Pythagorean cup
A drinking cup that empties itself when overfilled.
A Pythagorean cup—also called a Pythagoras cup, greedy cup, cup of justice, anti-greedy goblet, or Tantalus cup—is a drinking cup designed as a practical joke. If someone fills it past a certain level, a siphon mechanism empties the entire cup through its base. The device has been used to comment on greed.
The earliest surviving example is a silver Roman Tantalus cup from the late 4th century. Hero of Alexandria, writing in the 1st century, described a vessel with a siphon that drains when filled to a specific height. In the 9th century, the Banū Mūsā brothers included an identical mechanism in their *Book of Ingenious Devices*. Charles the Good bought such a cup in 1117, and a Tantalus cup from around 1200 was found in Zaporizhzhia Oblast. The 13th-century architect Villard de Honnecourt also depicted a trick cup that likely used a siphon. By the 16th century, these cups had reached Western Europe, and they were common in 18th- and 19th-century "cabinets of physics." A recent folk tradition links the cup's design to Pythagoras.
The cup looks ordinary but has a central column inside the bowl. This column sits directly over the stem and a hole at the stem's bottom. A small open pipe runs from that hole nearly to the top of the column, where there is an open chamber. A second pipe connects this chamber to the bottom of the column, with a hole exposing the pipe to the cup's contents. As liquid is poured in, it rises through the second pipe into the chamber, following Pascal's principle of communicating vessels. As long as the liquid stays below the chamber, the cup works normally. If it rises higher, liquid spills through the chamber into the first pipe and out the bottom. Gravity then creates a siphon through the central column, draining the entire cup.
The Pythagorean siphon has four chambers, with one central chamber for liquid to escape. As liquid fills the four chambers, pressure remains constant, so the liquid level stays the same in each. Once liquid reaches the top of the siphon, it begins to escape through the central chamber as gravity takes effect. Surface tension then forms a seal above the central chamber from the liquid in the two adjacent chambers. This seal prevents air from escaping through the central chamber, so the weight of the water in that chamber forces all remaining liquid out of the siphon.
Modern American flush toilets use the sam
- also_known_as
- Pythagoras cup, greedy cup, cup of justice, anti greedy goblet, Tantalus cup
- earliest_described_by
- Hero of Alexandria (1st century)
- earliest_surviving_example
- Silver Roman cup from the late 4th century
- mechanism_type
- Siphon
- modern_analogues
- Toilet flush, washing machine fabric softener tray
Lore & Background
Hero of Alexandria, in the 1st century, describes 'a vessel from which the contents flow when filled to a certain height', equipped with a siphon system. The earliest known surviving Tantalus cup is a silver Roman example from the late 4th century. The Banū Mūsā brothers, in the 9th century, included an identical mechanism in their Book of Ingenious Devices. Charles the Good purchased such a cup in 1117, and a Tantalus cup from around 1200 was discovered in Zaporizhzhia Oblast. Villard de Honnecourt, in the 13th century, also describes a trick cup of similar design, which may have had a siphon mechanism.
Reader's Guide
The Pythagorean cup is significant as an early example of a siphon-based practical joke device that also served as a moral statement about greed. Its design, described by Hero of Alexandria and later by the Banū Mūsā brothers, persisted through the medieval period, with examples purchased by Charles the Good and discovered in Ukraine. By the 16th century, such cups had been imported into Western Europe, and they were commonly included in 18th- and 19th-century 'cabinets of physics'. A recent folk tradition connects the cup's design to Pythagoras, though the article notes this connection is not historically verified. The cup's siphon mechanism is the same principle used in modern American flush toilets and the fabric softener tray in top-load washing machines, demonstrating its lasting influence on practical fluid dynamics.
Did You Know?
- The earliest known surviving Tantalus cup is a silver Roman example from the late 4th century.
- Charles the Good purchased a Pythagorean cup in 1117.
- A Tantalus cup from around 1200 was discovered in Zaporizhzhia Oblast.
- The cup's siphon mechanism is the same principle used in most modern American flush toilets.
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