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Snippet from Wikipedia: Pi

The number π ( ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.

The number π is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as ⁠22/7⁠ are commonly used to approximate it. Consequently, its decimal representation never ends, nor does it enter a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient problem of squaring the circle with a compass and straightedge. The decimal digits of π appear to be evenly distributed, but no proof of this conjecture has been found.

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. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later. The development of calculus in the 17th century soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have extended the decimal representation of π to hundreds of trillions of digits.

Because it relates to a circle, π is found in formulae in trigonometry and geometry, especially those concerning circles, ellipses and spheres. It is found as well in formulae from cosmology, fractals, thermodynamics, mechanics, and electromagnetism. It also appears in areas such as number theory, statistics, and in modern mathematical analysis π is ubiquitous.

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