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