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. Which of the following is false about the modern implications of Euclid's number theory?

2. Who was Heron?

3. Which of the following is true about pi, as described by Dunham.

4. What is true about prime numbers?

5. Heron devised which of the following methods?

Short Essay Questions

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

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

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

4. What did Dunham describe in the epilogue of the chapter?

5. Describe what Gauss discovered according to Dunham.

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

7. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

8. Describe Lindeman's work on the square of a circle, and state what he discovered.

9. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?

Essay Topic 2

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?

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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