Geodesic
Pair of lines and maximal probability
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2015), pp. 3-6

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In this paper we consider two independent and identically distributed lines, which intersect a planar convex domain $\mathbf{D}.$ We evaluate the probability $P_ {\, \mathbf{D}},$ for the lines to intersect inside $\mathbf{D}$. Translation invariant measures generating random lines is obtained, under which $P_ {\mathbf{D}}$ achieves its maximum for a disc and a rectangle. It is also shown that for every $p$ from the interval $[0, 1/2]$ and for every square there are measures generating random lines such that $P_ {\, \mathbf{D}}=p.$
Keywords: random line, translation invariant measure.
Mots-clés : convex domain 
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A. G. Gasparyan. Pair of lines and maximal probability. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2015), pp. 3-6. http://geodesic.mathdoc.fr/item/UZERU_2015_2_a0/