variangle

Variangle is a term used in geometry and design to denote a construct in which an angle is variable or controlled by a parameter. The word combines vari- (vary) with angle, and it is applied in several contexts to emphasize angle variation.

In mathematics, variangle describes a family of shapes whose angular measures depend on a single real parameter t. A variangle polygon of n sides has interior angles a1(t), a2(t), ..., an(t) subject to the sum a1(t) + a2(t) + ... + an(t) = (n−2)π for all t in a given interval. The parameterization allows continuous deformation of the polygon while preserving planarity; special cases include fixed-eangle polygons when all angles are constant, and equiangular polygons at certain parameter values where all ai(t) are equal.

In differential geometry and computer graphics, variangle concepts appear in the study of curves and surfaces with varying turning or dihedral angles. A variangle curve can be described as a path whose tangent-direction change is specified by a function of arc length, enabling controlled bending or twisting.

In practical design and engineering, variangle is used as a branding or descriptive term for adjustable-angle devices and fittings, such as camera mounts, display stands, or lighting rigs. These products feature joints that allow the output angle to vary within a defined range, enabling rapid reorientation without disassembly.

Variangle remains a niche or coined term rather than a standardized mathematical construct. Its usage highlights the idea of controlled angle variation across a structure or mechanism.