trigonoid

Trigonoid is a geometric term that has appeared in mathematics in several, often unrelated, contexts. There is no single standard definition, and different authors have used the word to refer to distinct objects that share a triangular or trigonometric origin.

In some texts, a trigonoid denotes a plane curve with triangular symmetry, that is, invariant under rotation by 120 degrees and reflection across the triangle's axes. In other uses, the term describes a locus or envelope arising from triangular constructions or from trigonometric parameterizations; the exact equation or construction is specific to the source. As a result, a trigonoid need not be a single well-defined object.

The term is more common in older mathematical literature and in discussions of plane curves that are loosely related to the pursuit of triangle-based or trigonometrically defined figures. The etymology combines tri- for three, gonia for angle, reflecting its triangle-related origin.

Because of its ambiguous usage, readers are advised to check the definition provided by the author when encountering the term.

See also: plane curves with triangular symmetry, deltoid, astroid, hypotrochoid.