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The first to use an electronic computer (the ENIAC) to calculate π [25] 70 hours 2,037: 1953: Kurt Mahler: Showed that π is not a Liouville number: 1954 S. C. Nicholson & J. Jeenel Using the NORC [26] 13 minutes 3,093: 1957 George E. Felton: Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct [27] [28] 33 ...
During his calculations, which took many tedious days of work, Shanks was said to have calculated new digits all morning and would then spend all afternoon checking his morning's work. [2] Shanks died in Houghton-le-Spring, County Durham, England in June 1882, aged 70, and was buried at the local Hillside Cemetery on 17 June 1882. [2] [3]
In 1789, the Slovene mathematician Jurij Vega improved John Machin's formula to calculate the first 140 digits, of which the first 126 were correct. [32] In 1841, William Rutherford calculated 208 digits, of which the first 152 were correct.
In 1844, a record was set by Zacharias Dase, who employed a Machin-like formula to calculate 200 decimals of π in his head at the behest of German mathematician Carl Friedrich Gauss. [88] In 1853, British mathematician William Shanks calculated π to 607 digits, but made a mistake in the 528th digit, rendering all subsequent digits incorrect ...
Google engineer Emma Haruka Iwao has calculated pi to 31 trillion digits, breaking the world record.
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.
Machin's formula [4] (for which the derivation is straightforward) is: = The benefit of the new formula, a variation on the Gregory–Leibniz series ( π / 4 = arctan 1), was that it had a significantly increased rate of convergence, which made it a much more practical method of calculation.
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