"The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi" (/paɪ/).
Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π. Consequently its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed; however, to date, no proof of this has been discovered. Also, π is a transcendental number – a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
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. In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of late 2013, over 12 trillion (10^13) 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. However, the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms." [Pi. Wikipedia]
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