Fourier Series Grapher

Sine and cosine waves can make other functions! Here you can add up functions and see the resulting graph.

images/fourier.js

What's happening here?

We are seeing the effect of adding sine or cosine functions. Here we see that adding two different sine waves make a new wave:

Two different sine waves adding together to form a combined wave pattern

When we add lots of them (using sigma notation Σ as a handy shorthand) we can get things like this:

Approximation of a square wave using the sum of twenty sine waves
sin(x) + sin(3x)/3 + sin(5x)/5 + ... + sin(39x)/39
(20 sine waves)

Try this: Start at n=1 to 1 (just the first sine wave), then increase to n=1 to 2 and so on. See the big wave start to smooth out into the new shape.