ABSTRACT
The idea to use random numbers in scientific computation dates back to the 18th century. The French mathematician, naturalist. and encyclopédist, Georges-Louis Leclerc, Comte de Buffon introduced a problem that we know today as Buffon’s needle problem [30]. It asks to find the probability that a randomly thrown needle of length l hits one of the parallel lines equally spaced on the floor a distance t > l https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315266954/a85766f8-14e4-4bbb-b5b7-768a0bb107fc/content/eq5240.tif"/> apart. We can assume that the distance of the center of the needle from the closest line is uniformly distributed between 0 and t 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315266954/a85766f8-14e4-4bbb-b5b7-768a0bb107fc/content/eq5241.tif"/> . We can also assume that the angle the needle closes with any of the parallel lines is also uniformly distributed between 0 and π. The needle hits one of the lines if () x < sin ( α ) l 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315266954/a85766f8-14e4-4bbb-b5b7-768a0bb107fc/content/eq5242.tif"/>
