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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.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

**2.** Who was Neil's Abel?

**3.** What did Archimedes manage to prove using Euclid's ideas?

**4.** Which of the following were an example of twin primes?

**5.** Who asked Tartaglia for his solution to cubic equations?

## Short Essay Questions

**1.** Give an example of a series who's sum is still unknown.

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

**3.** Who was Georg Cantor, and what was significant about his work in mathematics?

**4.** How did Archimedes find a number value for pi?

**5.** Describe what Gauss discovered according to Dunham.

**6.** Describe what the Bernoullis discovered about series, and give an example.

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

**8.** Describe Cantor's difficult personal life.

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

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

## Essay Topics

### Essay Topic 1

Explain the accuracy of Archimedes determination of pi. How did he determine the number value of pi? How accurate is Archimedes's measurement of pi? What other mathematician was able to determine a number value, though more accurate, for pi?

### Essay Topic 2

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

### 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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