Periodische

Periodische is the inflected form of the German adjective periodisch, meaning periodic or recurring at regular intervals. It is used before feminine nouns in the nominative or accusative singular and before all plural nouns (e.g., die periodische Funktion, periodische Folgen).

In mathematics, a function f is periodic with period T if f(x+T) = f(x) for all x; common examples include sine and cosine with period 2π. A periodic sequence repeats values after a fixed number of steps; in Fourier analysis, arbitrary signals are expressed as sums of periodic components.

In physics and engineering, periodic phenomena include harmonic motion and waveforms; periodic boundary conditions appear in simulations; time-series with repeating cycles are described as periodic.

In German technical language, the term occurs in many compound nouns such as periodische Funktion, periodische Bewegung, periodische Muster.