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## Final Test - Hard

Name: _________________________ | Period: ___________________ |

This test consists of 5 short answer questions and 1 (of 3) essay topics.

## Short Answer Questions

**1. To how many decimal places did Newton determine the number for pi?**

**2. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?**

**3. What did Gauss do with his best work?**

**4. Which of the following did Dunham concentrate on as one of Newton's great advances?**

**5. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?**

## Essay Topics

### Essay Topic 1

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 2

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 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?

This section contains 314 words(approx. 2 pages at 300 words per page) |