VOFN080 - Buffon’s needle
Fig. 80 (p. 217) - Buffon is remembered for a probability experiment known as Buffon’s Needle. The problem was first stated in 1777. The story goes that Buffon calculated pi by trowing some French stick loaves over his shoulder onto a tiled floor and counted the number of times the loaves covered the lines between the tiles.
A more practical form involves the dropping of a random number of needles (or toothpicks) on a lined sheet of paper and determining the probability of the needle crosses one of the lines on the page. The lengths of the needles/toothpicks and the distance between the lines play a role in the theoretical discussion of this matter (SCHROEDER, 1974), but the outcome will always approximate pi. Pi can be calculated from the needle drops by multiplying the number of drops by two and divide the outcome by the number of hits: 2 (total drops) / (number of hits) = pi (approximately).
Two parallel lines indicate a tri-fold world, which is invaded by a multitude (the French loaves or pins). The probability of crossing a line (visibility) is a value derived from a cyclic environment (pi). It is relevant in the history of division thinking, because it bridged a gap between the linear (Third) and the circular (Fourth Quadrant) vision.
SCHREUDER, L. (1974). Buffon’s needle problem. An exciting application of many mathematical concepts. Pp. 183 – 186 in: Mathematics Teacher, 67 (2).
VOFN080 - Buffon’s needle
Fig. 80 (p. 217) - Buffon is remembered for a probability experiment known as Buffon’s Needle. The problem was first stated in 1777. The story goes that Buffon calculated pi by trowing some French stick loaves over his shoulder onto a tiled floor and counted the number of times the loaves covered the lines between the tiles.
A more practical form involves the dropping of a random number of needles (or toothpicks) on a lined sheet of paper and determining the probability of the needle crosses one of the lines on the page. The lengths of the needles/toothpicks and the distance between the lines play a role in the theoretical discussion of this matter (SCHROEDER, 1974), but the outcome will always approximate pi. Pi can be calculated from the needle drops by multiplying the number of drops by two and divide the outcome by the number of hits: 2 (total drops) / (number of hits) = pi (approximately).
Two parallel lines indicate a tri-fold world, which is invaded by a multitude (the French loaves or pins). The probability of crossing a line (visibility) is a value derived from a cyclic environment (pi). It is relevant in the history of division thinking, because it bridged a gap between the linear (Third) and the circular (Fourth Quadrant) vision.
SCHREUDER, L. (1974). Buffon’s needle problem. An exciting application of many mathematical concepts. Pp. 183 – 186 in: Mathematics Teacher, 67 (2).