What is the number pi and what is its history

One of the most mysterious numbers known to mankind is certainly the number Π (read - pi). In algebra, this number reflects the value of the ratio of the length of the circle and its diameter. Earlier this value was called the ludolph number. How and where the number Pi came from is not known for sure, but mathematicians divide into 3 stages the whole history of the number Π, the ancient, classical and the era of digital computers.

The number n is irrational, that is, it can not be represented as a simple fraction, where the numerator and denominator are integers. Therefore, such a number has no end and is periodic. The irrationality of II was first proved by Lambert in 1761.

In addition to this property, the number Π can not be the root of any polynomial, and therefore is a transcendental number . This property, when it was proved in 1882, put an end to the almost sacred debate of mathematicians "about the quadrature of the circle," which lasted for 2,500 years.

It is known that Briton Jones first introduced the designation of this number in 1706. After the works of Euler appeared, the use of such a designation became generally accepted.

In order to understand in detail what the Pi number is, it should be said that its use is so wide that it is difficult even to name the field of science in which it is dispensed with. One of the simplest and most familiar from the school's program of values is the designation of the geometric period. The ratio of the length of the circle to the length of its diameter is constant and is equal to 3, 14. This value was known even to the oldest mathematicians in India, Greece, Babylon, Egypt. The earliest variant of calculating the ratio refers to the year 1900 BC. E. The Chinese scientist Liu Hui has calculated the value of P more close to modern, in addition, he also invented a quick way of such calculation. Its magnitude remained generally accepted for almost 900 years.

The classical period of development of mathematics was marked by the fact that in order to establish exactly what the Pi number is, scientists began to use methods of mathematical analysis. In the 1400s, the Indian mathematician Madhava used the theory of series to compute and determined the period of the number P with an accuracy of 11 digits after the decimal point. The first European, after Archimedes, who investigated the number P and made a significant contribution to its justification, was the Dutchman Ludolf van Zeilen, who had already determined 15 digits after the decimal point, and in the will wrote very entertaining words: "... who cares - let him go on." It was in honor of this scientist, the number P, that got its first and only name in the whole history.

The era of computer calculations introduced new details into the understanding of the essence of the number P. So in order to find out what the Pi number was, in 1949 the computer for ENIAC was first used, one of the developers of which was the future "father" of the theory of modern computers, J. von Neumann. The first measurement was carried out for 70 hours and gave 2037 digits after the decimal point in the period of the P. The mark of one million signs was reached in 1973. In addition, during this period other formulas reflecting the number of P. were also established. Thus, the Chudnovsky brothers were able to find one that allowed to calculate 1 011 196 691 figures of the period.

In general, it should be noted that in order to answer the question: "What is the Pi number?", Many studies began to resemble competitions. Today, supercomputers are already considering the question of what it really is, the Pi number. Interesting facts related to these studies, permeate almost the entire history of mathematics.

Today, for example, world championships are held to memorize the number P and record world records, the latter belongs to the Chinese Liu Ciao, for a day with a small, named 67,890 signs. In the world there is even a holiday of the number P, which is celebrated on March 14 as "Day of the Pi number".

According to data for 2011 already set 10 trillion digits of the period of the number.