I understand that Archimedes’ Principle used the displacement of fluid to determine an object’s mass and therefore proved whether the king’s gold crown was an alloy. But why was this so significant in the long term?

In: Physics

It lets you work out how to make boats out of metal, so that was pretty significant. Actually just boat design in general benefited a lot from a mathematical formula showing how/why things float.

My understanding of this was somewhat different to yours.

The first point I have is that I though the Archimedes Principle was: “An object receives an upthrust equal to the weight of the fluid displaced” which has many implications in nautical engineering for obvious reasons.

The problem you’re referring to did not measure the mass of a crown, this was very simple as the Greeks had scales so the mass was easily measured. Instead it measured the volume of the crown which by the method you spoke about. This had massive significance since the Greeks couldn’t measure the volume of irregular objects (such as the crown).

Interestingly, this method is still one way we use to measure the volume of irregular objects!

It was a creative solution to a problem that many people at the time thought didn’t have a solution. And it kept being the solution for these kinds of problems for around two-thousand years.