the property that each two together with some third be collinear has been the inspiration for numerous investigations. The original question was answered by the following theorem.
Edelstein, M.; Kelly, L. M. Bisecants of Finite Collections of Sets in Linear Spaces. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 375-380. doi: 10.4153/CJM-1966-039-2
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[1] 1. Clarkson, J. A., Uniformly convex spaces, Trans. Amer. Math. Soc., 40, (1936), 396–414. Google Scholar

[2] 2. Day, M. M., Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc., 78 (1955), 516–528. Google Scholar

[3] 3. Edelstein, M., Herzog, F., and Kelly, L. M., A further theorem cf the Sylvester type, Proc. Amer. Math. Soc., 14(1963), 359–363. Google Scholar

[4] 4. Kelly, L. M. and Moser, W. O. J., On the number of ordinary lines determined by n points, Can. J. Math., 10 (1958), 210–219. Google Scholar

[5] 5. Motzkin, Th., The lines and planes connecting the points of a finite set, Trans. Amer. Math. Soc, 70 (1951), 451–464. Google Scholar

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

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