Fourier Series of a Square

Livio Zucca

with the precious contribution of Danilo Minisini.


Imagine to run around a polygon measuring the radius: you could generate a periodic wave.

The polygon and the periodic wave

Each periodic wave could be represented by a Fourier Series. Therefore this is our theorem:

Each convex and each "not too concaves" plane figure
could be represented by a Fourier Series.


A square, for example!

From circle to square
Note: Each figure has the area = Pi-Greek. This is the true Squaring of the Circle!!!



A Gastropod

Gastropod
Mother-Nature already knew it.



We are working to extract the Fourier series of a Xomino and other interesting polygons.



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1st edition: 30 Apr 2000

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