Title

Fourier Series of Polygons
Author

 A. Robert
Journal / Anthology

 American Mathematical Monthly
 Year: 1994
 Volume: 101
 Issue: 5
 Page range: 420-428
Description

[A] complex Fourier series represents a 2pi-periodic map [which] can be viewed as a closed parametrized curve t -> f(t) \in C in the complex plane. In general, this curve wll have multiple points (namely, f is not one-to-one). It is our purpose to illustrate this point of view. In particular, we intend to show that, for n >= 2, f_n(t) = Sum[(e^ikt)/k^2, {k \[Congruent] 1(n)] is the Fourier series of a regular n-gon in the complex plane.
Subject

 Mathematics > Calculus and Analysis > Complex Analysis