Euclid's Elements of Geometry in ancient Greece (about the beginning of the 3rd century BC) mentioned that pi was a constant, and China's ancient calculation book Zhou Bi Shu Jing (about the 2nd century BC) recorded that pi was a constant. Many approximations of pi have been used in history, most of which were obtained by experiments in the early days. For example, π = (4/3) 4 ≈ 3. 1604 is taken from ancient Egyptian papyrus (about BC 1700). The first person to find pi scientifically was Archimedes. In The Measurement of a Circle (3rd century BC), he determined the upper and lower bounds of the circumference of a circle by using the circumference of a regular polygon inscribed and circumscribed by the circle. Starting with a regular hexagon, he multiplied it by a regular 96-hexagon and got (3+( 10/7 1)).

When Liu Hui, a mathematician in China, annotated Nine Chapters Arithmetic (263), he got the approximate value of π only by inscribing a regular polygon into a circle, and also got the value of π accurate to two decimal places. His method is called the secant circle method by later generations. He used secant technique until the circle inscribed the regular polygon of 192.

Zu Chongzhi, a mathematician in the Northern and Southern Dynasties, further obtained the π value accurate to 7 decimal places (about the second half of the 5th century), gave the insufficient approximation of 3. 14 15926 and the excessive approximation of 3. 14 15927, and also got two approximate fractional values, namely 355//. In the west, the secret rate was not obtained by German Otto until 1573, and was published in the work of Dutch engineer Antoine in 1625, which is called Antoine rate in Europe.

17 At the beginning of the 5th century, the Arabic mathematician Cassie got the exact decimal value of pi17, which broke the record kept by Zu Chongzhi for nearly a thousand years.

1596, the German mathematician Curran calculated the π value to 20 decimal places, and then spent his whole life calculating it to 35 decimal places of 16 10. This value is named Rudolph number after him.

1579 The French mathematician Veda gave the first analytical expression of π.

Since then, various expressions of π value such as infinite product, infinite continued fraction and infinite series have appeared one after another, and the calculation accuracy of π value has also improved rapidly. 1706, the British mathematician Mackin calculated the π value, which broke through the decimal mark of 100. 1873, another British mathematician Jean-Jacques calculated π to 707 decimal places, but his result was wrong from 528 decimal places. By 1948, Ferguson in Britain and Ronchi in the United States announced the 808-bit decimal value of π, which became the highest record of manual calculation of pi.

The appearance of electronic computer makes the calculation of π value develop by leaps and bounds. From 65438 to 0949, the Army Ballistics Research Laboratory in Aberdeen, Maryland, USA used a computer (ENIAC) to calculate π value for the first time, and it suddenly reached 2037 decimal places, exceeding thousands of digits. 1989, researchers at Columbia University in the United States used Cray-2 and IBM-VF supercomputers to calculate 480 million digits after the decimal point, and then continued to calculate to 10 1 100 million digits after the decimal point, setting a new record.

Besides the numerical calculation of π, its properties have also attracted many mathematicians. 176 1 year, Swiss mathematician Lambert first proved that π is an irrational number. 1794 French mathematician Legendre proved that π2 is also an irrational number. By 1882, German mathematician Lin Deman proved that π is a transcendental number for the first time, thus denying the problem of "turning a circle into a square" that has puzzled people for more than two thousand years. Others study the characteristics of π and its connection with other numbers. For example, 1929, the Soviet mathematician Gelfond proved that eπ is a transcendental number and so on.