Periodic function

Many aspects of the natural world have periodic behavior, such as the phases of the Moon, the swinging of a pendulum, and the beating of a heart. The length of the interval over which a periodic function repeats is called its period. Any function that is not periodic is called aperiodic. A function is defined as periodic if its values repeat at regular intervals. For example, the positions of the hands on a clock display periodic behavior as they cycle through the same positions every 12 hours. This repeating interval is known as the period. More formally, a function f {\displaystyle f} is periodic if there exists a nonzero constant P {\displaystyle P} such that f ( x + P ) = f ( x ) {\displaystyle f(x+P)=f(x)} for all values of x {\displaystyle x} in the domain. A nonzero constant P {\displaystyle P} for which this condition holds is called a period of the function.