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How many triangles? (English) Zbl 0920.51010
A result known as Robert’s Theorem (1889) states that \(n\) lines in general position in the plane determine at least \(n-2\) triangular regions. However, his arguments were not convincing (as mentioned in B. Grünbaum, Regional Conf. Series in Math. No. 10 Am. Math. Soc. (1972; Zbl 0249.50011)). R. W. Shannon gave a proof in 1979 [Geom. Dedicata 8, 179-187 (1979; Zbl 0423.51013)] which is not elementary. In this note a proof given by A. Ya. Belov [Russ. Math. Surv. 47, No. 3, 167-168 (1992); translation from Usp. Mat. Nauk 47, No. 3(285), 151-152 (1992; Zbl 0850.51006)] is neatly reproduced.
51N20 Euclidean analytic geometry