Abstract
Givenn lines in the real projective plane, Grünbaum conjectures that, for n≥16, the numberp 3 of triangular regions determined by the lines is at most 1/3n(n−1). We show that ifn≥7 thenp 3 ≤8/21n(n−1)+2/7, we also point out that if no vertex is a point of intersection of exactly three of the lines, thenp 3≤1/3n(n−1).
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Professor Gu died while on a visit to Poland in April 1997
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Gu, H. Triangles in arrangements of lines. J Geom 64, 89–94 (1999). https://doi.org/10.1007/BF01229215
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DOI: https://doi.org/10.1007/BF01229215