A parabolic spiral is a type of curve that spirals outward while gradually increasing in distance from a central point. It is defined mathematically by a specific equation that combines both linear and quadratic elements, resulting in a shape that resembles a spiral staircase. This curve can be found in various natural and man-made structures, such as shells and certain architectural designs. In geometry, the parabolic spiral is categorized as a member of the family of spirals, which also includes the Archimedean spiral and the logarithmic spiral. Its unique properties make it interesting for applications in physics and engineering, particularly in the study of motion and wave patterns.