Let's start with Buffon's throwing needle.
Buffon's Needle Problem 1777 French scientist Buffon put forward a method to calculate pi, which is called Buffon's Needle Problem. The method comprises the following steps:
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.
Tell me more about him.
George-Louis leclerc, Comte de Buffon (also translated by Buffon, Bifeng, George-Louis Leclerc, Count Buffon,17 September 707-14 July 788 16), French naturalist, mathematician and biologist. Buffon's thoughts influenced two generations of naturalists, including Darwin and Lamarck.
Buffon's works in natural history include On Human Research and Natural History, Earth Theory, Animal History and Natural History. Gé né rale et parti Culiè re (1749-88: 50 volumes were originally published, 36 volumes were published before his death, and 8 volumes were published by La Sepede after Buffon's death). This book contains all the knowledge about nature in society at that time. Buffon studied the similarities between humans and apes and the possibility that they came from the same ancestor. Duo Bangtong helped him write this masterpiece. Buffon's works have a far-reaching impact on modern ecology.
Buffon's needle throwing problem in probability theory is named after him.
In Problems of Nature (1778), Buffon explored the roots of the solar system and speculated that planets were formed by the collision of the sun and comets. He also suggested that the age of the earth is much longer than the 6,000 years claimed by the church. According to the cooling rate of iron, he deduced that the age of the earth should be 75000 years. He was condemned by the Catholic Church and his books were burned.
Buffon once published a theory that the natural environment in America is inferior to that in Eurasia. He believes that there are no powerful creatures in the local area, and even people are not as powerful as Europe. His explanation is that the local area is full of wetlands and dense forests.
In The Days of Fran-Claude, he introduced calculus into probability theory.
He translated the Statics of Vegetables by Newton and Steven hales into French.
He was born in Mongbar, Kodo province, and his father Ben Ming Jie Leclere was the Lord of Dijon and Mongbar. At the age of ten, he entered the Jesuit College. 1723 studied law according to his father's instructions. However, Buffon's achievements in school are mediocre and he has no potential to become a legal profession. Finally, from 65438 to 0728, he entered the University of Angers to study mathematics, but he also studied other subjects such as medicine and botany.
He corresponded with Gabriel Cramer. His topics include mechanics, geometry, probability, number theory and calculus.
/kloc-participated in a duel in 0/730 and was forced to leave the university. He embarked on a trip to Europe until his mother died.
He moved to Paris and met Voltaire and other intellectuals. At the age of 27, he joined the French National Academy of Sciences. 1739 July, was appointed as the manager of the Royal Garden in Paris (later French Botanical Garden). During his term of office, he turned the emperor's garden into a research center and museum, and the area of the park and the types of plants in it also increased greatly.
Buffon was widely respected when he was alive. However, in 1789 and 1 year after his death, the body was dragged out of the grave by the people of the great revolution and whipped.