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Correct the definition of triangle inequality to not include degenera… #375

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Correct the definition of triangle inequality to not include degenera…
durrellchamorro Sep 12, 2016
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Add clarity to the definition of triangle inequality.
durrellchamorro Sep 13, 2016
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Improve explanation of the triangle inequality theorem and add a Dig …
durrellchamorro Sep 18, 2016
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14 changes: 12 additions & 2 deletions exercises/triangle/description.md
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Expand Up @@ -2,6 +2,16 @@ The program should raise an error if the triangle cannot exist.

## Hint

The sum of the lengths of any two sides of a triangle always exceeds or
is equal to the length of the third side, a principle known as the _triangle
In mathematics, a degenerate case is a limiting case in which an element of a
class of objects is qualitatively different from the rest of the class and hence
belongs to another, usually simpler, class.

1. If the sum of the lengths of any two sides of a triangle is equal to the
length of the third side, there exists a degenerate triangle.
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it might be better to make clear that, more than the degenerate triangle existing, it is the triangle referred to earlier in the sentence that is degenerate (something like "that triangle is degenerate")


2. The sum of the lengths of any two sides of a triangle always exceeds or is
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Currently, there is a sentence about a degenerate case, then a numbered list, and the first item is a degenerate case, but the second isn't, and to me it seemed to make the relationship unclear (why are the two in a numbered list?). What if we start with saying the triangle inequality first, then explain the degenerate case of the inequality, as well as explaining what a degenerate triangle looks like? That would help us to understand what is meant by "qualitatively different from the rest of the class and hence belongs to another, usually simpler, class." by giving an example relevant to the exercise.

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@durrellchamorro durrellchamorro Sep 14, 2016 •
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What do you think of this?

The triangle inequality theorem states:
z ≤ x + y
where x,y, and z are the lengths of the sides of a triangle. In other words, the sum of the lengths of any two sides of a triangle always exceeds or is equal to the length of the third side.

A corollary to the triangle inequality theorem is there are two classes of triangles. If the sum of the lengths of any two sides of a triangle is greater than the length of the
third side, that triangle is two dimensional, has area, and belongs to the first class. If the sum of the lengths of any two sides of a triangle is equal to the length of the third side, that triangle is qualitatively different from all the triangles in the first class since it is one dimensional, looks like a straight line, and has no area. In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class. The degenerate case of the triangle inequality theorem is when the sum of the lengths of any two sides of a triangle is equal to the length of the third side. A triangle with such qualities is called a degenerate triangle and it belongs to the second class.

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Is there a chance that it will be unclear to a reader that the two classes of triangles mentioned (not degenerate vs degenerate) are a separate classification from the one resulting from the lengths of the sides (equilateral, isosceles, scalene)? If there is, we should try to find a way to make the distinction clearer. But if others find it understandable, I think this is good.

I think the last thing is: After a student has read this, the student might think "OK, I have just learned about degenerate triangles, and how should this knowledge apply to this exercise?" and we should give an answer to that potential question in the readme (that they don't violate the triangle inequality - but we won't test for them)

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@durrellchamorro durrellchamorro Sep 15, 2016 •
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Good points @petertseng. How about, "A corollary to the triangle inequality theorem is there are two classes of triangles--degenerate and nondegenerate. If the sum of the lengths of any two sides of a triangle is greater than the length of the third side (as is the case with equilateral, isosceles, and scalene triangles), that triangle is two dimensional, has area, and belongs to the nondegenerate class."

Regarding your second point, knowledge about degenerate triangles applies to the exercise because, at least for the Ruby and Coffescript exercises, the second to last test is for the degenerate case. Interestingly enough I don't see a test for the degenerate case in the Javascript exercise.

The main reason I wanted to point out degenerate triangles do not violate the triangle inequality theorem is the tests, at least for Ruby and Coffeescript, are currently wrong. The combination of incorrect tests and not understanding the triangle inequality theorem confused me. I thought either the tests were wrong or the definition of the triangle inequality theorem in the README was wrong. I incorrectly assumed the tests were right, hence the original pull request message regarding a correction to the definition of the triangle inequality theorem in the README. After a closer look I realized a 2,2,4 triangle satisfies the degenerate condition of the triangle inequality theorem, but In Coffeescript for example, the second to last test reads:

it 'is illegal when violating triangle inequality 2', ->
    expect(-> new Triangle(2,2,4)).toThrow("violation of triangle inequality")

If it is a mistake that the Ruby and Coffeescript exercises are testing for the degenerate case, then I'm happy to make pull requests to remove those tests. Otherwise, I'm happy to fix the tests in the languages I know if that is ok with you all.

