Talk:Uses of trigonometry

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As for the "number theory" section: Well, but in order to know which fractions are in lowest terms I have to already know the factorisation of 42, then I can evalue the Moebius function simplily using the definition. Therefore that formula is pretty useless. Army1987

I find the word therefore above to be a gross non-sequitur. Michael Hardy 21:59, 20 Apr 2005 (UTC)

[Somehow the person who wrote the above expects everyone to know that a DIFFERENT person wrote what is below. Michael Hardy 21:59, 20 Apr 2005 (UTC)]

Ok, now I've signed it. --Army1987 11:35, 1 May 2005 (UTC)

Please remove the the 1st two sentences (about the "Did you know" gag) as soon as that is off the front page. -The person who put them there.

Removed pre-schedule. ✏ Sverdrup 17:03, 26 Jun 2004 (UTC)

[edit] "Well-known applications..."

The article said:

Anyone who has taken a course on trigonometry knows that it has applications to such endeavors as navigation, land surveying, building, and the like, but that impression is misleading in that it fails to indicate the nature and enormous variety of the other scientific applications and other uses of trigonometry.

Matt Crypto changed it to:

Well-known applications of trigonometry include such endeavors as navigation, land surveying, building, and the like. In addition to these, there is an enormous variety of lesser-known scientific applications and other uses of trigonometry.

I think that fails to convey the intended meaning. The point was that any list uses that are readily seen by one who knows only trigonometry would be misleading.

Since the objection to the original phrasing expressed in the summary is that badly taught trigonometry courses don't necessarily convey even those uses that can be readily understood by those who know only trigonometry, I have changed it to:

Courses in trigonometry usually make clear the nature of some of its applications to such endeavors as navigation, land surveying, building, and the like, but that impression is misleading in that it fails to indicate the nature and enormous variety of the other scientific applications and other uses of trigonometry. Michael Hardy 22:09, 16 Sep 2004 (UTC)
I think this is OK, and corrects the original quibble. I find it strange, though, that the lead section is so focused on trigonometry courses, students and instructors — I think it would do better to avoid this emphasis. — Matt 22:34, 16 Sep 2004 (UTC)

[edit] The anecdote is useful

Matt Crypto also deleted this:

Student in a trigonometry course, to the instructor (incredulously): "What will we actually use this knowledge for?"
Classmate (giggles): "Well, you might want to know the height of a flagpole."

I think this is useful, in order to convey emphatically to those who teach trigonometry why their students might not be entirely respectful toward the subject matter without being told the things in this article. Such an instructor could hand out this Wikipedia article to the class. Michael Hardy 22:09, 16 Sep 2004 (UTC)

It's hard to argue for its inclusion for me, since this is simply not wikipedia style. We don't use this kind of teaching style, we present topics encyclopedically. This article was created on the border of this, and I support Matt's edits, because they modify this article to the right style. [[User:Sverdrup|❝Sverdrup❞]] 22:15, 16 Sep 2004 (UTC)
I don't think it should be included. An inline joke in the lead section is a little odd in an encyclopedia article, stylistically. It's also...hmm...well, either I don't get the punchline, or else I do get the punchline and I just don't find it funny.
Well, being funny was of course not the purpose; any humor in it is either epiphenomenal or subservient to the larger purpose. Michael Hardy 01:48, 17 Sep 2004 (UTC)
Maybe I don't have that great a sense of humour, but I think that humour is particularly difficult to get across in a way that's acceptable to a wide variety of cultures — sense of humour varies a lot from place to place. I do think it's got the potential to be confusing (it confuses me), and I think the informational purpose it serves is extremely limited.
More generally, it occurs to me that the article is, in places, geared towards the purpose of convincing students that trigonometry is useful...I think this might be a mistake in a general encyclopedia. We shouldn't really "tilt" our articles towards any particular task — while it should likely serve well for any purpose, it should present information in a balanced fashion, without any background agenda...not all readers will be trig students. — Matt 22:44, 16 Sep 2004 (UTC)

I wrote this article intending to make it comprehensible to persons who know essentially no more about trigonometry than what is taught in the trigonometry course usually required of a very broad class of students. I also wanted to convey efficiently why this material would be of value to those students: not only do they get a misleading impression of the role of trigonometry by seeing only those applications whose details can be understood without more advanced study, but they are also often understandably impatient with the subject for that reason. The "joke" was of course not intended primarily to be humorous, but rather to illustrate that point. I don't know a more efficient way to say that. More prosaic writing is often far less efficient than something like this. Michael Hardy 01:56, 17 Sep 2004 (UTC)

I think that the joke/anecdote seems to illustrate only the following point: "It is common for students to believe that the applications of trigonometry are limited to finding the height of objects; they can sometimes become impatient with the subject as a result." — surely that would serve as a prosaic substitute?
Making the article comprehensible to those without specialist knowledge of trigonometry is certainly a good idea. However, we cannot assume that the only type of reader is a student who has attended a basic trig class. They might not have done so, or equally they might be a professor of mathematics, and so on. I think the article, and the lead section in particular, currently suffers from this assumption because it immediately launches into addressing why students might not get the "wider picture" of the entire variety of applications. While this is worth mentioning, it shouldn't dominate the entire purpose of the article, which is, of course, to survey the "uses of trigonometry". For example, the article currently neglects major uses of trigonometry — such as "flagpole height finding". — Matt 07:15, 17 Sep 2004 (UTC)

