From Wikipedia, the free encyclopedia
Jump to: navigation, search
Former featured article Triangle is a former featured article. Please see the links under Article milestones below for its original nomination page (for older articles, check the nomination archive) and why it was removed.
Main Page trophy This article appeared on Wikipedia's Main Page as Today's featured article on May 14, 2004.
WikiProject Mathematics (Rated B-class, Top-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
B Class
Top Importance
 Field: Geometry
A vital article.
One of the 500 most frequently viewed mathematics articles.
Wikipedia Version 1.0 Editorial Team / Vital
WikiProject icon This article has been reviewed by the Version 1.0 Editorial Team.
B-Class article B  This article has been rated as B-Class on the quality scale.
Taskforce icon
This article is a vital article.

Exclusive definition of isosceles triangle[edit]

Is the exclusive definition of isosceles triangles (i.e. that equilateral triangles are not isosceles) still taught anywhere today? I don't think it is, and if it's not, I think it's being given undue weight in the article. Jackmcbarn (talk) 17:00, 4 January 2014 (UTC)

Yes, I think it is still taught, just as some American schools teach the exclusive definition of the trapezium (trapezoid). I agree that inclusive definitions are preferable. Dbfirs 22:11, 4 January 2014 (UTC)
Alas, it is taught, as I know only too well after decades of teaching mathematics in high schools. Would that it weren't. However, the article currently says "Some mathematicians define an isosceles triangle to have exactly two equal sides". Are there any mathematicians who define it that way, as opposed to school teachers? Is there a source for that? The article gives a source for the (as far as I know) more standard definition, where equilateralisosceles, but none for the other definition, and I personally have no memory of ever seeing the exclusive definition given by any serious mathematical source. JamesBWatson (talk) 22:13, 4 January 2014 (UTC)
Unfortunately, that's how Euclid's Elements defines it: "an isosceles triangle that which has two of its sides alone equal". Jackmcbarn (talk) 22:39, 4 January 2014 (UTC)
That is interesting, but not relevant here, because how a Wikipedia article should use a term is determined by the normally understood usage in early 21st century English, not 4th/3rd century BC Greek. JamesBWatson (talk) 21:16, 6 January 2014 (UTC)
The problem is that Euclidean geometry is still taught using Euclid's terms. Charles Lutwidge Dodgson wrote a book on Euclidean geometry (I've read it.) and also wrote:
"When I use a word," Humpty Dumpty said in a rather a scornful tone, "it means just what I choose it to mean – neither more nor less."
"The question is," said Alice, "whether you can make words mean so many different things."
"The question is," said Humpty Dumpty, "which is to be master – that's all."
My point being that there are two different "normally understood usage[s] in early 21st century English".
For a source, try lessons (though another lesson contradicts this usage). Dbfirs 23:11, 6 January 2014 (UTC)
The exclusive definition seems also to be implicit in mathopenref and is explicit in "Isosceles triangles have two sides with the same length, and one side that differs." that Google claims to find on the website (though I can't see those words there). I'm sure I can find some British school textbooks that use Euclid's definition, but they tend not to be published on the internet. Dbfirs 23:30, 6 January 2014 (UTC)
Yes indeed. There are certainly British school text books that give the exclusive definition, jsut as there are British school textbooks that state that 1 is a prime number. My question is whether ther are any mathematicians who use the term in that way, and I don't count someone who got a grade E at A level maths, went to a college to train to be a teacher, and after a few years of teaching decided to write a text book as a "mathematician". Is there any evidence of the use of the exclusive definition by serious academic mathematicians? JamesBWatson (talk) 12:26, 7 January 2014 (UTC)
I haven't seen the prime number error in British text books, but Euclidean geometry is still a valid branch of mathematics, so certainly Charles Dodgson used the exclusive definition. I don't think modern mathematicians worry about such trivialities. They don't write papers on such basic geometry. Dbfirs 14:45, 7 January 2014 (UTC)

Phrasing of Scalene Definition[edit]

The sentence "Right triangles are scalene if and only if not isosceles." sounds awkward and might even be incorrect, like it's saying a right triangle is isosceles and not isosceles. I think a better phrasing would be the simpler, "A right triangle is scalene only if it is not isosceles." — Preceding unsigned comment added by Threefour (talkcontribs) 04:13, 6 June 2014 (UTC)

The statement as given is true, but has nothing to do with right triangles. Any triangle is scalene if and only if it is not isosceles (one must consider equilateral triangles as isosceles for this statement to be correct - see above section). Your modification is simpler only because it throws out half of the statement being made. See If and only if for clarification of this linguistic construction. Bill Cherowitzo (talk) 04:47, 6 June 2014 (UTC)
Well the statement is true if and only if you use the inclusive definition of isosceles. I share Threefour's dislike of the form of the statement. How can we re-phrase it? Dbfirs 06:33, 6 June 2014 (UTC)
Sorry, early in the morning here, and my brain wasn't in gear! Dbfirs 06:43, 6 June 2014 (UTC)

Area by line integral[edit]

The section on getting the area specifies how to obtain the line integral between two consecutive vertices, but then doesn't specify how to go from that to actually get the area. The page on line integrals that is linked to is rather technical, which makes it difficult to find out how to use this method.

FreeFull (talk) 14:00, 4 August 2015 (UTC)