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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?

## 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

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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