What is the mathematical process used to calculate pi?

Question

I used to know this in grade school. I think it had something to do with repeatedly multiplying and dividing by a pattern of fractions...

Answer 1

nah man...its the circumference divided by the diameter...
oh wait....here is a series that can be used to find it:
π = 4 – 4⁄3 + 4⁄5 – 4⁄7 + 4⁄9 – 4⁄11 ...
go to wikipedia.org and type in "pi"
all the pi info is there....

Hope that helps!

Answer 2

The approximate value of pi to eight decimal places is 3.14159265. The ratio is actually an irrational number, meaning that its decimal places go on infinitely without repeating or ending in zeros. Mathematicians have found many unending equations with solutions equal to pi; one of the simplest is p = 4(1 - 1/3€ + 1/5ƒ - 1/7‡ + 1/9Š …). Computers can use such equations to quickly estimate pi with great accuracy; in this way the value of p has been figured to more than 1.2 trillion (1,200,000,000,000) decimal places.

The ratio pi was known in ancient times, and various approximations of its numerical value were used. In the Bible, the value of pi was taken to be 3. The Greek mathematician Archimedes correctly asserted that the value was between 3 10/70 and 3 10/71. The symbol p for the ratio was first used in 1706 by the Welsh mathematician William Jones, but it became popular only after its adoption by the Swiss mathematician Leonhard Euler in 1737. In 1882 the German mathematician Ferdinand Lindemann proved that p is a transcendental number—that is, it is not the root of any polynomial equation with rational coefficients .Consequently, Lindemann was able to demonstrate that it is impossible to square the circle (construct a square whose area equals that of a given circle) using algebra or a ruler and compass because the area of a square can always be expressed as a polynomial equation with rational coefficients.

I hope this helps!

Answer 3

The series mentioned by D is famous but converges too slowly to be very useful. Until computers came along (in other words, back when these calculations had to be done by hand), the most popular formulas utilized inverse tangent identities. For example, Machin developed a popular one in 1706, which he used to calculate pi to 100 places:

pi = 16 arctan(1/5) - 4 arctan(1/239)

http://ic.net/~jnbohr/java/Machin.html

Also, if you are interested in how the calculation of pi has progressed historically, you will love the following Web site:

http://documents.wolfram.com/v5/Demos/Notebooks/CalculatingPi.html

Answer 4

Pi is the ratio of the circumference of a circle to its diameter

Pi = circumference / diameter

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Click on the URL below for additional information concerning pr

mathforum.org/dr.math/faq/faq.pi.html

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Answer 5

From what I can remember; pi = 22/7