Eureka! How Archimedes Inspired Us

What does the word mean

Saying you had a “Eureka moment” means a solution arrived all at once, like a flash of inspiration, after wrestling with a hard problem — the phrase carries surprise, joy, and satisfaction all at once. Grammatically, the word “Eureka” (εὕρηκα) is the past tense of the ancient Greek verb “εὑρίσκω,” which means “to find,” and therefore the expression means “I found [it]!”

Who said Eureka!

This historical interjection is attributed to the brilliant mathematician and scientist Archimedes (c. 287–212 BC), who was born and worked in Syracuse, on the Greek-colonized island of Sicily. The story of this event is as follows. Hieron II [(308-215 BC), tyrant of Syracuse (270-215 BC)] asked him to check if the goldsmiths to whom he had ordered a heavy votive crown made of gold had adulterated the precious metal, and therefore deceived the ruler and his court.

The oldest surviving account of the story comes from the Roman architect Vitruvius, writing roughly two centuries later, who records that Hiero, having gained royal power in Syracuse, had contracted for a votive crown of gold at a fixed weight, and that when word reached him that the goldsmith had secretly swapped in silver, he asked Archimedes to look into it without damaging the crown.

It is rumored that Archimedes, while enjoying his bath one day, noticed that the more his body sank in the bathtub, the higher the water level rose. So, he discovered the principle of displacement, but at the same time he realized that he could measure the volume of the crown and the density of its materials.

Just like the water spilled over the edge when he entered his bathtub, the water in a glass will spill over when ice cubes are added to it. If the water that spilled out was weighed (weight is a downward force), it would equal the upward (buoyant) force on the object. From the buoyant force, the volume or average density of the object can be determined.

Archimedes’ principle

Archimedes was able to determine that the crown was not pure gold due to the volume of the displaced water, because even though the weight of the crown was identical to the weight of the gold that the king gave the crown maker, the volume was different due the various densities of the metals.

Delighted with his discovery and as a typical abstract scientist, he jumped out of the bathtub and came out naked on the street shouting “Eureka, Eureka!”, meaning “I found [it], I found [it]!”

The principle didn’t stay in the bathtub. The same displacement math is why a steel ship floats despite weighing hundreds of tons, why submarines can sink and surface on command by changing how much water they displace, and why a hydrometer can tell you the alcohol content of wine just by how deep it sits in the liquid.

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