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leverage

leverage. buoyancy. The screw pump. Archimedes (287 B.C. – 212 B.C.). Eureka!. Characters? King Hiero (308 B.C. – 215 B.C.) The goldsmith Archimedes (287 B.C.-212 B.C.) Place: The Kingdom of Syracuse. Eureka!. Q: What did the king want? The biggest crown. Eureka!.

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leverage

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  1. leverage

  2. buoyancy

  3. The screw pump

  4. Archimedes (287 B.C. – 212 B.C.)

  5. Eureka! • Characters? • King Hiero (308 B.C. – 215 B.C.) • The goldsmith • Archimedes (287 B.C.-212 B.C.) • Place: • The Kingdom of Syracuse

  6. Eureka! • Q: What did the king want? • The biggest crown.

  7. Eureka! • Q: Why did he want the biggest crown? • Because the country he reigned over was too small. • vs.

  8. Eureka! • Q: “Be sure that you put into it every grain of the gold I give you, and do not mix any other metal with it.” • Why did the king give the goldsmith this reminder? • He was careful about every grain he had (maybe because of the size of the country).

  9. Eureka! • Q: How many days did it take the goldsmith to fashion the bling bling gold crown? • Ninety days.

  10. Eureka! • Q: “When King Hiero put it on his head, it felt very uncomfortable, but he did not mind that—he was sure that no other king had so fine a headpiece.” • He could ignore the practical things just to get the biggest crown in the world. Vanity overtook him.

  11. Eureka! • Q: One move showed King Hiero was practical. What was that? • He put the crown on a scale to see if it was exactly ten pounds.

  12. Eureka! • Q: Why did the king invite Archimedes into the palace? • To admire the crown, not to judge the crown!

  13. Eureka! • What was Archimedes’ observation? • The gold was a brilliant yellow, rather than the same rich red color that it had been in the lump. • vs.

  14. Eureka! • Q: Did he say that the crown was a fake? • No! • Q: Why not? • That might annoy the king and threatened his life.

  15. Eureka! • Q: How did he express his doubts? • He showed his concern. “What if the goldsmith has kept out a pound or two of the gold and made up the weight by adding brass or silver?”

  16. Eureka! • Q: Why did the king respond to Archimedes by saying “The gold has merely changed its color in the working.” • He justified the goldsmith. (In a sense, he was defending himself.)

  17. Eureka! • Q: What was the difficulty for Archimedes to prove whether the crown was made of pure gold? • To test the purity of gold in the crown without damaging it.

  18. Eureka! • Where did he come up with the solution? • In the bathtub.

  19. Eureka! • Q: What was the solution? • “Since gold is much heavier(has higher density) than silver, 10 pounds of pure gold will not make so great a bulk (the volume) that 7 pounds of gold, mixed with 3 pounds of silver.” • 10 pounds ＜7 pounds of gold + of gold 3 pounds of silver

  20. Eureka! • In other words, the volume of 10 pounds of pure gold (in the crown) will be the same as that of 10 pounds of pure gold (in the lump). • 10 pounds of 10 pounds of • pure gold = pure gold • in the crown in the lump

  21. Eureka! • What did Archimedes holler when the solution dawned on him? • Eureka! • Eureka! • Eureka!”

  22. Eureka! • Q: What happened to the goldsmith in the end? • He was proved guilty (and might be beheaded).

  23. Eureka! • Now, please give as many adjectives as you can to describe Archimedes’ characteristics.

  24. Eureka! • intelligent • observant • prudent (cautious) • persevering (determined) • diplomatic (sophisticated)

  25. Eureka! • Oral Practice: • Have you even been faced with a difficulty/problem which seemed insolvable? How did you deal with it?

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