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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. How many sides did the pentadecagon have, as presented by Euclid?

2. After Hippocrates, what shape did the Greeks attempt to square without success?

3. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

4. Which of the following were an example of twin primes?

5. Which was true of Euclid's number theory?

Short Essay Questions

1. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

2. What was already known about circles before Archimedes?

3. Explain some puzzles suggested by Euclid's theories.

4. Describe what is quadrature and why it was useful in the time of Hippocrates.

5. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

6. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

7. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

8. Describe what Gauss discovered according to Dunham.

9. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

10. What did Dunham explain about the shift in learning from the West to the East?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Summarize the parts of Euclid's Elements. Use the following questions to guide your writing. What were the basic components to Elements? What were the most important theorems and proofs in Elements? How did Elements change the future of mathematics. Name a few mathematicians after Euclid who used Elements in their own work.

Essay Topic 2

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 3

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance mathematics?

(see the answer keys)

This section contains 855 words (approx. 3 pages at 300 words per page) View a FREE sample