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'.

**About Pi**

Pi
is an infinite decimal. Unlike numbers such as 3, 9.876, and 4.5, which have
finitely many nonzero numbers to the right of the decimal place, pi has
infinitely many numbers to the right of the decimal point.

If you write pi down in decimal form, the numbers to the
right of the 0 never repeat in a pattern. Some infinite decimals do have
patterns - for instance, the infinite decimal .3333333... has all 3's to the
right of the decimal point, and in the number .123456789123456789123456789...
the sequence 123456789 is repeated. However, although many mathematicians have
tried to find it, no repeating pattern for pi has been discovered - in fact, in
1768 Johann Lambert proved that there

*cannot*be any such repeating pattern.
As a number that cannot be written as a repeating decimal or
a finite decimal (you can never get to the end of it) pi is

*irrational:*it cannot be written as a fraction (the ratio of two integers).
Pi shows up in some unexpected places like probability, and
the 'famous five' equation connecting the five most important numbers in
mathematics, 0, 1, e, pi, and i: e^(i*pi) + 1 = 0.

Computers have calculated pi to many decimal places. It's
easy to find lists of them by Googling 'digits of pi'.

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