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In mathematics, Euler's identity[ note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .
It produces about 14 digits of π per term [130] and has been used for several record-setting π calculations, including the first to surpass 1 billion (10 9) digits in 1989 by the Chudnovsky brothers, 10 trillion (10 13) digits in 2011 by Alexander Yee and Shigeru Kondo, [131] and 100 trillion digits by Emma Haruka Iwao in 2022. [132]
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that. an alternating series . It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series ), [ 1] and was later ...
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As of July 2024, π has been calculated to 202 trillion decimal digits. The last 100 decimal digits of the latest world record computation are: [ 1] Graph showing how the record precision of numerical approximations to pi measured in decimal places (depicted on a logarithmic scale), evolved in human history.
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