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The number π could be a mathematical constant, the magnitude relation of a circle's circumference to its diameter, ordinarily approximated as three.14159. it's been depicted by the Greek letter "π" since the mid-18th century, although it's conjointly generally spelled out as "pi" (/paɪ/).

Being associate real number, π can't be expressed precisely as a typical fraction, though fractions like 22/7 and alternative rational numbers ar ordinarily accustomed approximate π. Consequently its decimal illustration ne'er ends and ne'er settles into a permanent continuance pattern. The digits seem to be willy-nilly distributed; but, to date, no proof of this has been discovered. Also, π could be a irrational number – variety that's not the foundation of any non-zero polynomial having rational coefficients. This transcendence of π implies that it's not possible to unravel the traditional challenge of squaring the circle with a compass and hand tool.

Although ancient civilizations required the worth of π to be computed accurately for sensible reasons, it had been not calculated to over seven digits, victimization geometrical techniques, in Chinese arithmetic and to regarding 5 in Indian arithmetic within the fifth century cerium. The traditionally 1st precise formula for π, supported infinite series, wasn't accessible till a millennium later, once within the fourteenth century the Madhava–Leibniz series was discovered in Indian arithmetic. within the twentieth and twenty first centuries, mathematicians and laptop scientists discovered new approaches that, once combined with increasing machine power, extended the decimal illustration of π to, as these days 2013, over 13.3 trillion (1013) digits.[3] Scientific applications typically need no over forty digits of π that the primary motivation for these computations is that the human want to interrupt records. However, the in depth calculations concerned are accustomed check supercomputers and high-precision multiplication algorithms.

Because its definition relates to the circle, π is found in several formulae in trig and pure mathematics, particularly those regarding circles, ellipses or spheres. it's conjointly found in formulae utilized in alternative branches of science like cosmology, variety theory, statistics, fractals, natural philosophy, mechanics and electromagnetism. The ubiquitousness of π makes it one among the foremost wide familiar mathematical constants each within and outdoors the scientific community: many books dedicated to it are revealed, the quantity is well known on Pi Day and record-setting calculations of the digits of π usually lead to news headlines. makes an attempt to con the worth of π with increasing preciseness have LED to records of over sixty seven,000 digits.

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