Eureka
lit. “I have found it”
Archimedes' shouted exclamation on discovering, in his bathtub, that the volume of an irregular object can be measured by how much water it displaces.
Origin
Around 250 BCE, Hiero II of Syracuse asked Archimedes to determine whether a goldsmith had adulterated his crown with silver, without melting the crown down. Archimedes is said to have spotted the answer while stepping into a bath and seeing the water rise: any object displaces a volume of water equal to its own. Density (mass per volume) would then expose any silver-for-gold substitution. He reportedly ran naked through Syracuse shouting 'εὕρηκα!' — heúrēka — 'I have found it!' The story is almost certainly embellished, but the displacement principle is real and is Archimedes' work.
Modern usage
The default English word for the moment of discovery — 'eureka moment,' 'I had a eureka,' 'eureka!' The cartoon lightbulb over the head is the visual version. Used both sincerely for breakthroughs and ironically for mundane realizations.
In the wild
After three hours of debugging, I had a eureka moment in the shower.— common usage
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