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After his marriage in 1846, Shanks earned his living by owning a boarding school at Houghton-le-Spring, which left him enough time to spend on his hobby of calculating mathematical constants. In addition to calculating π , Shanks also calculated e and the Euler–Mascheroni constant γ to many decimal places.
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.
The calculation was done between 4 May and 3 August, with the primary and secondary verifications taking 64 and 66 hours respectively. [ 43 ] In October 2011, Shigeru Kondo broke his own record by computing ten trillion (10 13 ) and fifty digits using the same method but with better hardware.
Shanks wrote the book Solved and Unsolved Problems in Number Theory, [3] which mostly depended on quadratic residues and Pell's equation.The third edition of the book contains a long essay on judging conjectures, [3]: 239 ff in which Shanks contended that unless there is a lot of evidence to suggest that something is true, it should not be classified as a conjecture, but rather as an open ...
A team from the University of Applied Sciences Graubünden in Switzerland claims it has calculated for 62.8 trillion digits of Pi.
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 ...
Although rough estimates for pi were given in the Zhou Li (compiled in the 2nd century BC), [29] it was Zhang Heng who was the first to make a concerted effort at creating a more accurate formula for pi. Zhang Heng approximated pi as 730/232 (or approx 3.1466), although he used another formula of pi in finding a spherical volume, using the ...
The version presented below is also known as the Gauss–Euler, Brent–Salamin (or Salamin–Brent) algorithm; [1] it was independently discovered in 1975 by Richard Brent and Eugene Salamin. It was used to compute the first 206,158,430,000 decimal digits of π on September 18 to 20, 1999, and the results were checked with Borwein's algorithm .