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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 allowed Cardano to justify publishing his book?
2. In Elements, how many postulates must be accepted as given?
3. Which of the following were an example of twin primes?
4. Who was Heron?
5. Which of the following is false about the modern implications of Euclid's number theory?
Short Essay Questions
1. Describe who was Archimedes and how Dunham described his character.
2. Explain when the knowledge of ancient scholars was rediscovered.
3. Explain what Neils Abel proved.
4. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?
5. Describe the contents of Cardano's book.
6. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?
7. According the Dunham, how did Euclid prove his theory on the infinitude of primes?
8. What did Dunham describe in the epilogue of the chapter?
9. Describe the ancient city Alexandria and name a few of its third century geniuses.
10. Who was Luca Pacioli, and what controversy was sparked over his writings?
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
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
Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?
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