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Calculated 127 decimal places, but not all were correct 112: 1721: Anonymous Calculation made in Philadelphia, Pennsylvania, giving the value of pi to 154 digits, 152 of which were correct. First discovered by F. X. von Zach in a library in Oxford, England in the 1780s, and reported to Jean-Étienne Montucla, who published an account of it. [20 ...
TachusPi by Fabrice Bellard [100] is the program used by himself to compute world record number of digits of pi in 2009. y -cruncher by Alexander Yee [ 48 ] is the program which every world record holder since Shigeru Kondo in 2010 has used to compute world record numbers of digits .
To compute π to 100 decimal places, he combined his formula with the Taylor series expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of pi-hunters for centuries (well into the computer era). Several other Machin-like formulae are known.
Google engineer Emma Haruka Iwao has calculated pi to 31 trillion digits, breaking the world record.
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
His works on the accurate value of pi describe the lengthy calculations involved. Zu used the Liu Hui's π algorithm described earlier by Liu Hui to inscribe a 12,288-gon. Zu's value of pi is precise to six decimal places and for almost nine hundred years thereafter no subsequent mathematician computed a value this precise. [9]
In addition to calculating π, Shanks also calculated e and the Euler–Mascheroni constant γ to many decimal places. He published a table of primes (and the periods of their reciprocals) up to 110,000 and found the natural logarithms of 2, 3, 5 and 10 to 137 places. During his calculations, which took many tedious days of work, Shanks was ...
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 ...