The Greedy Cup
The Greek philosopher Pythagoras is credited with changing the history of mathematics, ushering in an entire school of thought around numbers which still holds today. Most of what we know about him comes from the writings of his students, as he didn’t publish much of anything himself, so it’s hard to say definitively which works are actually his and which things are misattributed. Still, most experts consider him a father of modern mathematics, and his name is known around the world. That’s because of his most well known achievement — the formula now known as the Pythagorean Theorem — is taught at to math students nearly everywhere and at a relatively early age. When it comes to right triangles, a^2+b^2=c^2. (Here’s a neat animated gif demonstrating the theorem.)
But there’s something else Pythagoras is credited with — something less well-known and, if you’re a middle school student, a lot less practical: a cup which fought against excessive drinking.
If you want to get people to drink less, you can simply provide smaller cups. But Pythagoras wanted to go a bit further. He probably believed in the Greek principle of sophrosyne, the concept that moderation, self-control, etc. were necessary elements for a successful life. That may better be served by something more drastic — a cup which punishes people who try and drink too much.
As seen in the image above, the cup — called the Pythagorean Cup or the Greedy Cup — looks like a regular wine cup from the outside. But inside, you’ll see, there’s something sticking up from the center.
That central shaft is hiding a secret — a hole at the bottom of the cup. That hole is the opening to a pipe which runs up the center, which opens again near the top of the shaft. Running parallel to that pipe is a smaller pipe, running to the bottom of the cup’s basin, where there’s another opening. Combined, the two pipes create an upside-down J-shaped pathway for the liquid — at times, one which acts as escape out the bottom. But not always. The hidden piping system only kicks into action if too much wine (or whatever you drink) is in your cup. The image below of the cup’s cross-section, via Wikipedia, is instructive:
In image B, the wine isn’t quite at the level of the shaft, and, therefore, the wine inside the piping section hasn’t flowed over into the longer of the two pipes. As long as you don’t put any more in your cup than that, you’re fine — you can drink to your heart’s content. But cross that point of no return, as seen in image C, and the pipes act as a siphon, draining the entire cup — likely at the expense of your meal or, perhaps worse, your pants. Which is exactly the point.
If you want to see the cup in action, there’s a short video, here (from which those top two images come), showing the cup in action.
From the Archives: A Dog’s Life: The bonus fact is about the Pythagorean Theorem.
Related: A set of fancy Pythagorean Cups.