recurvature

Recurvature refers to the property or process by which curvature reappears or re-emerges after a change in direction or after a segment of a curve. In everyday use, it describes patterns where the amount or sign of bending repeats along a path, often implying some periodicity or recurrence.

In differential geometry, curvature κ(s) is a function of arc length s that measures how sharply a curve bends. A curve is said to have recurring curvature when κ(s) assumes similar values at different, regularly spaced values of s, such as when κ(s) is periodic. A simple example is a curve whose curvature is κ(s) = A sin(ωs); the curve bends in a repeating fashion as you move along its length.

Beyond pure geometry, recurvature is used descriptively in biology, architecture, and robotics to indicate a bend that returns toward a prior direction. For instance, plant morphology may describe recurved leaves; in design, recurved arches or blades bend back toward a central axis. In robotics or path planning, a trajectory with recurring curvature patterns may be chosen to satisfy constraints on steering or stability.

Terminology and formal status: Recurvature is not a standard technical term with a universal formal definition across all fields. More precise language often uses periodic curvature, recurring curvature, or curvature as a periodic function, depending on context. See also curvature, periodic function, plane curve, space curve.