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Liu Hui's method of calculating the area of a circle. Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei.Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter ...
Archimedes, in his Measurement of a Circle, created the first algorithm for the calculation of π based on the idea that the perimeter of any (convex) polygon inscribed in a circle is less than the circumference of the circle, which, in turn, is less than the perimeter of any circumscribed polygon. He started with inscribed and circumscribed ...
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.
Download as PDF; Printable version; ... This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in category "Pi algorithms"
A History of Pi (book) Indiana Pi Bill; Leibniz formula for pi; Lindemann–Weierstrass theorem (Proof that π is transcendental) List of circle topics; List of formulae involving π; Liu Hui's π algorithm; Mathematical constant (sorted by continued fraction representation) Mathematical constants and functions; Method of exhaustion; Milü; Pi ...
The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics .
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (π). For more detailed explanations for some of these calculations, see Approximations of π. As of July 2024, π has been calculated to 202,112,290,000,000 (approximately 202 trillion) decimal digits.
The calculations Archimedes used to approximate the area numerically were laborious, and he stopped with a polygon of 96 sides. A faster method uses ideas of Willebrord Snell ( Cyclometricus , 1621), further developed by Christiaan Huygens ( De Circuli Magnitudine Inventa , 1654), described in Gerretsen & Verdenduin (1983 , pp. 243–250).