Can Archimedes find out how the goldsmith tricked the king?

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1 Archimedes and the thieving goldsmith: Can Archimedes find out how the goldsmith tricked the king? Archimedes Part I: The plot is set. We have a king, a crown, and a sneaky goldsmith. (Missing-Still to come!) Archimedes Part II: Gold has been stolen, the king needs help! When the goldsmith left, he was sure there was no way that he could be caught and punished for his sin. The king paced the floor. Back and forth he went. "I'm sure he cheated me out of gold, but how can I prove it?" He weighed the crown again. The weight was the same as the piece of gold he gave the goldsmith. "Eureka, he said, "I've got it! If anyone can figure it out it's my cousin Archimedes. Yes, he's a little crazy, but boy he sure is smart. Servants, servants!" he shouted. "Go to my cousin Archimedes and bring him here right now!" "Yes, your majesty," they said. They ran to the home of Archimedes, and knocked on the door. "Archimedes!" they shouted. "The king calls for you. What do you want?" he said. "The king thinks that the goldsmith cheated him and he can't figure out how he did it." "Oh, don't bother me; can't you see I'm busy thinking? Besides, the king always thinks someone is cheating him. I'm not going. I'm too busy thinking. I'm trying to figure out why wood floats on water and why iron sinks to the bottom, but if I change the shape into a boat it floats. Tell the king I can't be bothered to come, I'm just too busy." The servants ran back to the king and told him Archimedes refused to come. The king got angry and said to go get Archimedes. He said not to kill or even hurt him, because he was too valuable. They were to pick him up and bring him whether he wants to come or not. When the servants

2 told Archimedes what the king said, he was angry to be disturbed from his thinking, but decided to go to the king. The king told Archimedes the whole story. "I gave the goldsmith a piece of gold that weighed 4.2 lbs. I weighed it in front of him so he would know I would weigh it again when he returned the crown. Here is the crown he made. Beautiful isn't it? Look, it weighs exactly the same as the lump of gold I gave him." Archimedes said, "Then what's your complaint? It weighs the same." "Oh Cousin Archimedes, somehow I know he cheated me but I can't figure out how he did it. I just know he is laughing at how he cheated me, and I can't figure out how he did it. Archimedes, here is the crown. I can't figure it out, but you're so smart. I'm sure you could figure it out, said the king. "My cousin, O King, why do you always think someone is cheating you?" said Archimedes. "The reason, Archimedes, I think someone is always trying to cheat me is because everybody is always trying to cheat me! Archimedes, you figure it out or I will cut your salary in half, and when I find out how he cheated me I will cut him in half!" What do you think? Now, we know how the goldsmith cheated the king. You ll remember that the goldsmith took a cubic inch of gold and replaced it with almost two cubic inches of silver. The king suspects he was cheated, but can't prove it. Archimedes is very intelligent, but is he smart enough to find out how the goldsmith was cheating the king? Archimedes Part III: Can Archimedes solve the problem? Archimedes went home with the piece of gold and the gold crown. He thought to himself, "How can I find out if the goldsmith cheated my cousin, the king?" he put the crown and the gold on a shelf. He thought a little, but couldn't solve the problem. He thought, "The king always thinks someone is cheating him. He thinks I'm crazy, but maybe the problem is he's crazy. I've got too many things to think about!" He began to think.

3 "Why does wood float on water? Why does a piece of iron sink to the bottom of water? Why, when I take the same piece of metal and change the shape into a ship, does it float?" Then Archimedes thought, "You know, I did hear the goldsmith was a crook, maybe he did cheat the king, but how did he do it? The crown weighs the same as the piece of gold." Archimedes really thought about it. When Archimedes began to think, he just sat with his head in his hands and a far away look in his eyes. "How can I find out? He thought and thought while hours went by, then days, then even a week went by, and he just thought. When you think and think for a long time and don't wash or bathe you begin to stink. Remember, it's great to think, but you also need to take a bath once in a while! The house began to stink because all Archimedes did was think. Finally the servants picked up Archimedes and carried him to the public baths. In those days people did not take a bath at home. You went to the public baths. The servants of Archimedes filled the bathtub too high and the water went up to the brim. They gently lowered Archimedes into the bathtub. It was filled to the brim. What happens when you fill the bathtub to the brim and then slip in? That's right, water spills over the top and your mom gets angry because the floor is all wet! When Archimedes was placed into the tub, the same thing happened. His body displaced the water and the water level rose up and over the top of the tub. When Archimedes saw that his eyes lit up and he shouted, "Eureka, I've got it, I've got it! I know how to find out if the goldsmith is a thief." He jumped out of the tub and began to run home shouting, "Eureka, eureka, I got it, I got it!" Can you see him running through the streets with no clothes on, with his servants running after him carrying his clothes shouting, "Master, master, your clothes, your clothes, put on your clothes!" The more they yelled, the faster he ran. I told you Archimedes was a little strange! He ran into his house, took down the gold and the golden crown, and again said, "Eureka, eureka, I've got it now, I can figure out if the king is correct, and if the goldsmith is a thief." Now just what did Archimedes learn in the bathtub that would help him solve the problem? Taking a bath will keep you from stinking, but how does it solve the problem of whether the goldsmith was a thief, or that the king mistaken?

