Periodic Graph Math
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Geometrically a periodic function can be defined as a function whose graph exhibits translational symmetry i e.
Periodic graph math. 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. As you might have noticed there is a relationship between the coefficient in front of θ and the period. There is some number p such that f x f x p for all x visually if you graphed the function then picked up the graph. Star top subjects are math and literature the definition of periodic is.
The general formula for s i n a θ or c o s a θ is. Periodicity f x cos 2x 5. A euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. A euclidean graph is periodic if there exists a basis of that euclidean space whose corresponding translations induce symmetries of that graph.
Periodicity y cos x sin x periodicity f left x right cos left 2x 5 right. Periodic graphs are closely related to tessellations of space and the geometry of their symmetry groups hence to geometric group theory as w. Equivalently a periodic euclidean graph is a periodic realization of an abelian covering graph over a finite graph. Period frac 2 pi color red a.
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