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We consider finite systems of straight lines in the Euclidean plane 𝐑 2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains determined by a given finite line-system in 𝐑 2 is presented and it is shown that this estimate is precise in a certain sense.
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 2007
Keywords: Euclidean plane; line-system; point-system; convex hull; Euler's formula
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