Pythagorean Cup – The clever mischievous cup !

The first thing which comes into my mind – A must do prank ! 😛

A Pythagorean Cup OR a Greedy Cup is a form  of a drinking cup which forces its user to consume less alcohol. It allows the user to fill the cup with wine, alcohol or any other liquid up to a certain level. If the user fills only up to this level, one can enjoy his drink in peace.
But if adds more of it by filling it more than the certain limit , the cup spills its entire content out of the bottom (onto the lap of a greedy drinker).

The Pythagorean cup was designed by Pythagoras (570 BC – 495 BC); an Ionian Greek philosopher & a great mathematician.

It is the same Pythagoras, we know one for the Pythagoras theorem which states,

For a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two lesser sides


Image showing the central column & the hole at the bottom.

The Pythagorean Cup looks like a normal cup except the central column in it. The column is placed over the small open pipe which leads to the spilling of the liquid through the hole.

The parts of the image(below):

A –
Simple cross section of the cup.

The 4 cases of a Pythagorean cup !

The 4 cases of a Pythagorean cup !

B –
The cup functions normal as the other cups as long as the level of the liquid doesn’t rise beyond the level of the column. Also the liquid rises into the smaller tube inside the column following Pascal’s principle of communicating vessels.

Principle of communicating vessels !

Principle of communicating vessels !

C –
Now if the level rises further, the liquid spills through the column into the tube and out of the bottom because adding more liquid to the cup adds extra pressure to the liquid into the smaller tube to rise upward & then gravity does the work of spilling it.

D –
It is a bit tricky to explain that how the whole liquid gets spilled down. Well, what happens is the weight of the liquid falling through the lower portion of the tube at the base of the glass reduces the pressure at the upper portion of the tube, allowing water to be pushed into the tube by the weight of the water remaining in the glass.

However you can prevent the spilling, by first pouring a heavy density liquid & then the liquid which we want to drink. In this case, the weight of the water is not enough to push the liquid up through the tube.

Here’s a video demonstration on the Pythagorean cup & also shows how can we prevent it by adding a high density fluid, here – Mercury, first.

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  1. its too gud…

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