Any repeating shape — a square wave, a sawtooth, your favourite tune — is just spinning circles added together. Watch a few sine waves stack into a crisp corner, then add more and see it sharpen.
Fourier's discovery: any repeating signal is a sum of pure tones whose frequencies are whole-number multiples of the base frequency. A square wave is 4/π · (sin x + ⅓ sin 3x + ⅕ sin 5x + …) — only odd harmonics, shrinking like 1/n. The more circles you stack, the sharper the corner gets. This one idea underlies MP3s, JPEGs, MRI scans, radio and quantum mechanics.