volume 17, issue 5, P959-967 2010
DOI: 10.4310/mrl.2010.v17.n5.a12
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Abstract: Let Cn be the n-th generation in the construction of the middlehalf Cantor set. The Cartesian square Kn = Cn × Cn consists of 4 n squares of side-length 4 −n . The chance that a long needle thrown at random in the unit square will meet Kn is essentially the average length of the projections of Kn, also known as the Favard length of Kn. A classical theorem of Besicovitch implies that the Favard length of Kn tends to zero. It is still an open problem to determine its exact rate of decay. Until recently, the onl…

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