4 Archimedes Part IV: The solution. Now, taking a bath will help you keep clean. It would prevent Archimedes from stinking and stinking while he was thinking and thinking, but how would Archimedes taking a bath help him find out if the goldsmith was a thief? Archimedes took a small bowl and a large bowl. He placed a scale on the counter (you know that a scale is used to weigh things), and Archimedes put a small bowl into a large bowl. He filled the small bowl up to the brim with water. He weighed the piece of gold and what he thought was a pure gold crown. They weighed the same! We know that the goldsmith had removed one cubic inch of gold and replaced it with two cubic inches of silver. Now instead of having a total of six cubic inches of gold, we have a crown made of five cubic inches of gold and two cubic inches of silver for a total of seven cubic inches. We know that seven cubic inches of the combination of silver and gold weighs the same as six cubic inches of pure gold, but the king and Archimedes don't know it. How did they find out? Archimedes took the six cubic inches of gold and gently put it into the small bowl filled with water. The water overflowed and ran into the outer bowl. Six cubic inches of water ran over the top into the outer bowl. He weighed the water and recorded it. He poured the water into a jar that measured volume in cubic inches. The jar said that the water's volume was six cubic inches. That is the same volume as the lump of gold. Archimedes now put the small bowl into the large bowl. He filled the small bowl with water just as before, to the brim. He put the crown in, remember the thieving goldsmith made the crown with a total of seven cubic inches of gold and silver. When the six cubic inch of gold and silver did not weigh enough, the goldsmith added another cubic inch of silver to make the weight right. The total volume was then seven cubic inches instead of six. When Archimedes put the crown that was seven cubic inches in volume in the small bowl, seven cubic inches of water flowed over the brim into the outer bowl. Archimedes compared how much water overflowed with the gold and how much overflowed with the crown. They didn't match up! The goldsmith had only received six cubic inches of gold. There was an extra cubic inch of something in the crown. Where did the extra cubic inch displaced by the crown come from? The weight was right, but the volume was wrong. It was seven cubic inches instead of six. When Archimedes put the seven

5 cubic inch crown into the water, seven cubic inches of water flowed over the top. Not six as before. Archimedes took the seven cubic inches of water and weighed it. It weighed too much for six cubic inches. Archimedes wondered why. So Archimedes poured the water into a jar used for measuring volume. It measured seven cubic inches. The goldsmith thought he was so smart that he could get away with lying, stealing, and sinning, but all he did was cook his own goose. Be sure your sin will find you out. What happened to the goldsmith, I really don't know. He committed his sin in secret, but now his thievery was no longer a secret. It was shouted from the rooftop and no one ever again trusted him to make jewelry. But was Archimedes so smart after all? He discovered the secret of water displacement by accident. Archimedes Part V: The conclusion Archimedes was a genius, even if he did discover density and water displacement by accident. (You can learn much more about Archimedes by reading the book Archimedes and the Door of Science by Jeanne Bendick from Bethlehem Books). How many bathtubs overflowed before Archimedes realized the scientific principle involved? Many people see things, but really see nothing. A friend of Archimedes, Eratosthenes, saw the reflection of the sun in a deep well. He saw the shadow of a building cast by the sun. He measured the angle of the shadow cast. He measured the distance between the well and the building and calculated the distance around the earth within 100 miles. He did this about 2,200 years ago. Many people see, but it is only a genius that realizes what he sees and acts upon it. Mr. Carrier in about 1900 made a device to reduce the water in the air during hot summer days. He did this so that printer ink would dry faster. By accident he discovered the room also cooled off and so today we have air conditioners, refrigerators, and freezers. Mr. Carrier was a genius because he not only saw something, but he realized what it could be. Lord Fleming, around 1940, saw a dish with different germs on it. Surrounding, he saw circles within which all germs had died. By accident he discovered Penicillin, the first antibiotic. In so doing he saved the lives of billions of people. Lord Fleming saw with his eyes, but the genius of

6 his brain realized what he had seen. Interestingly enough, Lord Fleming said, "My most important discovery was finding that I was a sinner and needed a Savior." How many people do you think have seen an apple fall from a tree? Isaac Newton saw an apple fall and thought, "Why does the apple fall down and not up?" Everyone else saw just an apple falling, but Newton asked why. While we really still don't understand gravity, we understand a lot about it. Without gravity we would have no air to breathe; no soil to grow food; and no ocean, lakes, or rivers. We still don't understand an awful lot about gravity. However we have learned a great deal all because one devout Christian, Isaac Newton, saw something millions of people had seen, but never proceeded to ask why. The genius of Archimedes, Lord Fleming, Isaac Newton and others is that they see something, and then question why it is.

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