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Figure of the month: 250

News Arnulf Hinkel, financial journalist – 01.07.2024

It was around 250 BC when Hieron II, king of Syracuse until 215, suspected his court jeweller of fraud: he had made a gold crown dedicated to the gods on behalf of the king, and Hieron II alleged that the jeweller had kept some of the provided gold for himself, instead producing the crown from a gold alloy of a lower purity than stipulated. But how could the authenticity of the crown be verified without damaging it? Hieron II entrusted this task to a young mathematician and physicist with a reputation for genius: Archimedes.

It all started with a bath: Archimedes’ principle

Historians still argue about whether the well-known anecdote about how Archimedes solved the problem of checking the authenticity of the gold crown really happened. During an extended visit to a bathtub, quite common for Archimedes, the scientist allegedly noticed how the water level dropped when he emerged from the tub. Exclaiming the now-famous “Eureka!”, he rushed, naked as the day he was born, to his place of work to capture his flash of inspiration and continue his studies. On that day, Archimedes discovered the Archimedean principle, which states that the upward  buoyant force that is exerted on a body immersed in fluid is equal to the weight of the fluid displaced by the body.

Principle still used today to determine purity of gold

In practice, Archimedes’ principle is applied by immersing an object – in this case gold – because the resulting water displacement determines the density of the object under investigation. This both ingenious and simple method enabled Archimedes to calculate the specific weight of any substance. That of gold of the highest purity is 19.3 g/cm3. To this day, the method is used not only for authenticity testing, but also to determine the purity of gold. Incidentally, examination of the gold crown revealed that the court jeweller had indeed cheated. The crown displaced more water than the gold bar of the same weight which served as a comparison for the test.
 

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