If you choose not to test for the degenerate case, then a way to document in the README how this knowledge about degenerate triangles applies to the exercise would be to add a "Dig Deeper" or "Extra Credit" or "Challenge" section where you explain how none of the tests checked for a degenerate triangle, but you can challenge the reader to add those tests. You can even put the whole explanation of the corollary to the triangle inequality theorem in the "Challenge" section itself. For OO languages you can challenge the reader to prevent degenerate triangles from being initialized directly from the Triangle class.

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A corollary to the triangle inequality theorem is there are two classes of triangles--degenerate and nondegenerate.

Thanks, I think this is good. Explicitly noting them will prevent the confusion.

at least for the Ruby and Coffescript exercises, the second to last test is for the degenerate case
Interestingly enough I don't see a test for the degenerate case in the Javascript exercise.

Ah. It appears that Javascript did have it at one point, but removed it for exercism/DEPRECATED.javascript#164 .

If it is a mistake that the Ruby and Coffeescript exercises are testing for the degenerate case, then I'm happy to make pull requests to remove those tests.

Ah, good point. Yes, the test should be removed altogether, as had been decided at #311 (comment) - tests for degenerate triangles are not in https://github.com/exercism/x-common/blob/master/exercises/triangle/canonical-data.json and tracks should be using this data, unless they have specific language-level concerns (and this likely isn't one).

If you choose not to test for the degenerate case, then a way to document in the README how this knowledge about degenerate triangles applies to the exercise would be to add a "Dig Deeper" or "Extra Credit" or "Challenge" section where you explain how none of the tests checked for a degenerate triangle, but you can challenge the reader to add those tests.

I like this! I don't have a strong opinion on which of the three proposed terms to use. If you made me pick I'd pick "dig deeper", but I can always be convinced otherwise.

You can even put the whole explanation of the corollary to the triangle inequality theorem in the "Challenge" section itself

I do think this sounds like a good idea.

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@durrellchamorro durrellchamorro Sep 16, 2016 •
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Ok. I was looking at the json here and you are not testing that triangles with negative sides are illegal. It seems like a good idea to test for that. The Ruby, Javascript and Coffeescript tests are currently testing for it.

What do you think of this?

Hint

The triangle inequality theorem states:
z ≤ x + y
where x,y, and z are the lengths of the sides of a triangle. In other words, the
sum of the lengths of any two sides of a triangle always exceeds or is equal to
the length of the third side.

A corollary to the triangle inequality theorem is there are two classes of
triangles--degenerate and non-degenerate. If the sum of the lengths of any two
sides of a triangle is greater than the length of the third side, that triangle
is two dimensional, has area, and belongs to the non-degenerate class. In
mathematics, a degenerate case is a limiting case in which an element of a class
of objects is qualitatively different from the rest of the class and hence
belongs to another, usually simpler, class. The degenerate case of the triangle
inequality theorem is when the sum of the lengths of any two sides of a triangle
is equal to the length of the third side. A triangle with such qualities is
qualitatively different from all the triangles in the non-degenerate class since
it is one dimensional, looks like a straight line, and has no area. Such
triangles are called degenerate triangles and they belong to the degenerate
class.

Dig Deeper

This exercise does not test for degenerate triangles. Feel free to add your own
tests to check for degenerate triangles.

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you are not testing that triangles with negative sides are illegal. It seems like a good idea to test for that. The Ruby, Javascript and Coffeescript tests are currently testing for it.

Ah! It would be good to send a PR for that, then. I will first say that at #311 we had decided against it because it's not specified clearly whether the classification function is responsible for normalising possibly-negative distances into absolute lengths as opposed to the caller being responsible. If you do feel strongly about this, it is of course open to discussion if we could get a PR on it.

What do you think of this?

Personally I am thinking it looks good, so 👍

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It's interesting because it leaves it open to the student what to do with the degenerate triangles. You gave a possible option earlier in our discussion: It shouldn't be possible to create them because they are different. Others may choose to allow them, and classify them as either scalene or isosceles (they can't be equilateral unless all sides are zero). Others may make degenerate a separate case altogether. We like to see variety, so leaving it open seems like a good idea, which is another reason I said 👍

equal to the length of the third side, a principle known as the _triangle
inequality_.

Therefore, a degenerate triangle does not violate the principle of _triangle
inequality_.