The number **π** (/paɪ/) is a mathematical constant that is the ratio of a circle's circumference to its diameter. The constant, sometimes written **pi**, is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century. π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers (such as 22/7 or other fractions that are commonly used to approximate π); consequently, its decimal representation never ends and never repeats. Moreover, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge. The digits in the decimal representation of π appear to be random, although no proof of this supposed randomness has yet been discovered.

For thousands of years, mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Before the 15th century, mathematicians such as Archimedes and Liu Hui used geometrical techniques, based on polygons, to estimate the value of π. Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of π, and were used by mathematicians including Madhava of Sangamagrama, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, and Srinivasa Ramanujan.

In the 20th century, mathematicians and computer scientists discovered new approaches that – when combined with increasing computational power – extended the decimal representation of π to over 10 trillion (1013) digits. Scientific applications generally require no more than 40 digits of π, so the primary motivation for these computations is the human desire to break records, but the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.

Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, or spheres. It is also found in formulae from other branches of science, such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics, and electromagnetism. The ubiquitous nature of π makes it one of the most widely known mathematical constants, both inside and outside the scientific community: Several books devoted to it have been published; the number is celebrated on Pi Day; and news headlines often contain reports about record-setting calculations of the digits of π. Several people have endeavored to memorize the value of π with increasing precision, leading to records of over 67,000 digits.

### Other articles related to "pi":

**Pi**- Outside The Sciences - In Popular Culture

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**pi**room" ... slide rule, MIT! GOOOOOO TECH! MIT cheer Many schools in the United States observe

**Pi**Day on 14 March (March is the third month, hence the date is 3/14) ... The digits of π have also been incorporated into the lyrics of the song "

**Pi**" from the album Aerial by Kate Bush, and a song by Hard 'n Phirm ...

**pi**

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**pi**is produced by steeping the aromatic wormwood flower heads in a strong, clear alcohol such as vodka or pure grain alcohol, it cannot be considered an equivalent to ...

**pi**- Raw Material

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**pi**liqueur, three species of Artemisia (the genus of the wormwoods) are particularly valued A ... rupestris (white géné

**pi**or rock wormwood), A ... genipi (black géné

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**Pi**- Reign

... Fu

**Pi**took measures to try to consolidate his current position—now largely only over modern Shanxi, although there were still many pockets of territory loyal to Former Qin in modern Shaanxi and Gansu, and there ... east, trying to return to their home land, requested Fu

**Pi**to grant permission to let them through ... Fu

**Pi**refused and tried to intercept them, but suffered a major defeat, in which Wang Yong and the major general Juqu Jushizi (沮渠俱石子) were ...

**Pi**Serpentis

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**Pi**Serpentis (π Ser, π Serpentis) is a star in the constellation Serpens, in its head (Serpens Caput) ...

**Pi**Serpentis is a white A-type main sequence dwarf with an apparent magnitude of +4.82 ...