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Name: _________________________ | Period: ___________________ |

This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

## Short Answer Questions

**1.** What did Euler's sum surprisingly connect?

**2.** Which of the following is a quote from Bertrand Russell included by Dunham?

**3.** What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?

**4.** What did Newton's calculus involve?

**5.** What concept did Dunham end his book with?

## Short Essay Questions

**1.** Explain any methods used by Cantor that were unsuccessful.

**2.** Why did Euler start working on the sum of series?

**3.** Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

**4.** Describe some of Gauss's work.

**5.** Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

**6.** Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.

**7.** Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

**8.** What was Gauss's major unpublished achievement in geometry?

**9.** What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

**10.** Describe the controversy that Newton was caught in with his publication of his calculus methods.

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain.

### Essay Topic 2

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 3

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?

This section contains 844 words(approx. 3 pages at 300 words per page) |