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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 true about Heron's theorem as described by Dunham?

2. Which of the following is true in modern math about twin primes?

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

4. What was Euclid's definition of a prime number?

5. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

Short Essay Questions

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

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

3. Describe the events that follow del Ferro's death between Fior and Tartaglia.

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

5. What was already known about circles before Archimedes?

6. Who was Heron, and what is known about him today?

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

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

9. What did Euclid state for his theory on prime numbers?

10. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?

Essay Topic 2

Write a three part essay on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

Essay Topic 3

Write a a three part essay to explain how Cantor's work in mathematics also fit into the cultural movements of the time.

Part 1) Describe the artistic movements of the 1860s and 1870s. In general, how could they be related to mathematical philosophy at the time?

Part 2) What was Cantor's work in mathematics in the 1860s and 1870s?

Part 3) Explain how Cantor's philosophy and mathematical theorems fit with the new artistic and philosophic ideas of the time.

(see the answer keys)

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