Symmetry of a Mystery Curve

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This Demonstration shows graphs of the function , where , , and are complex coefficients and the frequencies , , and are integers. In particular, for the frequencies 1, 6, and -14, the curve has five-fold symmetry.

Contributed by: Izidor Hafner (January 2016)
(Based on the work of Frank A. Farris)
Open content licensed under CC BY-NC-SA



The following theorem is shown [1, pp. 13]:

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 .


[1] F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015.

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