Please tell me how to calculate the PI

Please tell me how to calculate the PI

The circumference of a circle divided by its diameter is the PI

How is the PI calculated?

Calculation method of PI
Archimedes used the regular polygon to approximate the circumference of a circle. Archimedes used the positive 96 polygon to get the accuracy of 3 decimal places of PI. Liu Hui got 5-digit precision with 3072 polygon. Ludolph van ceulen got 35 bit accuracy by using positive 262 polygon. This geometry based algorithm has a large amount of calculation and slow speed, With the development of mathematics, mathematicians have found many formulas for calculating pi. Here are some classical formulas to introduce. In addition to these classical formulas, there are many other formulas and formulas derived from these classical formulas, which will not be listed one by one

What's the PI now How many people are there now?

The latest calculation record of PI was set by the Japanese team Yasunari kanada. In 2002, they calculated the pI value of 124110000000 decimal places, which broke the world record of 20600000000 decimal places set by them on September 18, 1999

How many digits of PI have been calculated? What is the specific number? What's after 3.1415926?

3.1415926535897932384626
Archimedes used the regular polygon to approximate the circumference of a circle. Archimedes used the positive 96 polygon to get the accuracy of 3 decimal places of PI. Liu Hui got 5-digit precision with 3072 polygon. Ludolph van ceulen got 35 bit accuracy by using positive 262 polygon. This geometry based algorithm has a large amount of calculation and slow speed, With the development of mathematics, mathematicians have found many formulas for calculating pi. Here are some classical formulas to introduce. In addition to these classical formulas, there are many other formulas and formulas derived from these classical formulas, which will not be listed one by one
Machin formula this formula was discovered by John machin, a British astronomy Professor, in 1706. He used this formula to calculate the Pi of 100 bits. Each term of machin formula can get 1.4 decimal precision. Because the multiplier and divisor are not larger than long integers, it can be easily programmed on the computer
The machine. C source program also has many arctangent formulas similar to machin's formula. Among all these formulas, the machin formula seems to be the fastest. Nevertheless, if you want to calculate more digits, such as tens of millions of bits, the machine formula will not be able to do it, These algorithms are more complicated to implement by program. Because the calculation process involves the multiplication and division of two large numbers, FFT (fast Fourier transform) algorithm is used. FFT can shorten the operation time of multiplication and division of two large numbers from O (N2) to o (NLog (n))
Ramanujan formula in 1914, the Indian mathematician Srinivasa Ramanujan published a series of 14 formulas for calculating the PI, which is one of them. Each calculation item of this formula can obtain 8 decimal precision. In 1985, Gosper used this formula to calculate 17500000 bits of PI, David & Gregory chudnovsky brothers improved Ramanujan formula into: this formula is called chudnovsky formula, each calculation can get 15 decimal precision. In 1994, chudnovsky brothers used this formula to calculate 4044000, Another more convenient form of chudnovsky formula for computer programming is: AGM (arithmetical geometric mean) algorithm Gauss Legendre formula: initial value: repeated calculation: final calculation: this formula will get double decimal precision every iteration, for example, to calculate 1 million bits, In September 1999, Takahashi and kanada used this algorithm to calculate 206158430000 bits of PI, setting a new world record. Borwein's fourth iteration formula: initial value: repeated calculation: final calculation: this formula was published by Jonathan borwein and Peter borwein in 1985, and it converges to the PI four times
Bailey borwein Plouffe algorithm this formula is referred to as BBP formula, which was jointly published by David Bailey, Peter borwein and Simon Plouffe in 1995. It breaks the traditional algorithm of PI. It can calculate any nth bit of PI without calculating the N-1 bit in front of it. This provides the feasibility for distributed computing of circumference, Fabrice bellard found a formula 40% faster than BBP: 3.1415926 < 3.1415927

How many digits of PI have been worked out so far

The latest record for calculating pi was set by the Japanese team Yasunari kanada, who in 2002 worked out a pI value of 124110000000 decimal places

What is the maximum percentage of the circumference?

Japan's computer prodigy Kondo used a combination of home computer and cloud computing to calculate the PI to 5 trillion digits after the decimal point
PI, 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. It is a key value for the accurate calculation of geometric shapes such as the circumference, area and volume of a circle

How many places has the PI been calculated

480 million

How is the PI calculated

In a circle with radius r, make an inscribed regular hexagon. In this case, the side length of a regular hexagon is equal to the radius r of a circle. Therefore, the circumference of a regular hexagon is equal to 6R

How to calculate the Pi?

The calculation process of PI is a well-known number. From the beginning of recorded history, this number has attracted the interest of laymen and scholars. As a very important constant, PI was first used to solve the calculation problem of circle

How is the PI calculated Please make it easy to understand!

Trigonometric function, very simple, the premise is that you have a calculator! Even calculated completely close to the real value, accurate to the small data point after 9. Junior high school level is OK