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...

x2 − 2y2 = −1.) Formulae of this kind are known as Machin-like formulae. Machin's particular formula was used well into the computer era for calculating...

London on 9 June 1751. Machin enjoyed a high mathematical reputation. In 1706, Machin computed the value of π with the formula given below to one hundred...

Attilio Bertolucci Award for his poetry. Takano also discovered a Machin-like formula for calculating pi. Takano, Kikuo (2004). Toward Meaning: Poems of...

continued fraction for arctan ⁠x/y⁠ cited above with the best-known Machin-like formula provides an even more rapidly, although still linearly, converging...

on the following identity without variables, due to Machin. This is known as a Machin-like formula: π 4 = 4 arctan ⁡ 1 5 − arctan ⁡ 1 239 {\displaystyle...

course of approximately two months, a record for the time, from the Machin-like formula: π 4 = arctan ⁡ 1 2 + arctan ⁡ 1 5 + arctan ⁡ 1 8 . {\displaystyle...

{\frac {1}{239}}.} Machin reached 100 digits of π with this formula. Other mathematicians created variants, now known as Machin-like formulae, that were...

Machen (disambiguation) Machin-like formula, a class of mathematical identities Machin series, a series of British stamps Cerro Machín, a volcano in Colombia...

arctangents of smaller values, eventually resulting in a variety of Machin-like formulas for ⁠ π {\displaystyle \pi } ⁠. Isaac Newton (1684) and other mathematicians...

(2021-09-04). "Algorithmic Determination of a Large Integer in the Two-Term Machin-like Formula for π". Mathematics. 9 (17): 2162. arXiv:2107.01027. doi:10.3390/math9172162...

problem a few years later. Next, he systematically investigated Machin-like formula by which the number π may be represented as a rational combination...

function can be approximated highly efficiently, formulas like this – known as Machin-like formulas – are used for high-precision approximations of π:...

C; Underwood, Robin; Bacquart, Thomas; Sutton, Gavin; Davidson, Stuart; Machin, Graham (1 October 2017). "Re-estimation of argon isotope ratios leading...

diameter, approximately equal to 3.14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit...

L; Sparasci, F; Plimmer, M D; de Podesta, M; Underwood, R; Sutton, G; Machin, G; Gavioso, R M; Madonna Ripa, D; Steur, P P M; Qu, J; Feng, X J; Zhang...

all time". GamesRadar+. p. 5. Archived from the original on June 3, 2020. Machin, Cole (January 2011). "The Making of: Sonic Spinball". Retro Gamer. No. 85...

{1^{2}\cdot 3^{2}\cdot 5^{2}}{2^{2}\cdot 4^{2}\cdot 6^{2}}}+\cdots } The Machin formula for π is 1 4 π = 4 arctan ⁡ 1 5 − arctan ⁡ 1 239 , {\textstyle {\tfrac...

calculi integralis 1789 – Jurij Vega improves Machin's formula and computes π to 140 decimal places, 1805 – FFT-like algorithm known by Carl Friedrich Gauss...

unemployment". Economics Help. Retrieved 2020-09-21. Dickens, Richard; Machin, Stephen; Manning, Alan (January 1999). "The Effects of Minimum Wages on...

the Joker is slowly dying due to the unstable properties of the Titan formula in his blood, and infects Batman with the same disease to force him to...

 1505–1556. doi:10.1093/qje/qjae001. hdl:10419/250624. Green, Francis; Machin, Stephen; Manning, Alan (1996). "The Employer Size–Wage Effect: Can Dynamic...

Lagrange discovers the divergence theorem. 1789 – Jurij Vega improves Machin's formula and computes π to 140 decimal places, 136 of which were correct. 1794 –...

Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places. 1789 — Jurij Vega improves Machin's formula and...

his central midfield position, he formed a legendary midfield alongside Machín and Ramón Gabilondo. In mid-1940, a decree issued by Francisco Franco banned...

notation comprises the symbols used to write mathematical equations and formulas. Notation generally implies a set of well-defined representations of quantities...

Police Hiring in Italy and the United States". In Philip J. Cook; Stephen Machin; Olivier Marie; Giovanni Mastrobuoni (eds.). Lessons from the Economics...

during his work on the problem in 1692–93, and told the astronomer John Machin that "his head never ached but when he was studying the subject". According...

Publishers. ISBN 978-0-7923-1874-3. Martin, Nicholas; Boomsma, Dorret; Machin, Geoffrey (1997). "A twin-pronged attack on complex traits" (PDF). Nature...

Evidence from an Allocation Policy in Germany". SSRN 2589824. Jaitman, Laura; Machin, Stephen (25 October 2013). "Crime and immigration: new evidence from England...