On a problem of Buffon type for triangular lattices and a ``non-small'' needle (Q2704109)

\textbf{I.C.Vladimirescu (Craiova)}: The author considers a lattice \(\mathbb{R}\) whose fundamental cell is a triangle \(T\) with sides of length \(a_1,a_2,a_3\) and with vertices \(A_1,A_2, A_3\) and a line segment \(S\) of constant length \(l\). The probability that \(S\) intersects a straight line of \(\mathbb{R}\) is calculated. NEWLINENEWLINENEWLINE\textbf{Ilya S.Molchanov (Glasgow)}: The author provides an expression for the probability that a ``non-small'' needle intersects a planar lattice whose fundamental cell is a general triangle. The condition that the needle is ``non-small'' means that it can be positioned inside the fundamental cell by an appropriate rotation and it always hits the lattice for another rotation angle. The results are derived using conventional trigonometry with particular cases depending on relationships between the sides of the fundamental triangle.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00040].