Talk:Calculus

The history section

Shouldn't the history section have at least some content? I mean, more than the link? --31.45.79.44 (talk) 22:46, 27 February 2012 (UTC)

In the main text we read: "Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. (André Weil: Number theory. An approach through history. From Hammurapi to Legendre. Birkhauser Boston, Inc., Boston, MA, 1984, ISBN 0-8176-4565-9, p. 28.) " I think that this is misleading. Fermat borrowed from Bachet de Meziriac's Latin translation of Diophantus’ Arithmetika the noun adaequalitas and the verb adaequare where they have a meaning in a completely different context, namely solving a special class of arithmetical problems by the method of false position. Fermat, however, uses those words (and the word adaequabitur) in his method of determining maxima and minima of algebraic terms and of computing tangents of conic sections and other algebraic curves. Fermat’s method is purely algebraic. There is no "infinitesimal error term". Fermat uses two different Latin words for "equals": aequabitur and adaequabitur. He uses aequabitur when the equation describes the identity of two constants or is used to determine a solution or represents a universally valid formula. Example:

$x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$.

And he uses the word adaequabitur ($\doteq$) when the equation describes a relation which is no valid formula. Example (Descartes' folium):

$x^{3}+y^{3}\doteq 3xy$.

Typical examples are:

$(x+e)(b-x-e)=bx-x^{2}-2ex+be-e^{2}$

and

$be\doteq 2ex+e^{2}$.

Equations which describe relations between two variables (x and y, x and e) were unknown to Vieta. So the 21-year-old Fermat felt compelled to introduce a new concept of equality and called it adaequalitas. Later, when he created his analytic geometry he abandoned this special terminology of his younger days. See my paper Barner, Klaus: Fermats <<adaequare>> - und kein Ende? Math. Semesterber. (2011) 58, 13-45, unfortunately written in German. 91.4.83.79 (talk) 17:28, 7 February 2013 (UTC) Klaus Barner (talk) 14:40, 5 February 2013 (UTC)

Very interesting. Is there perhaps a translation of your article online somewhere? Tkuvho (talk) 16:13, 6 February 2013 (UTC)

Unfortunately there is none. The reason is: my German is sophisticated and requires reading between the lines whereas my English ist rather weak. It is no artical about mathematics but about history of mathematics which requires a better command of English than I have. However I feel that I should produce a raw translation and ask a native speaker to improve it. Klaus Barner (talk) 19:09, 10 February 2013 (UTC)

https://www.google.com/imgres?imgurl=http://academic.pgcc.edu/~sjohnson/ancientcurvetext.jpg&imgrefurl=http://academic.pgcc.edu/~sjohnson/casestudy2.html&h=1012&w=1331&sz=324&tbnid=Wx15eqipFgydwM:&tbnh=90&tbnw=118&zoom=1&usg=__rwdu-Js_exE4O78S94CeAopgX1Q=&docid=H8UYTm3StwLcWM&sa=X&ei=yS5CUp0HrrbgA6TwgYAG&ved=0CDwQ9QEwAw

A text found at Saquara has a picture of a curve and under the curve the dimensions given in fingers to the right of the circle as reconstructed to the right. It was presumed the horizontal spacing was based on a royal cubit but the results if based on an ordinary cubit are different. It appears the value for PI being used is 3 '8 '64 '1024. which at 3.141601563 is slightly better than the Rhind value. The circumference of the circle is 1200 fingers and the diameter of the circle is 191 x 2 = 382 3 '8 '64 '1024 x 382 ~= 1200.0 The side of the square is 12 royal cubits and its area is 434 square feet. The area of the circle is 191^2 x 3.141601563. The algorithm suggests working with coordinates and numerical analysis to define a curve.

• 1
• 1 1
• 1 2 1
• 1 3 3 1
• 1 4 6 4 1
• 1 5 10 10 5 1
• 3
• 3 + 1/2y^3 is 3 '8, = 3.125
• 3 + 1/2y^3 + 1/2y^6 is 3 '8 '64,= 3.140625
• 3 + 1/2y^3 + 1/2y^6 + 1/2y^10 is 3 '8 '64 '1024 = 3.141601563

For purposes of comparison(3 '7 = 3.142857143)

From a published reference "Ancient Egyptian Construction and Architecture" Here it is as a Google Book. "Ancient Egyptian Construction and Architecture" See The referenced graphic Architects Curve What you see there was already referenced on the page as an artifact from Saqarra, but without the graphic. Its Fig. 53 p. 52. Figure 54 p. 53 is a scale drawing of it. The Graphic is in Wikipedia commons used in two other articles which have the text I copied to the talk page. "The algorithm suggests working with coordinates and numerical analysis to define a curve". Its similar to adequabiture and an exampl≤e of how Pascals triangle may be used to generate PI with a series formed by the third diagonal; 1,3,6,10.≤″24.93.139.28 (talk) 21:43, 2 June 2018 (UTC) https:/upwiki/wikipedia/en/f/f3/Egyptian_circle.png 24.93.139.28 (talk) 21:53, 2 June 2018 (UTC)

Just for the records:

adequabitur is the verb form 3rd sg fut ind pass of the verb adequare. The construction of a noun the adequabiture is a mystification.

