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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. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Volume.
(b) Metric system.
(c) Gravity.
(d) Area.

2. How did Lindeman prove his conclusion?
(a) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(b) Lindeman proved that all numbers are constructable with a compass and ruler.
(c) Lindeman proved that square roots are irrational numbers.
(d) Lindeman proved that some numbers are constructable without the use of a compass.

3. Which mathematician was first to take the challenge to solve cubic equations?
(a) Scipione del Ferro.
(b) Luca Pacioli.
(c) Tartaglia.
(d) Niccolo Fontana.

4. What do we know in modern times about Heron?
(a) We know very little, but much of his work survives.
(b) We know he was a teacher and philosopher but much of his work has been lost.
(c) We know he lived in Rome.
(d) We know he was an influencial scholar, but we don't know who his students were.

5. What was the bases of Hippocrates's proof ?
(a) Properties of squares and cubes.
(b) Properties of points and lines.
(c) Properties of triangles and semicircles.
(d) Properties of area to volume measurements.

Short Answer Questions

1. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

2. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

3. Who was Neil's Abel?

4. Which of the following can not be solved using algebra?

5. What did Hippocrates do that advanced mathematical methods?

Short Essay Questions

1. What did Dunham describe in the epilogue of the chapter?

2. How did Archimedes find a number value for pi?

3. How many definitions were in Euclid's book? List some of the definitions he included.

4. Describe the ancient city Alexandria and name a few of its third century geniuses.

5. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

6. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

7. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

8. Explain some puzzles suggested by Euclid's theories.

9. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

10. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

(see the answer keys)

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