Talk:Abraham de Moivre

Pronunciation of name
My university maths lecturers claimed one should pronounce his surname DE MOY-VER (i.e. in an english-phonetic way), saying that upon his exile to England he insisted people did so, as he was now thouroughly english and not in the least frenchy. If anyone else has heard this, then I think it should go into the article (but it smacks just a bit of the kind of nonsense maths lecturers come up with in order to break the tedium, so I'm not putting it in myself). -- Finlay McWalter | Talk 19:54, 1 Apr 2004 (UTC)

thank you for writing the pronunsiation note!

You can hear two pronunciations here.

Fibonacci Numbers
There is some believe that he discovered a method of finding the n-th Fibonacci number before Binet or Euler did. deMoivre vs Binet

See de Moivere's Miscellanea Analytica (London: 1730), p 26-42. for his solution to general linear recurrences deriving an expression linking Φ to the nth power to the nth Fibonacci number. See The Art of Computer Programming, Second Edition, 1973, p 82, by Donald E. Knuth.

WikiProject class rating
This article was automatically assessed because at least one article was rated and this bot brought all the other ratings up to at least that level. BetacommandBot 02:05, 27 August 2007 (

De Moivre was a good friend of Isaac Newton. He calculated when he would die. He slept fifteen minutes longer each day, and said that the day he slept 24 hours he would die, and his prediction was correct.

Too long day On April 21, 2009, the information about how he had calculated the day when he would die was changed into "1.5 minutes per day" plus the info that he did it when he was 42. As he died when he was 87, this would give 1.5 * ((87-42) * 365 + 12)/60 = 410.925 hours in a 24-hour day. I added 12 for leap years, but even without it it would be definitely too much. So when did he exactly predict it and how many minutes per day was it? Could anybody help correct it please? --C. Trifle (talk) 16:00, 27 April 2009 (UTC)

Citation for deMoivres formula
I've put a citation needed on the original thing deMoivre was supposed to have proven:


 * $$ \cos x = \frac{1}{2} (\cos(nx) + i\sin(nx))^{1/n} + \frac{1}{2}(\cos(nx) - i\sin(nx))^{1/n} $$

because it is only one pair of the roots for which this is true. Dmcq (talk) 17:24, 9 December 2009 (UTC)


 * Agreed, but different reason. I have a German text from 1903 that explains de Moivre's works.  It makes specific reference to
 * $$ \cos x = \frac{1}{2} (\cos(nx) + i\sin(nx))^{1/n} + \frac{1}{2}(\cos(nx) - i\sin(nx))^{1/n} $$
 * but, it says that this is how we (mathematicians of the 1900s) would write this. I've only seen de Moivre's original Miscellanea analytica, and the symbols of sin, cos, and i are not used despite that the solution methods are using trigonometric techniques.  Instead, de Moivre uses variables to represent things like the "ratio of the arc".  Most explanations of trigonometric properties are verbal, rather than sybolically noted.


 * But there is a problem, as Dmcq notes in this change. The author of the German text explains that DeMoivre was interested in the two equations
 * $$ y = \frac{1}{2}\sqrt[n]{\sqrt{1+a^2}+a} - \frac{1}{2}\sqrt[n]{\sqrt{1+a^2}-a}$$
 * $$ y = \frac{1}{2}\sqrt[n]{a + \sqrt{a^2 -1}} + \frac{1}{2}\sqrt[n]{a - \sqrt{a^2 -1}}$$
 * These equations were derived from a certain polynomial series where n is an odd integer. A citation shows that de Moivre knew that there were 5 roots when n=5 and works out such a problem, but it appears he was only interested in finding the real root in the solution process. Take note also that in these equations $$y = \sin{\phi}$$ and $$a = \sin{n \phi}$$.  I think the problem may be in giving context.


 * A copy of the German text is available freely on Google, but I don't know of an English translation: https://play.google.com/store/books/details/Anton_Braunm%C3%BChl_Edler_von_Vorlesungen_%C3%BCber_Geschic?id=uB0PAAAAIAAJ#?t=W251bGwsMSwyLDUwMSwiYm9vay11QjBQQUFBQUlBQUoiXQ..

