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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 was the same about Apollonius and Erosthanes?

2. Exactly what limit is reached at a quartic equation?

3. What was Hippocrates famous for?

4. Which mathematician was first to take the challenge to solve cubic equations?

5. What was the title of Cardano's book which contained the solution to the cubic?

Short Essay Questions

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

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

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

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

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

6. Describe the contents of Cardano's book.

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

8. Who was Luca Pacioli, and what controversy was sparked over his writings?

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

Essay Topic 2

What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain.

Essay Topic 3

Write a three part essay to compare Archimedes's and Newton's determination of a number value for pi.

Part 1) Explain what general approach each mathematician used in the determination of pi.

Part 2) What prior knowledge of mathematics is required to use each method?

Part 3) Which number determination for pi was more accurate, Newton's or Archimedes? Explain.

(see the answer keys)

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