Pi

The mathematical constant ? is the ratio of a circle's circumference (Greek ??????????, periphery) to its diameter and is commonly used in mathematics, physics, and engineering. The name of the Greek letter ? is pi (pronounced pie), and this spelling can be used in typographical contexts where the Greek letter is not available. ? is also known as Archimedes' constant (not to be confused with Archimedes' number) and Ludolph's number.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In Euclidean plane geometry, ? may be defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius. Advanced textbooks define ? analytically using trigonometric functions, for example as the smallest positive x for which sin(x) = 0, or as twice the smallest positive x for which cos(x) = 0.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

All these definitions are equivalent.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The numerical value of π rounded to 50 decimal places is:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37511

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Although this precision is more than sufficient for use in engineering and science, much effort over the last few centuries has been put into computing more digits and investigating the number's properties. Despite much analytical work, in addition to supercomputer calculations that have determined over 1 trillion digits of π, no pattern in the digits has ever been found. Digits of π are available from multiple resources on the Internet, and a regular personal computer can be used to compute billions of digits.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Mathematical constant: A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. Unlike physical constants, mathematical constants are defined independently of any physical measurement....

Ratio: In algebra, a ratio is the relationship between two quantities. It is expressed as the quotient of two numbers, or as two numbers separated by a colon (pronounced "to"). A number that can be written as a ratio of two integers is a rational number. In physics, a ratio between two magnitudes of the ...

Circle: :See The Circle for the distributed file storage system, and see ring (diacritic) for the diacritic mark....

Pi related Images and Photos (experimental)

A.P.I. Cioccolato	A.P.I. Cioccolato	A.P.I. Cioccolato	K-9 P.I. DVD (Widescreen)
pi*z*z*a	PI No. 8	Magnum P.I. - Helicopter	Magnum P.I. - Helicopter
Magnum P.I. Magnum Toys T-Shirt	Magnum P.I. Magnum Toys T-Shirt	Magnum P.I. - It's All About the 'Stache	Magnum P.I. The Complete Season 2 DVD (Full Frame)