[b]The Fourier Series[/b][br]With this application you can see how a sum of enough sinusoidal functions may lead to a very different periodical function. The Fourier theorem states that any (non pathological) periodic function can be written as an infinite sum of sinusoidal functions.

Change the value of [math]n[/math], representing the number of sinusoidal waves to add up. The maximum value for [math]k[/math], the index of the sum, is shown and the sum of the waves is shown in blue, too. For small values of [math]n[/math] you can also see the single terms of the sum.