**Updated! now displays the frequency spectrum of the triangle wave. I haven't done anything to make it faster, more like I made it slower. If you want FAST, DOWNLOAD & Turbo Speed NOW MORE EYE-FRIENDLY! with softer shades of colors, you won't have to squint and get a headache to look at the plot in detail (as much as before.) Additionally, you can press space to switch the background from black to white. black is best for big picture, white may be better for details.** The triangle wave converges SOOO fast!! well, maybe the fourier series is a little bit more complicated, but basically this is just the phase shift of the integral of the square wave. It contains only odd harmonics, it is an alternating series, and its frequencies roll off to 1/f^2 (faster than square or sawtooth. It approximates a continuous waveform this time, with no discontinuities, and the worst parts of it are non-differentiable points. This is the main reason it converges so quickly. http://en.wikipedia.org/wiki/Triangle_wave
