| The number π (pronounced “pi”) is a mathematical constant, expressing the relationship of a circle’s circumference to its diameter. It is designated by the Greek letter “pi”.
History:
For the first time, the designation of this number the Greek letter pi was used by the British mathematician Johns (1706) and was universally accepted after Euler's works. This designation occurs from the initial letter of the Greek words περιφέρεια —circle, periphery and περίμετρος — perimeter.
Valuation:
* 2 digits after the decimal:
π ≈ 3.14
Transcendence and irrationality:
The irrationality of the number π was proved for the first time by Johann Lambert in 1767.
In 1882, Ferdinand Lindemann, professor of Konigsberg University and Munich university could prove the transcendence of the number π. The proof was simplified by Felix Klein in 1894. His proof was attached to the work “Problems of Elementary and Higher Mathematics”, which was published in Gottingen in 1908.
Since the area of a circle and the circumference of a circle are functions of π in Euclidean Geometry, then the proof of the transcendence of π put an end to the dispute about the quadrature of the circle, which lasted for more than 2.5 thousand years.
To date it is not clear whether π is a normal number or not.
Calculation history:
Probably Archimedes was the first person who suggested the calculation method of π in a mathematical manner. For this purpose, he drew a circle and circumscribed regular polygons around the circle. By taking the diameter of the circle as 1, Archimedes studied the perimeter of the circumscribed polygons as the lower bound diameter of the circle and the perimeter of the circumscribed regular polygons as upper bound.
Various calculations are found in ancient Chinese works and popular the Chinese number 355/113 is the most accurate calculation.
In India, Aryabhatta and Bhaskaracharya used the approximation of 3.1416.
The result of the Arabian mathematician Ghiyath al-Din Jamshid ibn Mas’ud al-kashi deserves mention, who published works in 1424 under the name of “The Treatise on the Chord and Sine” in which he cites 17 digits of π (16 of them are correct).
In modern times, analytical methods based on identities, are used for calculating the π.
Amusing facts:
* The unofficial holiday “Pi Day” is celebrated on March 14, which in the American date format (month/day) is recorded as 3.14, which corresponds to approximate value of π;
* One more date, linked with π, is July 22, which is called as “Pi Approximation Day”, since this day in the European date format is recorded as 22/7 and the value of this fraction is the approximate value of π;
* The world record for remembering the digits of π belongs to Japanese Akira Haraguchi. He remembered π up to 100-thousand digits after the decimal. He needed almost 16 hours to spell out all the numbers.
* In the State of Indiana (USA), a bill was passed in 1897 for legislatively establishing the value of π as equaling 3.2. The mentioned bill did not become a law, thanks to the timely intervention of C.A. Waldo, professor of Purdue University who was present during consideration for passing the law.
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This Saturday is the international Pi Day when math enthusiasts around the wold celebrate the famous constant Pi, equal to the ratio of the circumference of a circle to its diameter. The reason Pi Day is celebrated on March 14 is because its first 3 digits are 3.14 (Pi = 3.1415926535...) March 14 also happens to be Albert Einstein's birthday. Pi is an irrational number, meaning that the sequence of its decimal digits continues to infinity without repeating itself.
The favorite way of celebrating Pi Day among geeks are eating a pie while reciting the first hundred digits of Pi.
