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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

Summarize the discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

### Essay Topic 2

Write a three part essay to compare the work of Euclid to the work of Gauss.

Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.

Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.

Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?

### 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 307 words(approx. 2 pages at 300 words per page) |