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 is true about prime numbers?

2. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

3. What is a "depressed cubic"?

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

5. Which of the following best describes Archimedes as discussed by Dunham?

Short Essay Questions

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

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

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

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

5. Who was Heron, and what is known about him today?

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

7. Describe who was Archimedes and how Dunham described his character.

8. What was Euclid's definition of composite and perfect numbers?

9. Explain what Neils Abel proved.

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

Essay Topics

Write an essay for ONE of the following 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

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 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)

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