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Bisecants of Finite Collections of Sets in Linear Spaces

Published online by Cambridge University Press:  20 November 2018

M. Edelstein  and
L. M. Kelly
M. Edelstein
Affiliation:
Michigan State University, Cambridge University and Dalhousie University
L. M. Kelly
Affiliation:
Michigan State University, Cambridge University and Dalhousie University
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 375 - 380
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Clarkson, J. A., Uniformly convex spaces, Trans. Amer. Math. Soc., 40, (1936), 396–414.Google Scholar
2. Day, M. M., Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc., 78 (1955), 516–528.Google Scholar
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. 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. Motzkin, Th., The lines and planes connecting the points of a finite set, Trans. Amer. Math. Soc, 70 (1951), 451–464.Google Scholar
6. Sylvester, J. J., Mathematical question 11851, Educational Times, 59 (1893), 98.Google Scholar