Make Your Own Pythagorean Cup

By Dave Richeson

My parents recently went to Greece. They brought me back a souvenir—a practical joke cup called a “Pythagorean cup.” The legend behind the cup is that Pythagoras or one of the Pythagoreans invented this cup to prevent gluttony. The vessel looks like a cup with an odd pillar in the center. When you fill it up, it holds the liquid as expected. But when it gets too full, all the liquid drains out through a hole in the base.

The key to the trick is that there is a hole at the bottom of the post that leads to a pipe that runs up through the post and down through the base of the cup. As the cup fills, so does the pipe. When the liquid gets to the top, it flows down the pipe and gravity does the rest. The pipe acts as a siphon much as the plumbing does in a modern toilet.

Credit: Nevit Dilmen

Here’s a video of me using the cup and me using a Pythagorean cup that I made.

To make the cup, I pushed a bendy straw through the bottom of a styrofoam cup. It was bent over on the inside so that the opening of the straw was at the base of the cup. (I also put a bead of clue around the hole in the cup so that the liquid wouldn’t leak out around the straw.) It worked beautifully!

If I were a talented potter or had any skills in designing objects for a 3D printer, I’d make a mug with the tube running through the handle. Here’s what I have in mind. If any of you make one, send me a photo—or better, a video—or better still, the real thing!

As for the name “Pythagorean cup”: Do any math/physics/Greek historians have information about the history of this cup? Based on nothing but a gut feeling, I highly doubt this was created by Pythagoras. But I’d definitely be interested in learning the source of this attribution.