The classical Buffon needle problem is to find the probability that a needle of length n when dropped on a floor made of boards of width b will cross a crack between the boards. This problem can be solved by evaluating a simple single integral. In his extension of the problem, Laplace considered a floor tiled by congruent rectangles and considered the probability of the needle crossing one or two of the cracks bettween the rectangles. In 1974 M. Stoka studies an extension of the Buffon-Laplace needle problem in the space Rn. In this paper we consider two extension of the Laplace problem in E3

### Extensions of Laplace Type Problems in the Euclidean Space

#### Abstract

The classical Buffon needle problem is to find the probability that a needle of length n when dropped on a floor made of boards of width b will cross a crack between the boards. This problem can be solved by evaluating a simple single integral. In his extension of the problem, Laplace considered a floor tiled by congruent rectangles and considered the probability of the needle crossing one or two of the cracks bettween the rectangles. In 1974 M. Stoka studies an extension of the Buffon-Laplace needle problem in the space Rn. In this paper we consider two extension of the Laplace problem in E3
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2014
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/2911968`
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