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?
$\endgroup$ 12 Answers
$\begingroup$Earliest Known Uses of Some of the Words of Mathematics traces "scalene" (in English) back to 1570. But I expect Euclid used σκαληνός.
$\endgroup$ 1 $\begingroup$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 .
$\endgroup$
