The Buffon Needle Problem Extended

Solutions of Buffon’s problems in the 19 century

The Buffon’s needle problem is a well known problem of geometric probability. But Buffon formulated and solved also other problems in this topic. We recall them and their solutions by Buffon, Laplace, Todhunter, Lamé and Barbier.

Principles & Problems A comparison of the significance and conceptual mathematics of Cavalieri ’ s Principle & Buffon ’ s Needle Problem

Fractals with Positive Length and Zero Buffon Needle Probability

It turns out that H1 is a measure, now called one-dimensional Hausdorff measure because it was generalized by Hausdorff [10] to the whole family of measures Hα, where α is any positive number (integer or noninteger). The modern theory of “fractals” is largely based on the notion of the Hausdorff dimension dimH (F) of a set F , defined by dimH (F) = inf{α > 0 : Hα(F) = 0}. We recommend the book ...

1 0 Ju n 20 09 . BUFFON NEEDLES LANDING NEAR SIERPINSKI GASKET

In this paper we modify the method of Nazarov, Peres, and Volberg [14] to get an estimate from above of the Buffon needle probability of the nth partially constructed Sierpinski gasket of Hausdorff dimension 1.

2 M ay 2 00 9 . BUFFON NEEDLES LANDING NEAR SIERPINSKI GASKET

In this paper we modify the method of Nazarov, Peres, and Volberg [14] to get an estimate from above of the Buffon needle probability of the nth partially constructed Sierpinski gasket of Hausdorff dimension 1.