I disagree for several reasons:

  • You say "they might be a professor of mathematics". To a considerable extent, that's who I intended the "joke" for! The exchange between two students happened nearly verbatim the way it's presented here when I taught trigonometry at the University of North Carolina. I was trying to say, in part: Here's why your students might want or need to see this article, which you can copy and distribute to them."
  • You say
students might not get the "wider picture" of the entire variety of applications. While this is worth mentioning, it shouldn't dominate the entire purpose of the article
I'd agree if this were titled "uses of optics", for example, or "uses of Fourier analysis". But I think the place of what is called trigonometry in the general culture of learned discourse makes that just the right audience. For example, many mathematicians do research in the mathematical theory known as Fourier analysis, relying heavily on trigonometric functions, and many statisticians do research in the theory of time series, again relying heavily on trigonometric functions. Some mathematicians even discover important and abstruse new theorems about those same trigonometric functions that are introduced to secondary-school pupils. But nonetheless, nobody describes their research field as "trigonometry", even when their discoveries are about trigonometric functions. Rather "trigonometry" is used as the name for the most elementary study of trigonometric functions, and not for research in which new results are found concerning those functions. Michael Hardy 00:30, 18 Sep 2004 (UTC)
My objection is to writing for any overly-narrow "target audience" — this article, particularly the lead section, is written presuming the reader is involved in trigonometry classes — both students and professors. While I understand why you want to make the point, I find it very strange that an article titled "Uses of trigonometry" spends most of its lead section discussing how trigonometry is taught! I think, however, that we're not going to come to an agreement on this. Accordingly, my suggestion would be that I go and prepare an alternative lead section (here on the Talk page), place it side-by-side with the current version, and solicit for community comment on which (if either!) is in the right direction; I presume you wouldn't have any objection to this? — Matt 00:51, 18 Sep 2004 (UTC)

Again, I'd agree if the topic were "optics" or "Fourier analysis". More later ... Michael Hardy 01:36, 18 Sep 2004 (UTC)

I feel that the entire opening is poor, especially the "joke" (if you can even call it that), and the statement This article attempts to address that kind of concern. has absolutely no place in Wikipedia. CryptoDerk 23:27, May 1, 2005 (UTC)

What do you mean by saying "if you can even call it that"? I DID NOT call it that!! I did not even suspect that anyone might think it was a joke when I wrote it. If you want to call it a "joke", that's you who are calling it that, not anyone else. Michael Hardy 23:59, 1 May 2005 (UTC)
Even as an anecdote, it doesn't work very well. I'm left wondering what the "message" of the anecdote is. Many of our readers would not understand it. — Matt Crypto 00:04, 2 May 2005 (UTC)
Its point is (obviously, I would have thought) that if one knows only the facts of elementary trigonometry, one may nonetheless have no impression of the subject's role in science, and it would easy consequently to think that the whole topic is unimportant. Michael Hardy 00:09, 2 May 2005 (UTC)
I understand the purpose, just not the anecdote itself, exactly. Regardless, the best way for an encyclopedia article is to simply describe the applications of trigonometry. An intelligent reader will appreciate its role in science if you describe the applications correctly. There is no need to coerce the reader, or ply them with unencyclopedic motivational narratives. — Matt Crypto 00:13, 2 May 2005 (UTC)
I've swapped out the lead section with another one. It's not great, but I think it's a move in the right direction. — Matt Crypto 23:44, 1 May 2005 (UTC)
Why don't you state what your ACTUAL objection to that anecdote is? I am still mystified. Michael Hardy 00:15, 2 May 2005 (UTC)
I should point out that I'm not calling it a joke, and I'm not saying other people think it is a joke. I'm simply referring to it as "joke" as that's the terminology that I noticed on this page being used more than once. In fact, my note in parentheses clearly shows that I don't think it is a joke. CryptoDerk 00:16, May 2, 2005 (UTC)

I actually read the whole article now and I'm convinced the entire tone of it is wrong. It's self-referential (Many fields make use of trigonometry in a more advanced way than can be discussed in this brief article) and frequently chatty (The value of the sum is −1. How do we know that? Because 42 has an odd number of prime factors, A Fourier series is something that looks like this). This is more of something you'd find on Wikibooks. CryptoDerk 23:48, May 1, 2005 (UTC)

[edit] "preconceptions"?

An edit summary said:

revert -- we should avoid a "lecturing" tone, and avoid assumptions about the preconceptions of the reader..

Where were there assumptions about the preconceptions of the reader? The material that got reverted said that knowledge of trigonometry alone does not give a good impression of the nature and scope of its uses. The only assumption about the reader is that the reader wants to find out how trigonometry is used and that the reader is familiar with at least some elementary trigonometry, especially the sine and cosine functions. Michael Hardy 03:00, 2 May 2005 (UTC)

This addition: "Knowledge of trigonometry alone can easily leave a very misleading impression about their nature and scope. One may think that trigonmetry is used primarialy for the sort of measurement problems in..."
We shouldn't make the assumption that the reader has a limited understanding of the breadth of trigonometry applications and needs to be convinced otherwise. — Matt Crypto 12:11, 2 May 2005 (UTC)

No. It just means that one who knows ONLY trigonometry would not understand the breadth of its applications. The topic of applications of trigonmetry is not included within knowledge of trigonometry. Michael Hardy 02:28, 30 December 2006 (UTC)