Does anybody know how do they calculate the value of pi?

Answer 1

Taylor series.

For example:

arctan(x) = sum ( (-1)^n)x^(2n+1)/2n+1 for

pi/4 = arctan(1) = 1 - 1/3 + 1/5 - 1/7 + 1/9 ...

For actual multimillion decimal place calculations, there are other function's expansions that converge more rapidly than this one.

Answer 2

By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it.

For the sake of usefulness people often need to approximate pi. For many purposes you can use 3.14159, which is really pretty good, but if you want a better approximation you can use a computer to get it. Here's pi to many more digits: 3.14159265358979323846.

The area of a circle is pi times the square of the length of the radius, or "pi r squared":

A = pi*r^2
A very brief history of pi

Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3; the Babylonians had an approximation of 3 1/8 (3.125), and the Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484), which is slightly less accurate and much harder to work with. For more, see A History of Pi by Petr Beckman (Dorset Press).
The modern symbol for pi was first used in our modern sense in 1706 by William Jones, who wrote:
There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to (16/5 - 4/239) - 1/3(16/5^3 - 4/239^3) + ... = 3.14159... = (see A History of Mathematical Notation by Florian Cajori).
Pi (rather than some other Greek letter like Alpha or Omega) was chosen as the letter to represent the number 3.141592... because the letter [] in Greek, pronounced like our letter 'p', stands for 'perimeter'.

Answer 3

roll out the dough into a circle and place into the tin
crimo the edges and fill with your favorite fruit
place a second circle of dough on top of the fruit filling and crimp the edges together
cut a small hole in the center of the PI to let the steam escape
bake at 350 degrees for 1 hour and serve with ice cream.

Answer 4

The usual method is to select some series that is known to converge to π (or some simple multiple of π) and start computing.

For example

Σ 1/(2k-1)² for k = 1 to infinity can be shown (analytically) to be π²/8

Another interesting formula is the infinite product

√(1/2)*√((1/2 + (1/2)*√(1/2)))*√(1/2 + (1/2)*√((1/2) +(1/2)*√(1/2)))) ∙∙∙

which is equal to 2/π

Any compendium of infinite series and/or infinite products wil have several such formula.


Doug

Answer 5

pi was originally discovered in the ancient times by mathematicians studying the porperty of circle,they used to draw a circle and used to calculate its circumference and divide it by the longest chord(diameter), and when they did so for different circles they observed that the ratio of perimeter or circumference of a circle to a diameter was always a constant that is pi, even if u see the formula of circumference of a circle you will notice that Circumference=2pi*radius, and 2* radius=diameter.

Answer 6

22/7

Answer 7

Have you heard of the term pi r square
well, pi are round cornbread r square.

Answer 8

divide the circumference of a circle by it's radius

Answer 9

http://www.pbs.org/wgbh/nova/archimedes/pi.html