Buffon’s Needle
I Introduction Formulated and eventually published in 1777, Buffon’s needle is a problem that Georges Louis-Leclerc, Comte de Buffon came up with. The problem was a simple one: when a needle drops onto a floor marked by equally spaced lines, what is the probability that the needle lands on one of the lines on the floor? The question by itself is an interesting one for me; when I first saw the problem I was actually surprised there was a mathematical way to solve the problem. However, Buffon’s needle also has an interesting application. Buffon’s needle can actually be used to approximate the value of π! In fact, in 1812, a mathematician by the name of Lazzarini was able to use a Buffon’s needle experiment to approximate the value of π to six decimal places(even though his results were subject to a bit of controversy) . The whole idea that something as random as dropping a needle onto a floor marked with lines intrigues me, and I would very much like to understand the theory behind Buffon’s needle and why it can be used to approximate π.
Investigation
Solving the Buffon’s Needle problem
Now a direct and simple way to find the probability of a needle crossing one of …show more content…
However there are quite a few limitations of real life simulation. First of all, in the simulation I conducted, the result only works if and only if the length of the needle(or toothpick in my case) is equal to the space between lines. If I wanted to find the probability when the length of the needle is not equal to the space between the lines, than I would have to conduct a new simulation with the specific length of needle and spacing between lines. Also, from Figure B, it can be seen that the results for the different trials are different. Instead, there should be a way to find the exact probability of a needle crossing a line when it is dropped onto a surface marked by equally spaced
I Introduction Formulated and eventually published in 1777, Buffon’s needle is a problem that Georges Louis-Leclerc, Comte de Buffon came up with. The problem was a simple one: when a needle drops onto a floor marked by equally spaced lines, what is the probability that the needle lands on one of the lines on the floor? The question by itself is an interesting one for me; when I first saw the problem I was actually surprised there was a mathematical way to solve the problem. However, Buffon’s needle also has an interesting application. Buffon’s needle can actually be used to approximate the value of π! In fact, in 1812, a mathematician by the name of Lazzarini was able to use a Buffon’s needle experiment to approximate the value of π to six decimal places(even though his results were subject to a bit of controversy) . The whole idea that something as random as dropping a needle onto a floor marked with lines intrigues me, and I would very much like to understand the theory behind Buffon’s needle and why it can be used to approximate π.
Investigation
Solving the Buffon’s Needle problem
Now a direct and simple way to find the probability of a needle crossing one of …show more content…
However there are quite a few limitations of real life simulation. First of all, in the simulation I conducted, the result only works if and only if the length of the needle(or toothpick in my case) is equal to the space between lines. If I wanted to find the probability when the length of the needle is not equal to the space between the lines, than I would have to conduct a new simulation with the specific length of needle and spacing between lines. Also, from Figure B, it can be seen that the results for the different trials are different. Instead, there should be a way to find the exact probability of a needle crossing a line when it is dropped onto a surface marked by equally spaced