Purgy (talk) 07:01, 3 June 2018 (UTC)

In the intro to this section "Fermat uses two different Latin words for equals". I'm expecting he means not "equals" necessarily, but adequately equal or something to that effect. I couldn't find an etymology that goes back before "adequate" from early 17th century Latin where the noun means "equal" and the "verb made equal to". 24.93.139.28 (talk) 08:16, 6 June 2018 (UTC)

Mathematics of the other beings

QUOTE: In the 14th century, Indian mathematicians gave a non-rigorous method of a sort of differentiation of some trigonometric functions. Madhava of Sangamagrama and the Kerala school of astronomy and mathematics thereby stated components of calculus.END OF QUOTE.

It is only right to assume that when the animal world acquires the skill to use English, computers etc., they will also come up with similar astounding claims. — Preceding unsigned comment added by 137.97.8.238 (talk) 22:01, 2 May 2017 (UTC)

Did I address your concern in my edit? Maybe, you should be more explicit of your concerns, and try to implement this on your own. Purgy (talk) 05:59, 3 May 2017 (UTC)

I put Indian back in. There's no problem about describing people from the south of India in medieval times as Indian. Dmcq (talk) 17:47, 3 May 2017 (UTC)

Maybe, I'm definitely not sure, it's you (please, note the italics), who does not see the problem, which others try to articulate. Purgy (talk) 19:19, 3 May 2017 (UTC)

Perhaps you can articulate what you see as what they were saying and therefore you did something about? In short say why South Asian Subcontinent is better than Indian in that context. Dmcq (talk) 14:31, 4 May 2017 (UTC)

I followed the (wrong again) assumption that the intentions of the OP were well known, or even stereotyped. I'll revise my presupposition that it is sufficiently established that there are people from this region, who prefer not all of their possible ancestors being subsumed under "ancient indians", for whatever reason, and in a similar vein like others feel justified to enforce the singular they on all linguistic corpora.

I hope this is articulate enough. In no way I oppose to having been reverted, I just tried to make WP a safer space. ;] Purgy (talk) 06:35, 5 May 2017 (UTC)

Most of that subcontinent has been referred to as India from long before then. People looking up this article on the English Wikipedia cannot be assumed to be familiar with the constituent parts of India, it is not a Hindi or Indian encyclopaedia. The article does immediately afterwards refer to Kerala so they would know from that vaguely where Kerala is. Those are the reasons I think saying Indian is best. It is all very well trying to cater for people but Wikipedia's main purpose is not to be a social forum but to be an encyclopaedia. They haven't answered your query about what their concern actually is. What did you think the intentions of the OP were or what type of stereotype did you think I had? There just is not enough there to get any handle on anything that I can see. Dmcq (talk) 10:10, 5 May 2017 (UTC)

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Thank you, wikipedia, for this opening line

Thank you, wikipedia, for this opening line:

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, like on an abacus) is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

— wp editors, Calculus, Isaac Newton

It clarifies so much for me. Actually, it says: "This is what math is". - DePiep (talk) 21:07, 1 February 2018 (UTC)

Well, this is the best "consensus" in WP could generate. You may want to look at the intense discussion about the lead here, here and here, too (scroll up ~20 lines, in case), to see the intense effort, just recently spent, to improve the lead, and you can also learn where to place your thanks more precisely. Purgy (talk) 08:22, 2 February 2018 (UTC)

Allow me to skip those readings. I'm so happy with the result as it is now. I didn't read "compromise", I read clarity. (I'm trying to understand QM these days. For example, this is the one, pre-wikipedia). -DePiep (talk) 00:18, 3 February 2018 (UTC)

No integral calculus page?

