π π of handwritten characters, generally expressed by π, is a common mathematical constant in mathematics and physics. It is defined as the ratio of the circumference to the diameter of a circle. It is also equal to the ratio of the area of a circle to the square of its radius. Accurate calculation of geometric shapes such as circle perimeter, circle area and sphere volume is the key. Analytically, π can be defined as the smallest x >；; 0 makes sin(x) = 0.

The commonly used π approximations are "22/7" and "355/ 1 13". Both are from Zu Chongzhi.

π is approximately equal to (accurate to 65438th place+000th place after decimal point).

3. 14 159 26535 89793 23846 26433 83279 50288 4 197 1

69399 375 10 58209 74944 59230 78 164 06286 20899

86280 34825 342 1 1 70680

Calculation and history of π

Because of the transcendence of π, π can only be calculated by approximate method. For general application, 3. 14 or 22/7 is enough, but in engineering, 3. 14 16 (5 digits) or 3. 14 159 (6 digits) is often used. As for the secret rate of 355/ 1 13, it is easy to remember and accurate to 7 significant figures.

experimental period

China ancient book cloud:' Wednesday's diameter is one', which means π=3. The Egyptian ancient book Ames papyrus (Ahmes, also known as Ames Papyrus Literature) in the 0/7th century BC; It was discovered by Englishman Henry Rhind in 1858, so it is also called "Rhind Grass Piece Literature"). Is the earliest approximate value of pi in the world, which is 256/81(3+1/9+1/27+1/865448).

Before Archimedes, the measurement of π value depended on physical measurement.

Geometric period? d？ Repeated tangent circle

Archimedes worked out the pi between 3 1/7 and 3 10/7 1.

In 263 AD, Liu Hui gave π=3. 140 14 by using "cyclotomy", and defined it as 3. 14, which is a good approximation? d？ D "If you cut carefully, you will lose very little. If you cut it again, you can't cut it. Then you will be surrounded and there will be no loss. " ; Have the idea of seeking the limit.

In 466 AD, Zu Chongzhi used pi to calculate the accuracy to seven decimal places, and this record remained in the world for a thousand years. In order to commemorate Zu Chongzhi's contribution to the development of China's pi, this calculated value is named "Zu Chongzhi pi" after him, which is called the ancestral rate for short.

Analysis period? d？ D infinite series

During this period, people began to get rid of complicated calculation by using the method of secant circle, and began to find π by using infinite series or infinite continuous product.

Ludolph van ceulen (about 1600) calculated the first 35 decimal digits. He was so proud of it that he carved it on his tombstone.

1789, the Slovenian mathematician Jurij Vega got the first decimal number of 140, in which 137 was correct. This world record has been maintained for fifty years. He used the number formula proposed by John McKin in 1706.

None of the above methods can calculate π quickly. The first fast algorithm was proposed by Machin:

Arctan(x) can be calculated by Taylor series. The analogy is called "Machin-like algorithm".