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:''"Aperiodic" and "Non-periodic" redirect here. For other uses, see Aperiodic (disambiguation).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 2''π'' radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.== Definition ==A function ''f'' is said to be periodic with period ''P'' (''P'' being a nonzero constant) if we have:f(x+P) = f(x) \,\!for all values of ''x'' in the domain. If there exists a least positiveFor some functions, like a constant function or the indicator function of the rational numbers, a least positive "period" may not exist (the infimum of possible positive ''P'' being zero).constant ''P'' with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) A function with period ''P'' will repeat on intervals of length ''P'', and these intervalsare 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.
:''"Aperiodic" and "Non-periodic" redirect here. For other uses, see Aperiodic (disambiguation).
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 2''π'' radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.
== 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'' in the domain. If there exists a least positive〔For some functions, like a constant function or the indicator function of the rational numbers, a least positive "period" may not exist (the infimum of possible positive ''P'' being zero).〕
constant ''P'' with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) A function with period ''P'' will repeat on intervals of length ''P'', and these intervals
are 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.
抄文引用元・出典: フリー百科事典『 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 2''π'' radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.== Definition ==A function ''f'' is said to be periodic with period ''P'' (''P'' being a nonzero constant) if we have:f(x+P) = f(x) \,\!for all values of ''x'' in the domain. If there exists a least positiveFor some functions, like a constant function or the indicator function of the rational numbers, a least positive "period" may not exist (the infimum of possible positive ''P'' being zero).constant ''P'' with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) A function with period ''P'' will repeat on intervals of length ''P'', and these intervalsare 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.">ウィキペディア（Wikipedia）』
■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 2''π'' radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.== Definition ==A function ''f'' is said to be periodic with period ''P'' (''P'' being a nonzero constant) if we have:f(x+P) = f(x) \,\!for all values of ''x'' in the domain. If there exists a least positiveFor some functions, like a constant function or the indicator function of the rational numbers, a least positive "period" may not exist (the infimum of possible positive ''P'' being zero).constant ''P'' with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) A function with period ''P'' will repeat on intervals of length ''P'', and these intervalsare 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.">ウィキペディアで「:''"Aperiodic" and "Non-periodic" redirect here. For other uses, see Aperiodic (disambiguation).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 2''π'' radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.== Definition ==A function ''f'' is said to be periodic with period ''P'' (''P'' being a nonzero constant) if we have:f(x+P) = f(x) \,\!for all values of ''x'' in the domain. If there exists a least positiveFor some functions, like a constant function or the indicator function of the rational numbers, a least positive "period" may not exist (the infimum of possible positive ''P'' being zero).constant ''P'' with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) A function with period ''P'' will repeat on intervals of length ''P'', and these intervalsare 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.」の詳細全文を読む
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