The word balayage can have two meanings: in cosmetics, it's a technique for highlighting hair that's supposed to lighten it in a natural way, and in mathematics it's a method for reconstructing a harmonic function. Both of these definitions comes from the French word bayalage, meaning "sweeping". The fashion thing is a reference to the way in which the color is applied with a sweeping motion, and the math thing is called that because a mass is "swept out" from a closed domain onto a boundary. Balayage is from the verb balayer, meaning "to sweep", and that's from the noun balai, meaning "broom". That's thought to either trace to the Old Breton word balan or the Gaulish word balano, which also meant "broom". According to Google NGrams, usage of balayage peaked in 1974 and has been on the decline since.
Hello! I'm Adam Aleksic, a junior studying government and linguistics at Harvard University, where I co-founded the Harvard Undergraduate Linguistics Society. In addition to etymology, I also really enjoy trivia, politics, vexillology, geography, board games, conlanging, art history, and law.