Talk:Trapezoidal rule

Define notation

Define the variables. You have mentioned x0 k and many others which are meaningless to me. --anon

Thanks, I just did that. Oleg Alexandrov (talk) 04:52, 22 February 2007 (UTC)

Possible mistake

Not sure if I'm misreading your equation, but I do not think there should be a factor 'n' in the denominator of your last form of the trapezium rule. It should read "a-b/2" rather than "a-b/2n" —Preceding unsigned comment added by 131.251.26.98 (talk) 15:59, 11 March 2008 (UTC)

If it was finding h alone you would be right. But b-a/2n is the same as b-a/2 * 1/2 or b-a/2/2. 79.65.108.70 (talk) 22:52, 1 May 2008 (UTC)

Requested move

The following is a closed discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was move Anthony Appleyard (talk) 09:47, 8 April 2009 (UTC)

I think this page should be moved. From what I've heard, "Trapezium rule" is a rare name. It is practically unheard of in the US. I am not one hundred percent sure on this, but I've been looking for references that name this rule. The earliest I was able to find was by E.T. Whittaker, a United Kingdom native. It was Whittaker, Edmund, "The Calculus of Observations: a treatise on numerical mathematics". 1924.. I have not read it in full, but he does call the rule the Trapezoidal Rule. Very clearly. I've talked with several of the Mathematics professors at the college I'm at. They all say that it should be "Trapezoidal Rule". Many of them have been in the UK. I'd trust them. So we should move this article.--Mjr162006 (talk) 04:13, 10 October 2008 (UTC)

I believe there are books that have been written since then. Oh wait, I thought you said 1724. Well, yes, even since 1924. Google books has 1,511 hits for trapezoidal rule, 707 for trapezoid rule, and 647 for trapezium rule. 199.125.109.124 (talk) 15:16, 2 April 2009 (UTC)

Also the references all call it trapezoid rule, as does the wikipedia page on the trapezoid. ... Okay, I did the move. 24.5.193.247 (talk) 08:17, 8 November 2008 (UTC)

"Trapezium rule" isn't a rare name. It's the normal British name for it. If for any reason a British native called it the "Trapezoidal Rule", it sounds to me to be because it's an American invention and the name "trapezium rule" hadn't been established at that time. But I could be wrong. Moreover, what exactly did you ask your professors (or lecturers as we Brits'd call them, assuming you're using the American meaning)?

• what they personally call it?
• what is the preferred name in the US?
• what is the preferred name in the UK?
• what is the preferred name in the world as a whole?
• something else entirely?

I think there's only one possible reason for it to be at Trapezoidal rule, namely consistency with the article Trapezoid being there rather than Trapezium. But I'm not sure what Wikipedia policy says about this.... -- Smjg (talk) 14:27, 8 November 2008 (UTC)

(Editorial Note: At this point, Smjg reverted the move implemented by 24.5.193.247. Jim (talk))

I agree that this page ought to be moved. Many universities in Britain use American calculus texts, making "trapezoid" much more common than "trapezium" in this context. According to Wikipedia article traffic statistics, about 80% of the people who arrive at this article do so through the Trapezoidal rule redirect page. "Trapezoidal rule" also gets many more hits on Google than "Trapezium rule":

• “Trapezium Rule” gets 14,000 hits.
• “Trapezoidal Rule” gets 152,000 hits

By contrast, "trapezoid" only gets about three times as many Google hits as "trapezium". Jim (talk) 22:42, 21 February 2009 (UTC)

The term "trapezoidal rule" is also used in the UK, so I also think that the page should be moved. For instance, it's in Iserles, First Course in Numerical Analysis of Differential Equations, Cambridge Univ. Press. On the other hand, Süli & Mayers, An Introduction to Numerical Analysis, Cambridge Univ. Press uses "trapezium rule". The authors have been teaching at English universities for a long time. -- Jitse Niesen (talk) 06:54, 2 April 2009 (UTC)

• Trapezoid rule and trapezoidal rule are the names used in the U.S. 199.125.109.124 (talk) 14:49, 2 April 2009 (UTC)

