Scaleni

Part of speech: noun

Pronunciation: /skeɪˈliˌnaɪ/

Definitions

1. Three non-collinear points in a plane forming a triangle with all sides having different lengths
2. A triangle characterized by having no two sides the same length, making it distinct from isosceles and equilateral triangles
3. An acute-angled triangle that has one angle larger than 90 degrees, showcasing its unique geometric properties

Etymology: "Scaleni" is the plural of "scalenus," a Latinized form of a Greek word, and it is one of the few geometry terms whose famous definition is wrong. In Greek, "skalenos" meant "uneven" or "unequal," and it was applied to triangles whose sides differ in length, the sense it still carries today. The noun "scalenus" was then used to name such a triangle, and "scaleni" is its plural, the form that shows up in plural contexts such as "all the scaleni in this figure." The definition given here, an acute-angled triangle with one angle over 90 degrees, describes an obtuse triangle, which is a contradiction in terms, since an obtuse triangle is by definition not acute. The defining feature of a scalene triangle is that all three sides have different lengths, and its angles are therefore all different too. The mismatch between the word's meaning and the stated definition is worth knowing, because the word's history points to unequal sides, not to any particular angle.