## 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

In Dunham's book, there were many descriptions of mathematicians and their personal lives. Write an essay to describe the common elements or characteristics that seem to be shared among these historically famous mathematicians. Also, explain what personal characteristics made them all excellent mathematicians.

### Essay Topic 2

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

### Essay Topic 3

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.

This section contains 303 words(approx. 2 pages at 300 words per page) |