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. Which of the following is true about pi, as described by Dunham.

2. What did Dunham claim about Archimedes's determination of a number value for pi?

3. What did most of Heron's work deal with?

4. What was true about Hippocrates's proof?

5. What was known about pi, during Archimedes' time?

Short Essay Questions

1. What was the great theorem of this chapter? Describe it briefly.

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

3. What great theorems and work of Newton did Dunham highlight?

4. What was Gauss's major unpublished achievement in geometry?

5. Describe who were Jakob and Johann Bernoulli.

6. Who was Georg Cantor, and what was significant about his work in mathematics?

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

8. 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.

9. Describe how Cardano eventually publishes the solution to cubic equations.

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain.

Essay Topic 2

Write a three part essay to compare the work of Euclid to the work of Gauss.

Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.

Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.

Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?

Essay Topic 3

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

(see the answer keys)

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