#MakeAmericaSmartAgain. Archimedes. Displacement. Boats. And the eureka moment.

Archimedes was a fascinating Greek scientist, engineer, inventor, and more who lived in the 300 b.c.e. range.  He understood mathematics, conceptuslized physics, and followed the movement of the stars. He found a means to calculate the area and of unusual shapes and worked to derive a value for pi. 

But there's one story that stands out, an anecdotal account about how he invented a method for determining the volume of an object with an irregular shape. 

King Hiero II asked for a crown made of gold, but he suspected that silver had replaced much of the gold inside the crown - and that the crown maker was a thief! 

Archimedes was asked to determine if this was true, without damaging the crown.  The obvious thing to do would be to melt it down into a regularly shaped body in order to calculate its density. But that was impossible. 

Inspiration struck him, as the story goes, as he was taking a bath.  He noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. 

Excited, he stood from the tub and ran naked through the streets yelling "Eureka!" Or "I have found it!"

What had he found?

In his assignment from the king, he realized that the submerged crown would displace an amount of water equal to its own volume. 

By dividing the mass (it's weight) of the crown by the volume of water displaced (i.e. How far the water moved up the tub), he would have the density of the crown. 

The density would be lower if cheaper and less dense metals had been added to the gold (and higher if it was all gold). 

The test was conducted, and he proved that silver had indeed been mixed in.  The crown maker was trying to pull a fast one and legend says the king had him executed. 

Now whether this story is entirely true is anyone's guess. But there is certainly some substance to it: Archimedes did discover and write about displacement of water as it relates to density. And the principle is still in use today. 

And his eureka moment extended further still. The principle is the reason a boat can stay bouyant. 

Of course boats don't actually float! The reason has everything to do with displacement of water. But it can be hard to wrap your head around. So here's a simple explanation that succinctly sums it up. 

http://www.boatsafe.com/kids/021598kidsques.htm

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