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

William Dunham (mathematician)
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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 Eratosthanes most famous for?

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

3. Which of the following becomes an important definition in mathematics that was first presented in Elements?

4. Where did Hippocrates come from?

5. Which city was the center of thinking and learning in Third century BC?

Short Essay Questions

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

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

3. Explain when the knowledge of ancient scholars was rediscovered.

4. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

5. How many definitions were in Euclid's book? List some of the definitions he included.

6. Who was Luca Pacioli, and what controversy was sparked over his writings?

7. 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.

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

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

10. Describe the contents of Cardano's book.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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.

Essay Topic 2

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

Essay Topic 3

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

(see the answer keys)

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