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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. Who were the first people to have ideas about gravity?
(a) Greek scientists.
(b) Egyptian scientists.
(c) Babylonian scientists.
(d) Persian scientists.

2. With Archimedes' polygons, how much more was the circumference than the diameter?
(a) 1 11/63 times.
(b) 2 5/84 times.
(c) 6 15/94 times.
(d) 3 10/71 times.

3. Where is the center of balance on a spoon?
(a) At the bowl of the spoon.
(b) In the center.
(c) Near the end of the spoon's handle.
(d) Near the bowl of the spoon.

4. What calculation today does not use the unusual mathematical properties of a spiral?
(a) Directions.
(b) Distances in space.
(c) Finding an unknown quantity.
(d) Speeds.

5. Who succeeded Hiero when he died?
(a) Hieronymus.
(b) Herodotus.
(c) Pericles.
(d) Hesiod.

Short Answer Questions

1. When Archimedes estimated the number of grains of sand that would fill the universe, what common Greek measure did he use?

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

3. What would be the area of a circle that had a radius of 3 inches?

4. How many banks of oars did the galleys have that a Roman general used to attack Syracuse?

5. How many galleys did the Roman general have who attacked Syracuse?

Short Essay Questions

1. What happens when a pebble is dropped into a pond?

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

3. How did Archimedes estimate the number of grains that would fill the universe?

4. Why is Archimedes' "Method" so important to all mathematicians who followed him?

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

6. Describe Carthage.

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

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

9. What interests mathematicians regarding Archimedes and square roots?

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

(see the answer keys)

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