Talk:Viète's formula

Viète's formula has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: July 6, 2021. (Reviewed version).

A fact from Viète's formula appeared on Wikipedia's Main Page in the Did you know column on 23 July 2021 (check views). The text of the entry was as follows:

Did you know... that in 1593, French amateur mathematician François Viète found the first formula in European mathematics to represent an infinite process, a product of square roots that he used to compute $π$ ?

A record of the entry may be seen at Wikipedia:Recent additions/2021/July. The nomination discussion and review may be seen at Template:Did you know nominations/Viète's formula.

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Need date for Viète's formula. —DIV (128.250.204.118 08:05, 13 August 2007 (UTC))[reply]

The above formula is a result of one of Leonhard Euler's formula[edit]

The formulation of the above is not exquisite ... Viete died one century before Euler's birth. I'd see for that : The above formula is now considered as a result of one of Leonhard Euler's formula - branded more than one century after (if we may get those dates). Thank you. -- DLL ^{.. T} 17:35, 17 December 2007 (UTC)[reply]

reference[edit]

could you give the complete name of (J. Munkhammar, pers. comm., April 27, 2000). including title and complete name of magezin?? --217.224.182.167 (talk) 13:05, 19 June 2009 (UTC)[reply]

request for mention of "Osler product"[edit]

Here is a suggested addition to the content, with reference. I have requested similar text be added to the page Thomas J. Osler and Wallis product.

In 1999, American mathematician Thomas J. Osler discovered that Viète's formula and the Wallis product (1656) are two special cases of a more general infinite product, which has been referred to as the Osler product by Arndt and Haenel, according to whom: "The Osler product [which takes a parameter $p$ ] turns into the Viète product as $p$ tends to infinity, and is equal to the Wallis product when $p=0$ . In the intermediate cases $p=1$ , $p=2$ , etc., we obtain combined Viète- and Wallis-like products"^[1]

Will an appropriate editor please make this addition? I have a COI. Thank you!Skymath1 (talk) 04:02, 28 November 2020 (UTC)[reply]

References

^ Arndt, Jörg; Haenel, Christoph (2001). "Section 12.8 Viète ✕ Wallis = Osler". π Unleashed. Berlin Heidelberg New York: Springer-Verlag. pp. 160–162. ISBN 3-540-66572-2.

I added a mention to the Thomas J. Osler article. I'm not convinced that mention is WP:DUE in this article, however. From a quick look through the literature, there appears to be a modest industry in finding formulas relating Viète and Wallis. Osler's result has modest citations in this area. It might be possible to write a section on relations between the two formulas (that is, to put Osler's result into context), but this would be a larger project. Russ Woodroofe (talk) 22:09, 29 November 2020 (UTC)[reply]

Did you know nomination[edit]

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Cwmhiraeth (talk) 05:47, 21 July 2021 (UTC)[reply]

(

Comment or view
Article history

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... that in 1593, French amateur mathematician François Viète found the first formula of European mathematics to represent an infinite process, a product of square roots that he used to compute $π$ ? Source for "first formula...": Maor, Trigonometric Delights, p. 50, "It was the first time an infinite process was explicitly written as a mathematical formula". Source for "that he used to compute $π$ ": Kreminski, " $π$ to thousands of digits from Vieta's formula", JSTOR:27643107.

Reviewed: Joan Bamford Fletcher

Improved to Good Article status by David Eppstein (talk). Self-nominated at 00:10, 8 July 2021 (UTC).[reply]

Article was nominated soon after promotion to Good Article status, and is sufficiently long and within guidelines. The hook is well sourced, interesting, and snappy. Well done! Hanjaf1 (talk)

The only alteration that suggests itself to me is "amateur mathematician", which seems anachronistic given the general absence of professional mathematicians in the the 16th century, which could be changed to simply "mathematician"? Or even "lawyer", since that was his actual profession? Hanjaf1 (talk) 07:15, 18 July 2021 (UTC)[reply]

"First infinite process?"[edit]

Well now, doesn't this beg the question of what exactly an "infinite process" is? Why wouldn't the harmonic series count? It's quite well known that Oresme proved the divergence of the harmonic series c. 1360.

Please give a clear argument why the harmonic series is not considered an "infinite process," including a suitable definition of the latter.

- Off Use 2601:647:C900:B6C0:99ED:F4A6:FA90:CDFA (talk) 07:40, 16 December 2022 (UTC)[reply]

You are missing a key word in your reading. It says it is "the first formula of European mathematics to represent an infinite process". The harmonic series can be represented in modern notation as a formula, but I suspect that Oresme did not use a formula to describe it. —David Eppstein (talk) 07:44, 16 December 2022 (UTC)[reply]

[1] Arndt, Jörg; Haenel, Christoph (2001). "Section 12.8 Viète ✕ Wallis = Osler". π Unleashed. Berlin Heidelberg New York: Springer-Verlag. pp. 160–162. ISBN 3-540-66572-2.

[1]