Periodic Functions with m-Fold Symmetry of Type k
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Suppose that and are relatively prime positive integers (i.e. ). Following [1, p. 14], define a curve with period to have -fold symmetry of type , of the form
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Contributed by: Izidor Hafner (March 2016)
Based on the work of: Frank A. Farris
Open content licensed under CC BY-NC-SA
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Details
The following theorem is shown in [1, pp. 13 ff.]:
Suppose that and are integers and that all the frequency numbers in the finite sum
satisfy .
Then, for any choice of the coefficients , satisfies the symmetry condition for all , so it has -fold symmetry of type .
Reference
[1] F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.
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