1) Take a piece of white paper and draw many parallel lines with a distance of d on it.
2) Take a root with the length of l (l
3) Calculate the probability that the needle intersects the straight line.
/kloc-in the 8th century, French mathematicians Buffon and leclerc put forward the problem of throwing needles, which was recorded in Buffon's book published in 1777: "Draw a set of parallel lines with a distance of d on the plane, and put the length of L (L
P=2l/(πd) π is π.
Using this formula, the approximate value of pi can be obtained by probability method. Here is some information.
Pi estimation of the intersection times of the annual throwing times of the experimenter
Wolf1850 5000 25313.1596
Smith1855 32041219 3.1554
De Morgan 1680 600 383.438+037
Fox 1884 654438
lazzerini 190 1 3408 1808 3. 14 15929。
Lai Na 1925 2520 859 3.6438+0795
Buffon's throwing needle experiment is the first example of expressing probability problems in geometric form. He used random experiments to deal with deterministic mathematical problems for the first time, which promoted the development of probability theory to some extent.
Like the needle throwing experiment, we use the probability obtained through the probability experiment to estimate a quantity we are interested in. This method is called Monte Carlo method. Monte Carlo method rose and developed with the birth of computer during the Second World War. This method is widely used in applied physics, atomic energy, solid state physics, chemistry, ecology, sociology and economic behavior.
The French mathematician Buffon (1707- 1788) first designed the needle throwing experiment. 1777 gives a formula for calculating the intersection probability of a needle and a parallel line, P=2L/πd (where l is the length of the needle, d is the distance between parallel lines, and π is π).
Because it is related to π, people think of using the throwing needle test to estimate the value of π.
In addition, the probability p that three positive numbers can be randomly named to form an obtuse triangle is also related to π.
It is worth noting that the method adopted here is to design a suitable experiment, the probability of which is related to a quantity we are interested in (such as π), and then estimate this quantity with the experimental results. With the development of modern technology such as computer, this method has developed into a widely used Monte Carlo method.
Needle insertion test-one of the most unusual methods to calculate π.
One of the strangest ways to calculate π is18th century French naturalist C Buffon and his needle throwing experiment: on a plane, draw a set of parallel lines at the distance d with a ruler; Throw a needle with a length less than d on the drawn plane; If the needle intersects the line, throwing is considered favorable, otherwise it is unfavorable.
Buffon was surprised to find that the ratio of the times of favorable throwing and unfavorable throwing is an expression containing π. If the length of the needle is equal to d, the probability of favorable throwing is 2/π. The more times you throw, the more accurate π value you can get.
In A.D. 190 1 year, Italian mathematician Laslini made 3408 injections and gave the value of π as 3.1415929-accurate to six decimal places. However, regardless of whether Laslini actually injected the needle, his experiment was supported by L. Barge of Ogden National Weber University in Utah, USA.