Pi
constant ratio of the circumference of a circle to its diameter
The number π ( ; spelled out as pi) is a mathematical constant that is the ratio of a circle's circumference to its diameter. It is approximately equal to: 3.141592653589793238462643383279...
It appears in many formulae across mathematics and physics. Some of these formulae are used as definitions of π to avoid relying on the definition of the length of a curve.
π is an irrational number, meaning that it cannot be expressed exactly as a ratio of integers (although fractions such as
22
7
{\displaystyle {\tfrac {22}{7}}}
are commonly used to approximate it). Consequently, its decimal representation never ends, nor does it enter a permanently repeating pattern. It is also a transcendental number, meaning it is not a root of any non-zero polynomial with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient problem of squaring the circle with a compass and straightedge.
Mathematicians have long attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations.
Begin with the source’s own compact description: “Pi” is constant ratio of the circumference of a circle to its diameter. The dossier treats that line as a proposition to test through constant, ratio and circumference, not as a finished interpretation.
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This entry incorporates text from “Pi” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.