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. Why did Cardano take an oath to secrecy?

2. Which words best describe how solid proofs were developed in Elements?

3. Which of the following was an important proposition given by Euclid's number theory?

4. Who was Heron?

5. What provided most of the content in the book Elements?

Short Essay Questions

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

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

3. What was already known about circles before Archimedes?

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

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

6. 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.

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

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 three part essay on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

(see the answer keys)

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