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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 did Apollonius work with in mathematics?

2. According to Dunham, who was most able to collect knowledge from around the globe?

3. Which of the following were an example of twin primes?

4. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

5. What was Hippocrates's great advance to mathematics?

Short Essay Questions

1. Describe the contents of Cardano's book.

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

3. Explain what Neils Abel proved.

4. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

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

6. Describe what is quadrature and why it was useful in the time of Hippocrates.

7. Describe Lindeman's work on the square of a circle, and state what he discovered.

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

9. Describe who was Archimedes and how Dunham described his character.

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

Essay Topic 2

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.

Essay Topic 3

Summarize the discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

(see the answer keys)

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