Archimedes greatest dicovery
Archimedes's tale takes place some 2,200 years ago when King Hieron II of Syracuse in Sicily gave a jeweller a bar of gold and ordered him to make it into a crown. The king, however, suspected that the jeweller had substituted some of the gold for cheaper metal like silver, while pocketing the leftover gold.
The king had no way of proving his suspicions, so he asked Archimedes – a Greek mathematician, engineer, inventor, and astronomer – to find a definitive answer. Archimedes had spent a long time trying to figure out the answer, which came to him when he noticed how water would splash out of his bath tub the moment he stepped into it, and the more he stepped into the tub, even more water got displaced.
At the time, Archimedes had known that gold was denser than silver, so if a certain weight of silver had been substituted for the same weight of gold, the crown would occupy a larger space than an identical one of pure gold.
So to find the crown’s volume, all Archimedes had to do was essentially immerse the crown and exact measurement of pure gold in a tub filled with water to the brim, measure the spillage, and compare the volume of spillages – if the jeweller had indeed made a crown of pure gold the volume should be the same.
Archimedes was said to be so thrilled with this discovery that he immediately hopped out of the bath and ran onto the streets naked shouting 'Eureka!' 'Eureka!'.
And in case you were wondering, the jeweller was indeed cheating the king.
What probably happened
Archimedes's discovery was told by Vitruvius, a Roman architect, writer and engineer (smart people back then seemed to be doing everything) in a book written two centuries after Archimedes had died. Where Vitruvius got his sources from, he didn't say, but he did write about a scene where Archimedes was running out naked and wet, after he had leaped from his bath following that discovery.
Whether or not Archimedes used such a simple...