In 245 BC, in order to celebrate the grand Moon Festival, King Henon gave the goldsmith a piece of gold as a pure gold crown. Although the finished crown was as heavy as the previous gold, the king still suspected that the goldsmith had adulterated it. He ordered Archimedes to identify whether the crown was pure gold, but he was not allowed to destroy it. This seems an impossible thing. 、

Archimedes discovered buoyancy when taking a bath in a public bathroom, and through experiments with stones and wood blocks, it was proved that buoyancy was related to the displacement (volume) of the object, but not to the weight of the object. How heavy an object feels in water is bound to be related to the density of water (the mass of water per unit volume).

Archimedes found a solution to the king's problem here, and the key to the problem lies in density. If the crown contains other metals, its density will be different and the volume of the crown will be different under the same weight. Putting the crown and the same weight of gold into water, it was found that the crown discharged more water than gold, indicating that the crown was adulterated.

Extended data:

Archimedes discovered the principle of buoyancy, that is, the buoyancy of liquid to an object is equal to the gravity of the object displacing liquid. An important principle of hydrostatics points out that an object immersed in a static fluid is subjected to a buoyancy force, the magnitude of which is equal to the weight of the fluid displaced by the object, the direction is vertical and upward, and it passes through the center of mass of the displaced fluid. This conclusion was first put forward by Archimedes, so it is called Archimedes principle.

Reference: Baidu Encyclopedia-Archimedes Principle