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 an example of a perfect number?

2. What did Plato use his inspiration from Euclid for?

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

4. Where was the modern number system developed?

5. Who was the author of the book Elements?

Short Essay Questions

1. 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.

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

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

4. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

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

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

7. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

8. What was already known about circles before Archimedes?

9. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

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

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

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance mathematics?

Essay Topic 3

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

(see the answer keys)

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