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Topic: Leibniz formula

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	Encyclopedia :: encyclopedia : Calculus (Site not responding. Last check: 2007-11-01)
		It was generations after Newton and Leibniz that Cauchy and other mathematicians finally put calculus on a rigorous basis, with the definition of the limit.
		Newton was the first to apply calculus to physics and Leibniz developed much of the notation used in calculus today; he often spent days to come up with just the right symbolism.
		Rather a formula is developed for the quotient Distance/Time in which division by zero can be avoided, by a method called "taking the limit".
	www.hallencyclopedia.com /Calculus (2145 words)

	Pi - Wikipedia, the free encyclopedia
		In 1789, the Slovene mathematician Jurij Vega improved John Machin's formula from 1706 and calculated the first 140 decimal places for π of which the first 126 were correct [1] and held the world record for 52 years until 1841, when William Rutherford calculated 208 decimal places of which the first 152 were correct.
		All of these formulae are a consequence of the formula for circumference.
		Formulæ of this kind are known as Machin-like formulae.
	en.wikipedia.org /wiki/Pi (4789 words)

	Learn more about Pi in the online encyclopedia. (Site not responding. Last check: 2007-11-01)
		Formulas of this kind are known as Machin-like formulas.
		Bailey and Crandall showed in 2000 that the existence of the above mentioned Bailey-Borwein-Plouffe formula and similar formulas imply that the normality in base 2 of π and various other constants can be reduced to a plausible conjecture of chaos theory.
		In non-Euclidean geometry the sum of the angles of a triangle may be more or less than π, and the ratio of a circle's circumference to its diameter may also differ from π.
	www.onlineencyclopedia.org /p/pi/pi.html (1284 words)

	The Disconsolation of Philosophy, Part 7: Entropy and Information at God of the Machine
		The comments to the previous sections on alpha theory are loaded with objections that stem from an inability, or unwillingness, to keep this in mind.
		Another approach, from analysis, is to use the Leibniz formula:
		For shorthand symbols can always, of course, be replaced by the longer expressions, the defining formulae, for which they stand.
	www.godofthemachine.com /archives/00000571.html (7490 words)

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