Moved from WP:RM. 199.125.109.126 (talk) 16:34, 7 April 2009 (UTC)

• Then how would you explain the fact that the article doesn't even mention the name "trapezoid rule" at the moment? It mentions the name "trapezoidal rule", but that's all. "Trapezoidal rule" is also the only name mentioned on MathWorld. -- Smjg (talk) 00:25, 7 April 2009 (UTC)

For the record, "trapezoid rule" is considerably less popular than "trapezoidal rule" on Google, with only 26,000 hits. Jim (talk) 02:50, 8 April 2009 (UTC)

The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Mistake in asymptotic error estimate

I just got out Atkinson from the library and went through the proof for this and there seems to be a mistake in the article when it comes to the asymptotic estimate:

${\text{error}}=-{\frac {(b-a)^{3}}{12n^{2}}}{\big (}f'(b)-f'(a){\big )}+O(n^{-3}).$

Atkinson Equation 5.1.9 actually reads:

${\text{error}}=-{\frac {h^{2}}{12}}{\big (}f'(b)-f'(a){\big )}$

Now I'm presuming that the big O term was added to the wiki equation to represent the error in the $n\rightarrow \infty$ approximation...? If this is the case then the correct equation should be:

${\text{error}}=-{\frac {(b-a)^{2}}{12n^{2}}}{\big (}f'(b)-f'(a){\big )}+O(n^{-3}).$

Will leave this open for discussion before I go and change it because I don't know what the big O term represents

Perceptual Chaos (talk) 06:45, 31 March 2009 (UTC)

I introduced that mistake. You're completely right. Thanks very much for noticing this. -- Jitse Niesen (talk) 07:55, 31 March 2009 (UTC)

---

Re: Error analysis section -- previous comment taken back; I've edited the section to improve the wording, please check.

Python example incorrect?

Looking at the code, it seems alright, however it gives erroneous results. Running it with f(x):x**2, a=1, b=5 gives me 30 with 10000 sub intervals. Any thoughts? 198.164.31.14 (talk) 20:47, 12 March 2010 (UTC)

Tai's rule?

Why on earth does that appear here? Is it a joke? —Preceding unsigned comment added by 132.77.4.43 (talk) 14:32, 16 December 2010 (UTC)

I just deleted this reference. I know we all got a kick out of that but it really doesn't belong here and adds nothing to the page aside from a chuckle. —Preceding unsigned comment added by 98.231.139.36 (talk) 02:21, 21 December 2010 (UTC)

As a joke people now are citing dr. Tai's work (http://care.diabetesjournals.org/content/17/2/152.abstract) in their papers. While that obviously is meant as a joke, it might be prudent to explain it on this page?

I am not sure that the majority of the 250+ citations on Google Scholar are jokes. It might be worth incorporating something from the old page for Tai's method, which was later merged and redirected here. --Rumping (talk) 10:32, 14 September 2015 (UTC)

The paper "A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves Mary M Tai, MS, EDD" costs $35 to download here. Is there a summary of the results available? Rybu (talk) 05:35, 15 January 2020 (UTC)

Priorities

I think it might be best to stop worrying about the scemantics of the naming convention and actually focus on whether or not the mathematics in this article is correct. For example, the MATLAB syntax doesn't seem to be correct, as I've tried it and it doesn't work. If somebody could fix and/or check that rather than worry about trivialites, it would help a lot. —Preceding unsigned comment added by 128.243.253.101 (talk) 17:04, 14 February 2011 (UTC)

In continuation to my previous post I feel it would be best if this actually was completed soon, and that there was a message posted on this discussion page to notify the readers of this, rather than having inane edit wars about thi article's format. —Preceding unsigned comment added by 86.10.90.70 (talk) 01:18, 21 February 2011 (UTC)

too many implementations

There are too many implementations of the algorithm. From MOS:CODE: "Multiple source code implementations are not appropriate unless they contrast specific aspects of the code and that contrast is important to the encyclopedic content of the article. " Bubba73 ^{You talkin' to me?} 00:50, 5 December 2013 (UTC)