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.

Related Topics:
Mathematical constant - Ratio - Circle - Circumference - Greek - Diameter - Mathematics - Physics - Engineering - Greek letter - ? - Archimedes - Archimedes' number - Ludolph

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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.

Related Topics:
Euclidean plane geometry - Ratio - Circle - Circumference - Diameter - Area - Analytically - Trigonometric function

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All these definitions are equivalent.

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The numerical value of π rounded to 50 decimal places {{OEIS|id=A000796}} is:

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:3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37511

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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.

Related Topics:
Engineering - Science - Supercomputer - Personal computer

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