Talk:Euler's formula

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One of the 500 most frequently viewed mathematics articles.

e to the pi i[edit]

Somewhere in the introduction the familiar (and amazing!) expression e**pi*i = -1 needs to be shown. Casey (talk) 22:51, 25 September 2013 (UTC)

The equation that this article talks about is just a generalization of that expression. See this page. (talk) 01:20, 28 January 2017 (UTC)

(I think that) the main page should mention that i^(2×x÷π)=cos(x)+i×sin(x)=e^(i×x).[edit]

If you need proof, press the link. Equation Simplifier 2601:2C1:C003:EF7A:157E:69D0:9FC2:8328 (talk) 02:13, 2 April 2016 (UTC)

Possible Vandalism[edit]

The introduction to this article today reads:

"Deniz is the best basketball player in the world and friends with Mr. Euler it is documented that deniz had a big contrubution to euler's formula"

This doesn't show up when I try to edit the page so it's difficult to remove this.

Does anyone have any idea what might have happened here? (talk) 20:24, 31 August 2016 (UTC)

Already done Probably it was removed just before you tried to edit. Thanks for reporting it. Gap9551 (talk) 20:32, 31 August 2016 (UTC)

The sentence still shows up in the very first paragraph, and disappears when entering edit mode. Something still seems to be very wrong here.. — Preceding unsigned comment added by (talk) 07:59, 1 September 2016 (UTC)

The text is not seen in my browser when logged in or when not logged in. Possibly there is a caching issue on your browser, or conceivably a proxy server. Try WP:BYPASS. Johnuniq (talk) 08:57, 1 September 2016 (UTC)

Proposed merge with Cis (mathematics)[edit]

The cis function is rare and redundant to Euler's formula. A former AfD, Wikipedia:Articles for deletion/Cis (mathematics), was closed as no consensus. GeoffreyT2000 (talk, contribs) 05:34, 12 December 2016 (UTC)

  • Oppose "Rare" is not "non-notable".
It is likely that any readers searching for cis() will find cis(), not Euler. There they are already given an adequate explanation of it in both trigonometry and history, with an appropriate pointer to this article. Readers finding Euler will find Euler, and that's what they need, im likely blissful ignorance of cis(). How does a merged article improve upon this? This is not paper. We are not short of pages. Andy Dingley (talk) 02:14, 13 December 2016 (UTC)
  • Oppose. Obviously, Euler's formula and the cis() function are related but they have different histories to be told and different use cases, and we therefore would not do either of them a favour by discussing them in a single article. They kind of approach a problem from different angles. To someone, who hasn't learnt about exponential functions, the redundancy does not exist. To some, cis() is a sometimes very convenient abbreviation or shorthand notation, for others it is a vehicle in math education.
Regarding the previous AfD (which was still about an article in a much weaker state and with lacking sources), there were prior discussions in the past decade and they suggested to discuss the cis() info in a separate article, because readers felt that the info on cis() did not belong into the Euler article and it was inadequately covered there.
As has meanwhile been established by plenty of reliable sources, cis() has 150 years of history and is a notable topic by itself. Yes, it is not in main-stream use, but this doesn't make it non-notable. After all, we're an encyclopedia and it is our duty to document things from a neutral point of view and not suppress information.
--Matthiaspaul (talk) 12:43, 20 December 2016 (UTC)
  • Oppose Many Wikipedia topics are rare. That is not a reason to make them go away because this is an encyclopedia and so should cover the full circle of knowledge. Andrew D. (talk) 14:24, 20 December 2016 (UTC)
  • Oppose It's not even that rare. It comes in handy in computer documentation where superscript typography is not so easy. Here is a relatively high traffic example: I think the article's extremely negative intro needs to be toned down.--agr (talk) 15:19, 20 December 2016 (UTC)
  • Oppose I just came here looking for cis and not for eulers formula. Someone might want to remove that sign above the article. (talk) 01:15, 6 January 2017 (UTC)
  • Oppose. One certainly could discuss cis within an article on Euler's formula, but cis (mathematics) has so much material on the usage of that specific notation that I think that it works better as a separate article. You wouldn't want to either get rid of that or try to stuff it all in here (which would make this article unbalanced). ―Toby Bartels (talk) 15:00, 10 January 2017 (UTC)
  • I oppose. Cis(x) is an equation, and its uses are not limited to calculating eix. Also, Euler's formula can be written as exi=cos(x)+i×sin(x) without even acknowledging that there is a shorter way to write cos(x)+i×sin(x). I do not feel that the subjects of these two articles are closely enough related to merit merging. (talk) 01:12, 28 January 2017 (UTC)

Just for the records and to help avoid unnecessary further discussion, User:GeoffreyT2000 closed the discussion as "Don't merge" on 2017-03-24T02:08:43‎. [1] Somewhere we have some nice wrapping template for closed discussions, but I can't seem to find it right now...

--Matthiaspaul (talk) 21:18, 27 March 2017 (UTC)

External links modified[edit]

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Cotes equation[edit]

I'm confused and hoping for explanation. How is it rationally possible to posit or envision the Cotes equation cited in this article without x being in radians and fully understood (by Cotes) as a periodic function of pi, as is stated in the article? How did Cotes instead define x? Wikibearwithme (talk) 23:46, 13 January 2018 (UTC)

Thanks. The article statement is unsourced and seems thoroughly dubious, and I've added a Citation Needed requesting a supporting citation or a suitable re-wording. What Cotes actually used is not too clear to me (tho I think it is basically radians as found in an arc of a quadrant of a circle, seemingly with no need to consider periodicity for the specific problem that he was dealing with, irrespective of whether he was aware of such periodicity or not - although I suppose it is conceivable that ignoring periodicity may have introduced a flaw into his proof). What he actually wrote, plus a modern interpretation thereof, can be seen in the lengthy footnote (currently numbered [5]) in his biographical article Roger Cotes (although this footnote is basically just dealing with his conclusion, and is not dealing with his proof, which is available online, but possibly only in Latin - although his archaic English terminology would presumably also be a problem for any Wikipedian trying to read it).Tlhslobus (talk) 07:05, 16 January 2018 (UTC)

Hi - Thanks. I agree, and think without an explicit statement by Cotes of this supposed limitation of the argument, the supposed limitation of Cotes in this article does not seem to be a supportable inference. Wikibearwithme (talk) 08:57, 19 January 2018 (UTC)

Thanks. At the moment I'm waiting for a decent period of time (I'm never clear how long that should be) for somebody to come up with a supporting citation (which seems unlikely, but just about possible if there's an error in his proof as a result). However such waiting always carries the risk that it will never get fixed, so I won't object if anybody else decides to fix it straight away. I'm not 100% sure what the ideal rewording should be, but perhaps something along the lines of "The term Euler's formula is used because Euler's exponential formulation, although it came later, has been preferred to Cotes's logarithmic formulation because a complex number actually has an infinite number of natural logarithms due to the periodicity of trigonometric functions." Tlhslobus (talk) 06:11, 20 January 2018 (UTC)