There is a nice article for differential calculus, which describes it as a branch of calculus and gives some history, but there is no corresponding page for integral calculus. There is only a redirect to integral. Why then is differential calculus not a redirect to derivative? 121.216.128.241 (talk) 10:59, 9 February 2018 (UTC)

Hi. Your best bet at finding editors who are interested and know enough about this subject is at Wikipedia:WikiProject Mathematics. Perhaps bring this up at their talk page (Wikipedia talk:WikiProject Mathematics). Bennv3771 (talk) 11:57, 9 February 2018 (UTC)

(edit conflict) "Integral calculus" is much less used than "differential calculus". This is probably the reason for not having Integral calculus. Also, having a separate article needs to have content that is not covered by the target of the redirect. It seems that this is not the case here. D.Lazard (talk) 12:39, 9 February 2018 (UTC)

Separate Section

The lead sentence does not include the alternate term infinitesimal calculus, which would help clarify. I'd change it myself, but Wikipedia... — Preceding unsigned comment added by 96.40.48.159 (talk) 23:43, 8 June 2019 (UTC)

Also this article is the target of the redirect infinitesimal calculus. I have thus exchanged the places of this term and the etymology. By the way, I have done some other modifications. D.Lazard (talk) 08:19, 9 June 2019 (UTC)

Unaware of Lazard’s edit, I also made changes! Dolphin (t) 08:21, 9 June 2019 (UTC)

I have removed the second mention of "infinitesimal calculus", as, placed there, it is unclear whether it denotes integral calculus, differential calculus, or both. By the way, it is astonishing that there was no edit conflict: I have edited all paragraphs of the lead but one, and Dolphin51 has edited the only paragraph that I have left unchanged! D.Lazard (talk) 08:45, 9 June 2019 (UTC)

D.Lazard’s changes are sound. I have no intention to meddle any further. I agree it is puzzling that I saw no alert to an Edit conflict. It seems that Edit conflicts occur when I would prefer they didn’t, and an Edit conflict doesn’t occur when it would actually be beneficial! Dolphin (t) 09:33, 9 June 2019 (UTC)

Semi-protected edit request on 12 January 2020

"developed independently in the late 17th"? How can it be? Both Leibniz and Newton died in 18th century. Datdinhquoc (talk) 23:24, 12 January 2020 (UTC)

 Not done Newton died in 1726, which is during the 18th century. His work on the calculus was done in the late 1600's, which is the 17th century. This offset of the century number is due to the fact that there is no "zero" century. --Bill Cherowitzo (talk) 23:35, 12 January 2020 (UTC)

Oh yes, 16xx is 17th century. — Preceding unsigned comment added by Datdinhquoc (talk • contribs) 22:29, 13 January 2020 (UTC)

Contested April 2020 additions

@Prototypehumanoid: WP:BRD is a very good idea to follow. The short version: there already is some material in the history section about precursors to the Calculus in South Asia. Overloading the lead with that, though, would probably lend WP:UNDUE weight to the overall importance of that with respect to the rest of the article. We also don't discuss the precursors in ancient Greece in the lead. Moreover, changing to a statement like "Modern calculus was developed in AD 1530 by Jyesthadeva of the Kerala school of mathematics ..." is simply not reflective of the mainstream view and violates WP:FRINGE. –Deacon Vorbis (carbon • videos) 14:18, 25 April 2020 (UTC)

Sorry, but you seem to be missing the point. Your edit incorrectly ascribes development of modern calculus to 17th century, which contemporary scholarship disproves. You keep stating that this is not mainstream view while providing no evidence. I have backed up my edits with reputable references including Royal Asiatic Society of Great Britain & University of St Andrews, Scotland. I wouldn't refer to them as 'fringe' views. This is the mainstream contemporary consensus. If you are reading material from the 1950s, I suggest kindly refer to the latest scholarship. Please note, I have not taken anything away from the article, simply adding the latest material. You seem to be doing the opposite. European contributions are amply provided in the page including precursors. But the chronology needs to be correct. In the absence of you providing evidence to disprove my references, I will be reincorporating the latest scholarship onto this article. May I suggest, please explain how you are arriving at the conclusion where you are dismissing the latest global scholarship on the subject. Please provide reference for such. Prototypehumanoid (talk) 14:50, 25 April 2020 (UTC)

Please, take your nationalist POV nonsense elsewhere. --JBL (talk) 15:05, 25 April 2020 (UTC)

(edit conflict) The mainstream view is that while there were pieces of the Calculus worked out, a full-fledged picture with the general tookit of it that resembles its modern form wasn't put together until Newton & Leibniz. One single paper (the Raju one, which has some problems, which we can discuss if needed) does not allow you to make this kind of claim in the article. Your other sources are either junk (some slides, some weird poster with a nationalist POV, etc), or are just backing up secondary stuff, like the basics of the work itself. –Deacon Vorbis (carbon • videos) 15:16, 25 April 2020 (UTC)

I think I agree with @Prototypehumanoid. Further references could be added. Including Divakarans papers. Also the original paper 'Yuktibasha'. Madhava is increasingly seen as the true inventor. Marcus du sautoy for instance has done previous studies that showcase - lack of due credit to eastern mathematicians (during 17th to 21st century Europe). Imagetoimageless (talk) 12:16, 23 August 2020 (UTC)

Evidence based change should be made welcome. There has been an increasing consensus for many elements- See Madhava series, formula for pi etc... Imagetoimageless (talk) 13:50, 23 August 2020 (UTC)