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. How did Archimedes arrive at a number value for pi?

2. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

3. When was the work of these early thinkers rediscovered again in history?

4. Where was Archimedes born?

5. What was true about Heron's theorem as described by Dunham?

Short Essay Questions

1. What was already known about circles before Archimedes?

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

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

4. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

5. Explain what Neils Abel proved.

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

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?

Essay Topic 2

Summarize the parts of Euclid's Elements. Use the following questions to guide your writing. What were the basic components to Elements? What were the most important theorems and proofs in Elements? How did Elements change the future of mathematics. Name a few mathematicians after Euclid who used Elements in their own work.

Essay Topic 3

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?

(see the answer keys)

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