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- W2066103694 abstract "n lines in general position in the real projective plane determine (n2-n+2)/2 convex polygons. It has been observed ([1], [2]) that for almost all arrangements of n>3 lines that one or more of these polygons must be quadrilaterals. In fact, only three arrangements, one each for n=3, 6 and 10, have been reported in which there are no quadrilaterals. Because of this, Branko Griinbaum has recently conjectured [3] that for all n $3, 6 or 10 at least one quadrilateral will be formed by every possible arrangement of n lines in the projective plane. The figure shows that this conjecture is not true by displaying an" @default.
- W2066103694 created "2016-06-24" @default.
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- W2066103694 date "1972-01-01" @default.
- W2066103694 modified "2023-09-26" @default.
- W2066103694 title "A quadrilateral-free arrangement of sixteen lines" @default.
- W2066103694 cites W2004110115 @default.
- W2066103694 doi "https://doi.org/10.1090/s0002-9939-1972-0295191-2" @default.
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