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John Machin (bapt. c. 1686 – June 9, 1751) [1] was a professor of astronomy at Gresham College, London. He is best known for developing a quickly converging series for pi in 1706 and using it to compute pi to 100 decimal places.
In mathematics, Machin-like formulas are a popular technique for computing π (the ratio of the circumference to the diameter of a circle) to a large number of digits. They are generalizations of John Machin 's formula from 1706:
Calculated pi to 72 digits, but not all were correct 71: 1706: John Machin [2] 100: 1706: William Jones: Introduced the Greek letter ' π ' 1719: Thomas Fantet de Lagny [2] Calculated 127 decimal places, but not all were correct 112: 1721: Anonymous Calculation made in Philadelphia, Pennsylvania, giving the
The digits of pi extend into infinity, and pi is itself an irrational number, meaning it can’t be truly represented by an integer fraction (the one we often learn in school, 22/7, is not very ...
The Babylonians were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near Susa in 1936 (dated to between the 19th and 17th centuries BCE) gives a better approximation of π as 25 ⁄ 8 = 3.125, about 0.528% below the exact value. [8] [9] [10] [11]
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
John Wallis, English mathematician who is given partial credit for the development of infinitesimal calculus and pi. Viète's formula, a different infinite product formula for . Leibniz formula for π, an infinite sum that can be converted into an infinite Euler product for π. Wallis sieve
Madhava's correction term is a mathematical expression attributed to Madhava of Sangamagrama (c. 1340 – c. 1425), the founder of the Kerala school of astronomy and mathematics, that can be used to give a better approximation to the value of the mathematical constant π (pi) than the partial sum approximation obtained by truncating the Madhava–Leibniz infinite series for π.