Archimedes and the Crown

You remember Archimedes, right? Every schoolchild learns that he's the guy who leapt out of the public bath and ran through the streets shouting Eureka! Supposedly that's because he had figured out a way to tell if the king's crown was pure gold, or had been doped with less-valuable silver by an unscrupulous goldsmith.

I probably heard this story in junior high, and since I considered myself a genius (this is before I took Calculus of Variations), I figured that I too would have figured out the method that was suggested as Archimedes process of detection, viz, to fill up a bowl with water and see how much overflowed when the crown was placed in it. Do the same with the same weight of gold, and compare the two.

I confess that it did bother me a bit wondering how to measure the water accurately, but I never really gave it much thought. Until now. I came across a website that shows that the bowl method just wouldn't work, and also suggests that Archimedes was more clever than that. Before clicking on the link, see if you can figure out how to do a better job of comparing the crown to an identical weight in pure gold. It's pretty cool.