Even nonperiodic and arbitrary curves can be built exactly from sinusoids.

Evidence

Nonperiodic functions can also be expanded in terms of sinusoidal functions. We have already mentioned that a function such as is not periodic, having an irrational ratio of its component frequencies. Clearly, if this y(t) were presented as a puzzle, the answer is just the equation in the preceding sentence, so this example hints at the fact that all nonperiodic functions also can also be written as a Fourier series. As Sir James Jeans, a famous mathematical physicist of the late nineteenth and first half of the twentieth century, and himself an author of an excellent popular book, Science and Music, put it, “Fourier’s theorem tells us that every curve, no matter what its nature may be, or in what way it was originally obtained, can be exactly reproduced by superposing a sufficient number of simple harmonic curves [sinusoidal curves]—in brief, every curve can be built up by piling up waves.” — Eric J. Heller, Why You Hear What You Hear- An…, 329

Categorization

• CANDY: A shareable quote: ‘every curve can be built up by piling up waves’ — elegant and memorable.