High Quality Content by WIKIPEDIA articles! In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2 . Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry. Specifically, a function f is periodic with period P if the graph of f is invariant under translation in the x-direction by a distance of P. This definition of periodic can be extended to other geometric shapes and patterns, such as periodic tessellations of the plane.