## 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 a three part essay to explain how Cantor's work in mathematics also fit into the cultural movements of the time.

Part 1) Describe the artistic movements of the 1860s and 1870s. In general, how could they be related to mathematical philosophy at the time?

Part 2) What was Cantor's work in mathematics in the 1860s and 1870s?

Part 3) Explain how Cantor's philosophy and mathematical theorems fit with the new artistic and philosophic ideas of the time.

### 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

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

This section contains 325 words(approx. 2 pages at 300 words per page) |