Thelema418 (talk) 00:06, 21 August 2012 (UTC)

Death Prediction
Can anyone find an accurate source for his prediction of death? —Preceding unsigned comment added by Hmyt (talk • contribs) 19:56, 31 January 2010 (UTC)

Here is a nice discussion of the topic: http://hsm.stackexchange.com/questions/333/did-abraham-de-moivre-really-predict-his-own-death This "fact" is said to be used in the books on number theory and history of mathematics, but is not supported by any of biographies. — Preceding unsigned comment added by Ideruga (talk • contribs) 17:14, 6 August 2015 (UTC)

amateur mathematician
for some reason Wikipedia lists Abraham de Moivre on the "List of amateur mathematicians." The description is "people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics." After reading this page, I would debate de Moivre's inclusion on this list; he certainly seemed to be involved with mathematics as his primary vocation. Owen214 (talk) 06:59, 8 August 2011 (UTC)

Probability
The attribution of the normal distribution to de Moivre is not quite correct. I think this needs expanding upon. De Moivre found a large sample approximation to binomial probabilities in terms of what we now know as a normal distribution. However, he was only interested in discrete distributions and did not think of his formula as a probability distribution in its own right. For this reason he is not usually credited with the discovery of the normal distribution.TerryM--re (talk) 04:30, 9 March 2014 (UTC)

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Stirling's approximation
At present the section that's titled "Stirling's approximation" states: "Stirling's formula was first discovered and proven by de Moivre … " That claim is wrong. "Stirling's approximation" was first conceived in 1730 by the Scottish mathematician James Stirling (1692–1770).

De Moivre had been studying probability, and his investigations required him to calculate binomial coefficients, which in turn required him to calculate factorials. In 1730 de Moivre published his book Miscellanea Analytica …, and on pages 103–104 of that book were tables of log (N!). A few days after the book's publication, de Moivre received a letter from Stirling stating that there were errors in the tables. Furthermore, Stirling included a series for calculating log (N!) — although he didn't include a proof that the series was correct. Stirling's series also contained the factor log (√2$\pi$ ). De Moivre soon derived his own series for log (N!), which was similar to Stirling's series.

Later in 1730 Stirling published his book Methodus Differentialis …, in which he included his series for log (N!).

Meanwhile, also in 1730, de Moivre had an appendix or Supplementum added to his book, which included quotes from Stirling's letter, Stirling's series for log (N!), and de Moivre's own series for log (N!). When de Moivre published in 1756 the fourth edition of his book Doctrine of Chances, he again credited Stirling with finding a series for log (N!).

Thus, although later authors have misattributed Stirling's approximation, de Moivre himself repeatedly and explicitly credited Stirling.

Sources documenting Stirling's priority include:
 * Jacques Gélinas (2017) "Original proofs of Stirling's series for log (N!)"
 * Isaac Todhunter (1865) A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace

VexorAbVikipædia (talk) 03:03, 10 June 2020 (UTC)

What about de Moivre's central limit theorem for Bernoulli random variables?
I have read in various places that de Moivre proved the first case of the central limit theorem for what we would now call a Bernoulli random variable. That is, if a coin landing heads with probability p in (0, 1) and tails with probabiity 1-p is flipped repeatedly, independently, then Let H(n) denote the number of heads.

the probability that the standardized number SH(n) of heads after n flips lies in the interval [A, B] is asymptotic to the integral of the standard normal density

d(x) = (1/√(2π)) * exp(-x2/2)

over the interval [A, B], where the standardized number of heads SH(n) is defined as

SH(n) =  (H(n)-𝜇n) / 𝜎n

where the mean 𝜇n = np and the standard deviation 𝜎n = √(n p (1-p)).

This was an extremely important development in probability theory, and I am very surprised not to see it mentioned in the article. 2601:200:C000:1A0:B844:D24:C76:F0D6 (talk) 00:57, 13 July 2022 (UTC)

De Moivre's formula
The section on De Moivre's formula just has so many problems. Particular roots need to be taken to get the result. And De Moivre's formula says the opposite about it being true for all real n. I haven't the foggiest how to reframe the section so it is correct. NadVolum (talk) 09:42, 6 November 2023 (UTC)