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

2. How long did Marcellus hold Syracuse in siege.

3. When did Marcellus notice a poorly guarded wall and tower in Syracuse?

4. What did Marcellus have his workmen build when he noticed a poorly guarded wall and tower in Syracuse?

5. With Archimedes' polygons, how much more was the circumference than the diameter?

Short Essay Questions

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

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

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

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

5. Before Archimedes, how did people find the area of a circle?

6. How do modern scientists work with very large numbers?

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

8. What are some reasons why Archimedes is held in such high esteem by mathematicians?

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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

Essay Topic 2

Syracuse was under siege by Marcellus for three years until 212 B.C., when they finally conquered the city. Discuss why and how the Romans conquered Syracuse.

Essay Topic 3

Discuss how and why Archimedes created the Archimedean screw.

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