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 were the proofs in Elements based on?

2. In what century did Archimedes live?

3. What did Dunham discuss for many pages in this chapter?

4. Where was the modern number system developed?

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

Short Essay Questions

1. Describe the contents of Cardano's book.

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

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

4. Describe the events that follow del Ferro's death between Fior and Tartaglia.

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

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

7. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

8. What did Dunham explain about the shift in learning from the West to the East?

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

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

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

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 discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

(see the answer keys)

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