Talk:Triangle

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Triangle definition[edit]

Shouldn't the definition state that a triangle has only or exactly three sides and angles? After all, a square also has three sides and angles. The article's opening sentence reads: "A triangle is ... a polygon with three corners or vertices and three sides...." The definition at thefreedictionary.com states that a triangle is the plane figure formed by connecting three points not in a straight line by straight line segments; a three-sided polygon. Urgos (talk) 23:31, 17 June 2012 (UTC)

This sounds reasonable to me, but it would be inconsistent with the other polygon articles, so I'm not sure. I would look to see if this has been discussed anywhere else first. Nat2 (talk) 22:45, 25 July 2012 (UTC)

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 math.com 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 freemathhelp.com 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)