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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 else, besides a solution to cubic equations, was in Cardano's book?

2. What was known about pi, during Archimedes' time?

3. According to Dunham, who was most able to collect knowledge from around the globe?

4. Dunham showed that Heron's proof could also be used as which of the following?

5. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

Short Essay Questions

1. How did Archimedes find a number value for pi?

2. Describe the contents of Cardano's book.

3. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

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

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

6. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

7. Describe the events that follow del Ferro's death between Fior and Tartaglia.

8. What did Euclid state for his theory on prime numbers?

9. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

10. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

Essay Topic 2

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 3

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.

(see the answer keys)

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