The Pythagorean cup is a vessel that spills all the drink poured into it once a person gets greedy. And what does that mean? Say you were supposed to pour a liter of water into a cup and no more than that. If you were using the Pythagorean cup, what happens is very interesting. Nothing special happens when you pour just the amount of water required into the cup but if you decide to add just a little bit more, the whole drink spills from the cup and you will be left with nothing.
The Pythagorean Cup [Image source: Pythagorean Cup]
The Pythagorean cup looks like an ordinary cup, but it has one very fundamental distinction. There is a column in the middle of the cup which serves the purpose of spilling the drink when a person is too greedy.
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The cup works by utilizing Pascal’s principle of communicating vessels. The principle basically states that when we have a set of connected containers with a certain liquid inside them, the level of the liquid in all the containers will always be the same. Now let us have a look at the Pythagorean cup and see how this all makes sense.
A cross section of the Pythagorean cup [Image Source: Wikipedia]
As we can see, when we initially put water into the cup, it behaves exactly the way an ordinary cup would and the water rises through the second pipe. However, when water is over-poured, the water in the first (shorter) pipe now passes over to the second (longer) pipe, creating a siphon. This siphon makes the water in the cup drain through the first pipe till there is nothing left in the cup.
A cross section of the Pythagorean cup after being filled [Image Source: Wikipedia]