The king suspected that the goldsmith had cheated him. The king thought the goldsmith had mixed some of the gold for the cheaper silver, while keeping the leftover gold. However, the king had no way of proving his suspicions, so he asked Archimedes to find out whether the crown was made from pure gold, without damaging the crown.
He told the king he would need a few days to think about it. One day, while he was concentrating about this problem, he decided to take a bath in a tub full of water. He immediately noticed that the water splashed out of his bath tub onto the floor the moment he stepped into it, and the more he stepped into the tub, even more water got displaced out of the tub. He realized that he had made a real mess. Archimedes questioned- what if he put the crown in water? How much water would it displace?
And could he apply this to prove that the crown was made of pure gold? Archimedes already knew that gold was denser than silver. He first took a piece of gold and a piece of silver with exactly the same mass. He dropped the gold into a bowl filled to the brim with water and measured the volume of water that spilled out. Then he did the same thing with the piece of silver.
Although both metals had the same mass, the silver had a larger volume; therefore, it displaced more water than did the gold. So he realized that if a certain amount of silver had been substituted for the same amount of gold, the crown would occupy a larger space compared to an identical amount of pure gold. He then reasoned that if the goldsmith had had indeed made a crown of pure gold, then the volume displaced should be the same as that of a bar of pure gold of the same mass.
See an animation here. Now it was time to check out the crown. Then he took a bar of pure gold of the same mass and compared the volume of spilled water to determine if crown is indeed made of pure gold. Surprise, surprise — the numbers were different! The crown displaced more water than the piece of gold. Trading vessels from Egypt, Greece and Phoenicia filled the city-state's harbor. It was also a hub of commerce, art and science , according to the Archimedes Palimpsest.
After studying geometry and astronomy in Alexandria, the "greatest intellectual center in the ancient world," according to Scientific American, Archimedes settled down in Syracuse to pursue a life of thought and invention. One of his inventions was the Archimedes screw. This device uses a corkscrew with a hollow tube. When the screw turns, water is pulled up the tube.
It was originally used to empty sea water from a ship's hull. It is still used today as a method of irrigation in developing countries, according to the Archimedes Palimpsest. Archimedes famously said, "Give me a lever and a place to stand, and I'll move the world. Archimedes realized that in order to accomplish the same amount or work, one could make a trade-off between force and distance using a lever. His Law of the Lever states, "Magnitudes are in equilibrium at distances reciprocally proportional to their weights," according to "Archimedes in the 21st Century," a virtual book by Chris Rorres at New York University.
Archimedes also devised defenses for Syracuse against invading armies. He strengthened the walls of Syracuse and constructed war machines. His works held off the Romans for two years. However, in B. Marcellus had respect for Archimedes and sent soldiers to get him so he could meet the famous mathematician. According to the Archimedes Palimpsest, he was so focused on solving a mathematical problem that he did not know the Romans had stormed the city.
When a soldier told him to accompany him to see the general, Archimedes told him to go away. The enraged soldier struck him down. Marcellus ordered that Archimedes be buried with honors. Kenchikusho in Japanese, trans. Morita Keiichi. Google Scholar. Galileo Galilei. The Little Balance in Japanese, trans. Toshiyuki Fujita.
Skaino-Meicho, , 36—41 Original work published Archimedes Homepage by Prof. Chris Rorres of Drexel University. Encyclopaedia Britannica Inc. The New Encyclopaedia Britannica. Encyclopaedia Britannica, Kuroki H. Amsterdam: Springer, , — Heath T L. The Works of Archimedes.
Cambridge: Cambridge University Press, , — Download references.
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