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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. What part of the Mediterranean Sea did the ships of Carthage control?

2. What is pi?

3. What is the solid of a square?

4. How much larger did Archimedes believe that the universe (all the stars) was than the Greek universe?

5. What is the circumference of a circle?

Short Essay Questions

1. Why isn't the center of gravity always at the center of an object?

2. Why is it possible for a person to balance standing on one foot?

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

4. What is the difference between a plane and a solid figure?

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

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

7. Why did Marcellus watch the battle for Syracuse with tears in his eyes?

8. Why did Archimedes not want to help King Hiero make plans to defend Syracuse from a possible attack?

9. What did Archimedes set out to prove in "The Sand Reckoner"?

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Archimedes wanted to be more exact than mathematicians before him when figuring the area of a circle. Discuss different methods that Archimedes, mathematicians before him, and mathematicians after him have used to find the area of a circle.

Essay Topic 2

War came to Syracuse as King Hiero had feared. Discuss how Syracuse defended their city.

Essay Topic 3

Archimedes made many contributions to astronomy. Discuss Archimedes' contributions to astronomy.

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