Richard Dawkins’ Unweaving the Rainbow includes a great discussion of the scientific uses of the Fourier transform. Most amusingly: “The side-to-side waving of the urine trail on the road was presumably produced by the long [elephant] penis acting as a pendulum (it would be a sine wave if the penis were a perfect, Newtonian pendulum, which it is not) interacting with the more complicated periodicity of the lumbering four-legged gait of the whole animal.” (p. 73)
This video provides an accessible visual explanation of how this mathematical tool breaks down a complicated curve into its constituent sine waves, and some of the useful applications for that transformation: