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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. That properties of specific shapes were early Egyptians aware of?

2. What did Archimedes manage to prove using Euclid's ideas?

3. How did Lindeman prove his conclusion?

4. What did Hippocrates do that advanced mathematical methods?

5. Which words best describe how solid proofs were developed in Elements?

Short Essay Questions

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

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

3. Describe in two sentences Archimedes's method for determining circular area.

4. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

6. Describe the contents of Cardano's book.

7. What did Dunham explain about the shift in learning from the West to the East?

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

9. Explain when the knowledge of ancient scholars was rediscovered.

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance mathematics?

Essay Topic 2

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

Essay Topic 3

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

(see the answer keys)

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