Pi

Number, approximately 3.14

The number Ī€ is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number Ī€ appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. The transcendence of Ī€ implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of Ī€ appear to be randomly distributed, but no proof of this conjecture has been found.

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