Overview
A spiral is a class of mathematical curve characterized by a path that winds around a central point while the distance from that point changes continuously. Typically a spiral begins near a center and proceeds to revolve around it while moving outward (or, in some cases, inward), so successive turns do not coincide.
Properties
- Non‑closing: Spirals are open curves, meaning they do not form a closed loop and do not return to the same position after a finite number of turns.
- Radial change: The separation from the center varies with the angle; different named spirals use different relationships between radius and angle (for example, linear growth or exponential growth).
- Applications: Spirals appear in geometry, physics, biology, and engineering as models for growth patterns, wavefronts, and motion paths in mathematics and applied sciences.
How spirals differ from closed curves
Unlike a circle, where every point lies a constant distance from the center, or an ellipse, which is a closed oval shape with repeating distances around the center, a spiral’s radius does not repeat periodically. This means a point moving along a spiral continues to move away from (or toward) the center rather than tracing a bounded loop.