A Pythagorean, or “greedy” cup, is one that automatically drains itself once filled to a certain level. In other words, it’s a self-starting siphon – one that triggers only at certain fill level. And chances are you have an example of this mechanism close at hand: inside your washing machine’s soap tray. That’s why the tray has such a clearly marked maximum fill line; if you were to put more soap than that in the tray, it would automatically drain! (Image and video credit: S. Mould)
According to legend, Pythagoras invented a cup to prevent his students from drinking too greedily. If they overfilled the cup, it would immediately drain out all the fluid. The trick works thanks to a U-shaped tube in the center of the cup. As long as the liquid level is below the highest point in the U-tube, only the entrance side of the tube will be filled. As soon as the liquid level in the cup is higher, the weight of all that fluid forces liquid up and around the bend. This kicks off a siphoning effect that pulls all the fluid out. Coincidentally, this is the same way that toilet flushing works! Pulling the handle releases extra water into the bowl that raises the fluid level higher than the highest point in a U-bend. That establishes a siphon, which (provided nothing has clogged the pipe), empties the toilet bowl. (Video credit: Periodic Videos)