Cut-through illustration of a Pythagorean cup.

A Pythagorean cup (also known as a Pythagoras cup) is a form of drinking cup which forces its user to imbibe only in moderation. Credited to Pythagoras of Samos, it allows the user to fill the cup with wine (a popular beverage in Pythagoras' time) up to a certain level. If the user fills the cup only up to that level he may enjoy his drink in peace. If he exhibits gluttony however, the cup spills its contents out the bottom (the intention being: onto the lap of the immodest drinker).

Form and function

A Pythagorean cup looks exactly like a normal drinking cup, except that the bowl has a central column in it – giving it a shape not unlike a Bundt pan. The central column of the bowl is positioned directly over the stem of the cup and over the hole at the bottom of the stem. A small, open pipe runs from this hole almost to the top of the central column, where there is an open chamber. The chamber is connected by a second pipe to the bottom of the central column, where a hole in the column exposes the pipe to (the contents of) the bowl of the cup.

When the cup is filled, liquid rises through the second pipe up to the chamber at the top of the central column, following Pascal's principle of communicating vessels. As long as the level of the liquid does not rise beyond the level of the chamber, the cup functions as normal. If the level rises further however, the liquid spills through the chamber into the first pipe and out the bottom. Hydrostatic pressure then creates a siphon through the central column causing the entire contents of the cup to be emptied through the hole at the bottom of the stem.

Common occurrences

The Pythagorean cup is credited as an invention to Pythagoras. For this reason, it is sold often on the Greek island of Samos as a tourist souvenir. It is also sold in some toy stores as a practical joke gift.

Weblinks

• http://www.grand-illusions.com/toycollection/pythagoras_cup Video from a Pythagorean cup

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