One of the most mysterious numbers known to mankind, of course, is the number Ξ (read pi). In algebra, this number reflects the ratio of the circumference of a circle to its diameter. Previously, this value was called the ludolph number. How and where the Pi number came from is not known for certain, but mathematicians divide into 3 stages the entire history of the number Ξ , into the ancient, classical and the era of digital computers.
The number P is irrational, that is, it cannot be represented as a simple fraction, where the numerator and denominator are integers. Therefore, such a number has no ending and is periodic. The irrationality of P was first proved by I. Lambert in 1761.
In addition to this property, the number cannot also 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 "on the quadrature of the circle", which lasted for 2,500 years.
It is known that the first introduced the designation of this number by the British Jones in 1706. After the works of Euler appeared, the use of such a designation became generally accepted.
To understand in detail what is the number of Pi, it should be said that its use is so wide that it is difficult to even name a field of science in which they would manage without it. One of the simplest and most familiar values ββfrom the school curriculum is the designation of the geometric period. The ratio of the length of a circle to the length of its diameter is constant, equal to 3, 14. This value was known to the most ancient mathematicians in India, Greece, Babylon, Egypt. The earliest version of calculating the ratio dates back to 1900 BC. e. A closer to the modern value of P was calculated by the Chinese scientist Liu Hui, in addition, he also invented a quick way to such a calculation. Its value has remained generally accepted for almost 900 years.
The classical period in the development of mathematics was marked by the fact that in order to establish exactly what the Pi number was, scientists began to use methods of mathematical analysis. In the 1400s, the Indian mathematician Madhava used series theory to calculate and determined the period of the number up to 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 identified 15 digits after the decimal point, and wrote very entertaining words in his will: β... who cares, let him go further.β It was in honor of this scientist that the number P received its first and only personal name in history.
The era of computer computing has brought new details to the understanding of the essence of the number P. So, to find out what the number Pi is, in 1949 the ENIAK computer was used for the first time, one of the developers of which was the future βfatherβ 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 number P. The mark of a million characters was reached in 1973. In addition, other formulas reflecting the number P. were established during this period. Thus, the Chudnovsky brothers were able to find one that made it possible to calculate 1 011 196 691 digits of the period.
In general, it should be noted that in order to answer the question: βWhat is the Pi number?β, Many studies began to resemble competitions. Today, supercomputers are already dealing with the question of what kind of Pi it really is. 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 world records are recorded, the latter belongs to the Chinese Liu Chao, a day with a little, he named 67,890 characters. In the world there is even a celebration of the number P, which is celebrated on March 14 as "Day of the number of Pi."
According to data for 2011, 10 trillion digits of the period of the number have already been established.