Regardless of how comfortable you are with math, you’ve probably heard of Pythagoras – or at the very least, the Pythagorean Theorem that bears his name. 

But if that’s all you know about the ancient Greek philosopher, you’re missing out. Firstly, because Pythagoras was not, in fact, the first guy to come up with a2 + b2 = c2 – he was much more of a numerologist than a mathematician in any case – but mostly because all the other things he actually spent his time doing were, frankly, way more interesting than some little equation.

What is the Pythagorean cup?

It might seem at odds with the popular image of Pythagoras as a serious, be-toga-ed philosopher, but, when he wasn’t coming up with strange theories about beans and musical stars and planets, he appears to have been something of a prankster. 

How do we know? Because of the Pythagorean cup – a practical joke item designed, legend has it, by Pythagoras himself. The idea behind it: to teach a karmic lesson to those greedy drinkers who poured themselves too much wine.

Now, to be fair, there’s really no evidence that Pythagoras himself came up with the invention – and the earliest examples we have of actual Pythagorean cups date from the fourth century CE, around a millennium after the philosopher’s lifetime. But it’s become associated with the ancient thinker through popular imagination, with the story going that it was invented to remind his followers to drink only in moderation.

At first glance, the Pythagorean cup looks more or less like a normal drinking vessel – albeit one with a strange kind of central hump inside it, like a smaller version of a bundt cake tin. And in fact, so long as you don’t try to put too much liquid inside, that’s basically what it is: just a kind of funny-looking cup.

The punchline to the prank only shows up when you try to pour too much into it. Fill the cup past a certain point, and the liquid inside will start to drain out through the vessel’s stem – presumably ruining your himation or chiton with wine stains in the process. 

How does the Pythagorean cup work?

To understand what’s going on, let’s take a look at the precise design of the cup. The trick, unsurprisingly, is all thanks to that weird bump in the middle: it’s not just a strange aesthetic choice, but a sneaky siphon, hiding an open channel to let all the liquid out through the stem of the cup.

But it’s not as simple as “put liquid in and it will pour out again” – the Pythagorean cup is particularly tricksy, only kicking into action once you pour too much of your preferred libation into it. So how does that work?

Well, while it may have been invented multiple millennia ago, the idea behind this ancient prank is surprisingly sophisticated. In modern engineering terms, it comes down to a principle called Pascal’s Theorem of Communicating Vessels – a physical law stating that when liquid is poured into two or more connected vessels, they will come to equilibrium at the same height.

That might sound complex, but it’s really just common sense: imagine two containers, connected by a tube – if you pour water into one side, it will eventually flow through the connector into the other. When you stop pouring, the amount of liquid in both sides will be equal. 

The Pythagorean cup works exactly the same way. As the main cavity fills up, so too does the beginning of the pipe that eventually threads through the vessel’s stem – but only to the same level as the drink poured in so far. 

Once you go past that point, however, the liquid will overflow into the stem itself – and this is where the Theorem of Communicating Vessels goes from “physics law” to “prank war”. Suddenly, there’s a “second vessel” connected to the first, just waiting for all the liquid in the cup to siphon out until the levels reach that equilibrium.

Unfortunately, that second vessel is, well, the entire world – meaning that all that precious wine or mead you were hoping to guzzle down is just going to continue disappearing until the cup is completely empty.

Modern Pythagorean cups

While your dad may be right that “they don’t make ‘em like they used to”, it probably takes a little more than a sneaky cup to get an audience laughing their asses off these days. That may be why modern Pythagorean cups – or other devices based on the same ideas – tend to be less “practical jokes” and more “fun science experiments to help explain everyday concepts.”

So, for example, there are a plethora of YouTube tutorials out there teaching you how to make your own Pythagorean cup – ranging from clear demonstrations of the physical laws at work to intricate recreations of the device on a pottery wheel. 

If that’s too much effort for you, you can always just take a little trip to your bathroom, where you’ve been sitting on your very own Pythagorean cup for years. Literally – the exact same principles behind the prank are what keeps your flushing toilet from overflowing.

In fact, modern physics and engineering techniques haven’t just reused the idea for everyday marvels like sanitation. Never let it be said that scientists don’t have a sense of humor: there are plenty of ever-more ingenious versions of the device out there, designed and created by engineers riffing on this ancient prank presumably just for the fun of it.

Take the “devious Pythagorean cup”, for example. Designed by US Naval Research Laboratory postdoctoral research associate John Steuben and posted to Thingiverse in 2013, it takes the original invention and makes it even sneakier: no more can you rely on the appearance of a great big bump in the middle of your goblet to clue you in to your soon-to-be-pranked status – the modern descendent of the Pythagoras cup looks just like a normal goblet. 

You know – right up until your drink starts disappearing.