Journey Through Genius: The Great Theorems of Mathematics Test | Final Test - Hard

William Dunham (mathematician)
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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

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.

Essay Topic 2

Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?

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?

(see the answer keys)

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