1. leverage

3. buoyancy

4. The screw pump

5. Archimedes (287 B.C. – 212 B.C.)

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

9. Eureka!  Q: What did the king want?  The biggest crown.

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

11. 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).

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

13. 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.

14. 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.

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

16. 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.

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

18. 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?”

19. 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.)

20. 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.

21. Eureka!  Where did he come up with the solution?  In the bathtub.

22. 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

23. 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

24. Eureka!  What did Archimedes holler when the solution dawned on him?  Eureka!  Eureka! ”

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

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

27. Eureka!  intelligent  observant  prudent (cautious)  persevering (determined)  diplomatic (sophisticated)

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