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. Who was Eratosthanes?

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

3. Which of the following best describes Cardano's character?

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?

5. What was the bases of Hippocrates's proof ?

Short Essay Questions

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

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

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

4. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

5. Describe what Gauss discovered according to Dunham.

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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.

Essay Topic 2

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

Essay Topic 3

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?

(see the answer keys)

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