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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 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

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

### Essay Topic 3

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

This section contains 313 words(approx. 2 pages at 300 words per page) |