caa a22 4500 465825397 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112289 doi (NATIONALLICENCE)springer-10.1007/BF02112289 A survey of Sylvester's problem and its generalizations [Elektronische Daten] [P. Borwein, W. Moser] Summary: LetP be a finite set of three or more noncollinear points in the plane. A line which contains two or more points ofP is called aconnecting line (determined byP), and we call a connecting lineordinary if it contains precisely two points ofP. Almost a century ago, Sylvester posed the disarmingly simple question:Must every set P determine at least one ordinary line? No solution was offered at that time and the problem seemed to have been forgotten. Forty years later it was independently rediscovered by Erdös, and solved by Gallai. In 1943 Erdös proposed the problem in the American Mathematical Monthly, still unaware that it had been asked fifty years earlier, and the following year Gallai's solution appeared in print. Since then there has appeared a substantial literature on the problem and its generalizations. In this survey we review, in the first two sections, Sylvester's problem and its generalization to higher dimension. Then we gather results about the connecting lines, that is, the lines containing two or more of the points. Following this we look at the generalization to finite collections of sets of points. Finally, the points will be colored and the search will be for monochromatic connecting lines. Birkhäuser Verlag, 1990 Primary 51A20 nationallicence Secondary 52A37 nationallicence Borwein P. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke St. West, H3A 2K6, Montreal, Quebec, Canada aut Moser W. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke St. West, H3A 2K6, Montreal, Quebec, Canada aut aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 111-135 0001-9054 40:1<111 1990 40 10 https://doi.org/10.1007/BF02112289 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112289 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Borwein P. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke St. West, H3A 2K6, Montreal, Quebec, Canada aut NATIONALLICENCE 700 1- Moser W. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke St. West, H3A 2K6, Montreal, Quebec, Canada aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 111-135 0001-9054 40:1<111 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer