Triangulus

Triangulus is a term sometimes used in geometry to denote a triangle, or a triangle embedded within a figure. In certain historical and pedagogical writings, triangulus serves as a Latin-inspired label for a three-sided polygon, distinguishing a single triangle from broader collections such as a polygonal mesh.

Etymology: The word derives from Latin triangulus, a diminutive of angulus meaning angle, with the prefix tri- meaning three. The form literally suggests “little triangle.”

In modern mathematical writing, triangulus is rarely used; most texts simply say triangle. When it appears, it refers to a triangle with vertices labeled A, B, and C. Its basic properties include side lengths a, b, c and interior angles A, B, and C. The area can be computed by Heron’s formula or by 1/2 ab sin C, and the Law of Cosines relates sides and angles. In a coordinate setting, the area can be calculated as 1/2|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|.

In applied contexts, triangulus appears in discussions of triangulations, mesh generation, and computer graphics as a fundamental constituent element. It also features in tiling and polygonal network analyses, where the focus is on individual triangles within a larger structure.

History: The term triangulus appears in some Latin or medieval geometry sources; its modern usage is largely historical or pedagogical, with the standard term triangle prevailing in contemporary discourse. See also triangle, triangulation, polygon.