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A "scalene triangle" is a triangle with three unequal sides. As far as I can tell, this term is not in much use in serious mathematics — in fact, before I became a high school math teacher, I'd forgotten the term existed. However, it is almost universally stressed as an important class of triangles in high school geometry courses in the United States.

I have two questions:

Q1: Who developed/popularized the use of the term scalene to refer to triangles of this type? Why, even, is this term useful? Unlike "isosceles" or "equilateral," being "scalene" is not really a special property of a triangle, but rather seems to be the default condition of an arbitrary triangle.

Q2: How was this term enshrined in American geometry education? Is there any justification for its prominence in the standard curriculum?

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Your Q2 might also be of interest at Mathematics Educators. – senshin May 5 '14 at 15:00

Earliest Known Uses of Some of the Words of Mathematics traces "scalene" (in English) back to 1570. But I expect Euclid used σκαληνός.

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Terrific resource, thanks! – Jon May 5 '14 at 17:08

Robert Israel is correct: Euclid introduces "equilateral", "isosceles" and "scalene" (spelled $\sigma \kappa \alpha \lambda \eta \nu \acute{\omicron} \nu$) in Definition 20 of Book I of the Elements.

Source: Richard Fitzpatrick's edition of the Elements, available at

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