John Machin, (1680—June 9, 1751), a professor of astronomy in London, is best known for developing a quickly converging series for π in 1706 and using it to compute π to 100 decimal places. Events First Portuguese governor was appointed to Macau The Swedish city Karlskrona was founded as the Royal Swedish Navy relocated there. ... Jump to: navigation, search June 9 is the 160th day of the year in the Gregorian calendar (161st in leap years), with 205 days remaining. ... Events Adam Smith is appointed professor of logic at the University of Glasgow March 31 - The future King George III of the United Kingdom succeeds his father as Prince of Wales. ... Jump to: navigation, search Lower-case pi The mathematical constant Ï€ is the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter and is commonly used in mathematics, physics, and engineering. ... Events March 27 - Concluding that Emperor Iyasus I of Ethiopia had abdicated by retiring to a monastery, a council of high officials appoint Tekle Haymanot I Emperor of Ethiopia May 23 - Battle of Ramillies September 7 - The Battle of Turin in the War of Spanish Succession - forces of Austria and...

Machin's formula 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. Jump to: navigation, search Lower-case pi The mathematical constant Ï€ is the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter and is commonly used in mathematics, physics, and engineering. ...

To compute π to 100 decimal places, he combined his formula with the Taylor series(of ducks) expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of π-hunters for centuries (well into the computer era). Jump to: navigation, search As the degree of the Taylor series rises, it approaches the correct function. ... Brook Taylor (August 18, 1685 – December 29, 1731) was an English mathematician. ... REDIRECT [1] ...

Several other Machin-like formulas are known. In mathematics, Machin-like formulas are a class of identities involving π = 3. ...

John Machin served as secretary of the Royal Society from 1718 to 1747. He was also member of the commission which decided the Calculus priority dispute between Leibniz and Newton in 1712. The Royal Society of London for the Improvement of Natural Knowledge, known simply as the Royal Society, is claimed to be the oldest learned society still in existence. ... Jump to: navigation, search Gottfried Leibniz Gottfried Wilhelm von Leibniz (also Leibnitz) (Leipzig July 1 (June 21 O.S.), 1646 – November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer. ... Jump to: navigation, search Sir Isaac Newton at 46 in Godfrey Knellers 1689 portrait Sir Isaac Newton, PRS (25 December 1642 (OS) – 20 March 1727 (OS) / 4 January 1643 (NS) – 31 March 1727 (NS)) was an English physicist, mathematician, astronomer, philosopher, and alchemist. ...

External links

• Biography at the MacTutor archive
• Machin's Formula at MathWorld