Because those sinusoidal waves are merely projections (in the real and complex plane) of the true elemental component of the FT, the complex exponential, which

Because those sinusoidal waves are merely projections (in the real and complex plane) of the true elemental component of the FT, the complex exponential, which is really a helix: http://m.eet.com/media/1068017/lyons_pt2_3.gif http://m.eet.com/media/1068017/lyons_pt2_3.gif A while ago I made some drafts for a series of diagrams to help visualize this (http://imgur.com/vEcnVdn http://imgur.com/vEcnVdn) but unfortunately never got around to finish it (https://en.wikipedia.org/wiki/Wikipedia:Graphics_Lab/Illustration_workshop/Archive/Sep_2013#RfC_-_Visualization_of_exponential_function https://en.wikipedia.org/wiki/Wikipedia:Graphics_Lab/Illustr...). Anyway, for those who find it easier to think of sinusoidal curves, the animation in the Wikipedia article (https://commons.wikimedia.org/wiki/File:Fourier_transform_time_and_frequency_domains_(small).gif https://commons.wikimedia.org/wiki/File:Fourier_transform_ti...) is a very good visualization (also, BetterExplained's rant on sines being explained as circles may resonate: http://betterexplained.com/articles/intuitive-understanding-of-sine-waves/ http://betterexplained.com/articles/intuitive-understanding-...)