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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. Where is the center of balance on a spoon?

2. How long did Marcellus hold Syracuse in siege.

3. In what book did Archimedes give mathematicians a logical way to start any problem and an orderly way of setting things down?

4. What did Archimedes want on his tomb?

5. In how many books that Archimedes sent to his friends, did he make deliberate errors?

Short Essay Questions

1. What calculations did Archimedes use to show how numbers were infinite?

2. What practical joke did Archimedes play on his friends in Alexandria?

3. How did Archimedes figure the area of a circle?

4. How do mathematicians figure the area of a circle?

5. How do people know that some of Archimedes' writing have been lost?

6. Describe Marcellus' fleet that he sent to attack Syracuse.

7. Where is the earth's center of gravity?

8. What happened when a soldier came to bring Archimedes to Marcellus?

9. What did Marcellus do while he held Syracuse in siege?

10. What agreement did the Romans and Carthaginians make to divide the Mediterranean between themselves?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Archimedes believed that numbers never ended. Discuss large numbers and why Archimedes believed that numbers are infinite.

Essay Topic 2

Discuss the principles that Archimedes learned about liquids which led to the beginning of hydrostatics.

Essay Topic 3

King Hiero was concerned that sooner or later Syracuse was going to be caught in the war between Rome and Carthage. Discuss why King Hiero was concerned about war and what he did about his concerns.

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