What is pi divided by?

Is 10000 bits enough? 3.1415926535 8979323846 2643383279 5028841971 6939937510 58209744944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502

How did you get 3.14 Pi? To write the calculation process yo! If you dare to challenge, please answer. Please read the supplementary question clearly and answer it, friend.

The calculation method of PI: 13:14, 2006-11-03, the ancients calculated the PI, In general, the circumscribed or circumscribed regular polygon of a circle is used to approximate the circumference of a circle. Archimedes uses the regular 96 polygon to obtain the accuracy of 3 decimal places of the PI; Liu Hui uses the positive 3072 polygon to get the 5-digit accuracy; ludolph van ceulen gets the 35 bit accuracy with the positive 262 polygon. The mathematical analysis appearing in the 17th century makes the calculation history of π enter a new stage, Weida's unusual formula is the earliest analytical expression of π. Even today, the beauty of this formula is amazing. It shows that the value of π can be calculated by a series of addition, multiplication, division and square root with the aid of the number 2
Then there are many expressions. For example, Wallis gave in 1650: some classical and commonly used formulas for calculating the ratio of circumference, machin formula. This formula was given by John, British astronomy professor Machin discovered it in 1706. He used this formula to calculate the Pi of 100 bits. Each term of machin's 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
There are many arctangent formulas similar to machin's formula. Among all these formulas, machin's formula seems to be the fastest. However, if you want to calculate more digits, such as tens of millions of bits, the machine formula will not be able to do it. The algorithm described below takes about a day to calculate on a PC, 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 term of this formula can get 8 decimal precision. In 1985, Gosper used this formula to calculate 17.5 million digits of PI
In 1989, David & Gregory chudnovsky brothers improved the Ramanujan formula into:
This formula is called the chudnovsky formula. Each calculation item can get 15 decimal precision. In 1994, the chudnovsky brothers used this formula to calculate 4044000000 bits. Another more convenient form of chudnovsky formula is as follows:
AGM (arithmetic geometric mean) algorithm
Gauss Legendre formula:
Initial value:
Repeated calculation:
The final calculation is as follows:
For example, 20 iterations are enough to calculate 1 million bits. In September 1999, Takahashi and kanada used this algorithm to calculate 206158 430000 bits of PI, setting a new world record
Borwein's fourth iteration formula is as follows
Initial value:
Repeated calculation:
The final calculation is as follows:
This formula was published by Jonathan borwein and Peter borwein in 1985. It converges to the PI four times
Bailey borwein Plouffe algorithm
This formula is abbreviated as BBP formula, which was jointly published by David Bailey, Peter borwein and Simon Plouffe in 1995. It breaks the traditional algorithm of PI and can calculate any nth bit of PI instead of the previous n-1 bit. This provides a feasibility for distributed calculation of PI. In 1997, Fabrice bellard found a formula 40% faster than BBP
If the circumference of a circle that can wrap the solar system can be calculated by using the 35 bit pI value calculated by ludolph van ceulen, the error is less than one millionth of the proton diameter
"Ten decimals are enough to make the earth's perimeter within an inch, and thirty decimals can make the circumference of the entire visible universe more accurate than even the most powerful microscope can tell."

How do you get the Pi? I know that Pi is equal to PI by dividing the circumference of a circle by the diameter of a circle. But how do people know the circumference of a circle? To find the circumference, we need to use the ratio of circumference to calculate the circumference of a circle. There is a reciprocal relationship between them, The circumference and Pi of a circle are calculated first. Which one? How? Who? When? Who? Who? When? Who? Who? Who? When? Who? Who? Who? Who? Who? Who? Who? Who? Who discovered the Pi? What's the use of Pi? Why is PI so useful? If you cheat, you can report me

Well, it's a good question to ask, because there is no most accurate PI. It should be the circumference of a circle. As for other questions, it was worked out by the ancient Chinese Zu Chongzhi (male). I know him in mathematics books

How is the PI obtained

In order to find out the relationship between the circumference and area of a garden and the diameter and radius of the garden, the ancients first made a garden and measured the circumference and diameter of the garden by measuring the two. After repeated exploration, it was found that the ratio of diameter to perimeter of any garden was a certain number, which was PI. Later, people used the same method, First, the area of the circle was calculated by the method of "patching up". Then the coach found the relationship among the area, radius and PI. The formula was deduced in this way

Is π a positive number? A positive number belongs to a rational number, and π is an infinite acyclic decimal number. Therefore, π can't be classified as a positive number, right?

Positive numbers in irrational numbers

Who knows all the figures of Pi 3.141492654. Please write it all out

3.141592653589793238462643383279502884197169399375105820974944 59230781640628620899 86280 34825 34211 7067982148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 055...

Is π (PI) rational or irrational? Is π (PI) a fraction? Is π (PI) a positive number?

One third of π (PI) is irrational
One third of π (PI) is a fraction
One third of π (PI) is positive

() found the PI, which is expressed by ()

Zu Chongzhi
PI

What is the expression of Pi fast

PI refers to the ratio of circumference to diameter of a circle on a plane. It is represented by the Greek letter π (read "Pai"). In ancient China, there are names of PI, PI, Zhou, etc. (in general calculation, people always convert π into 3.14, which is infinitely non cyclic decimal)

How is the PI calculated

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

What is pi divided by?