The two algorithms introduced in the calculation of π-valve algorithm 1995 have opened up a new way to study π. Because every number is calculated, it will not appear in the subsequent calculation process like water flowing through the valve. This new algorithm is called valve algorithm. This is in contrast to infinite series and iterative algorithm, which involve the intermediate values calculated in all the previous steps from beginning to end.
1995, American mathematicians Stan Wagner and Stanley Rabinowitz invented a simple valve algorithm, which is similar to arctan algorithm, but slower than iterative algorithm.
Bailey-Baldwin-Plouffe formula (BBP) is another valve algorithm, which belongs to a digital extraction algorithm. 1995, discovered by simon plouffe et al.
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Pi is a mathematical constant, which is the ratio of the circumference of a circle to its diameter, which is approximately equal to 3. 14 159. /kloc-After the middle of the 0/8th century, it was generally referred to by the Greek letter π, sometimes spelled "pi".
Because π is an irrational number, it cannot be completely expressed by fractions (that is, its fractional part is an infinite acyclic decimal). Of course, it can also be expressed by an approximation of a rational number such as 22/7. The sequence of π is considered to be randomly distributed and has special statistical randomness, but it has not been proved so far. In addition, π is also a transcendental number-it is not the root of any rational number coefficient polynomial. Because of the transcendental nature of π, it is impossible to draw a circle into a square with a ruler.
In order to facilitate the calculation in production, several ancient civilizations have long needed to calculate a more accurate value of π. In the 5th century AD, Zu Chongzhi, a mathematician in the Southern Song Dynasty, used geometric methods to calculate pi to 7 decimal places. At about the same time, Indian mathematicians also calculated pi to five decimal places. The first accurate formula of infinite series of π in history (that is, Leibniz formula of π) was not discovered by Indian mathematicians until about 1000 years later. In 20th century and 2nd1century, due to the rapid development of computer technology, the accuracy of π has been rapidly improved by computer calculation. As of 20 15, the decimal precision of π has reached 10 13 digits. At present, the main reason for human beings to calculate π value is to break records and test the calculation ability of supercomputers and high-precision multiplication algorithms, because almost all scientific research requires π accuracy not to exceed several hundred digits.
Because the definition of π involves a circle, π is widely used in many formulas of trigonometry and geometry, especially in the related formulas of circle, ellipsoid or sphere. Because of the special function of π in eigenvalue, it also appears in some fields of mathematics and science (such as the geometry of calculated data in number theory and statistics), as well as cosmology, thermodynamics, mechanics and electromagnetism. The wide application of π makes it one of the most widely known constants inside and outside the scientific community. People have published several books devoted to π, and the breakthrough records of pi day (14, March) and π value calculation often become the headlines of newspapers. In addition, the world record of reciting π values has reached 70,000 digits.
Source: Pi- Wikipedia