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

## Short Answer Questions

**1.** What was Dunham central theorem for this chapter?

**2.** What did George Cantor discover?

**3.** To how many decimal places did Newton determine the number for pi?

**4.** How did Cantor finally prove his theory?

**5.** In the Bernoulli's time, what was the current definition of a series?

## Short Essay Questions

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

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

**3.** Describe Newton's days in Cambridge and what he eventually came to discover.

**4.** Describe Cantor's difficult personal life.

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

**6.** Describe some of the characteristics of Leonhard Euler, and what made him successful.

**7.** Who was Georg Cantor, and what was significant about his work in mathematics?

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

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

**10.** Explain how Gottfried Leibniz was able to publish his method of calculus.

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

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.

### Essay Topic 2

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

### Essay Topic 3

Write a three part essay to describe third century Alexandra.

Part 1) Describe the geographic location of Alexandria. Why did its location affect its scholars?

Part 2) Name and describe the work of a few scholars in third century Alexandria.

Part 3) Who was Heron? How did his achievements improve mathematics?

This section contains 825 words(approx. 3 pages at 300 words per page) |