Definition
A function f is said to be periodic with period P (P being a nonzero constant) if we have
for all values of x. If there exists a least positive constant P with this property, it is called the prime period. A function with period P will repeat on intervals of length P, and these intervals are sometimes also referred to as periods.
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.
A function that is not periodic is called aperiodic.
Read more about this topic: Periodic Function
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Is God by definition indifferent, beyond us all?
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—Richard Eberhart (b. 1904)