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 was true about Cardano, according to Dunham?

2. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

3. Who acted as the gate keepers of knowledge?

4. In what time period did mathematicians find a solution to cubic equations?

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

Short Essay Questions

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

2. Explain when the knowledge of ancient scholars was rediscovered.

3. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

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

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

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

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

8. Describe in two sentences Archimedes's method for determining circular area.

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

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

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 a three part essay to explain how Cantor's work in mathematics also fit into the cultural movements of the time.

Part 1) Describe the artistic movements of the 1860s and 1870s. In general, how could they be related to mathematical philosophy at the time?

Part 2) What was Cantor's work in mathematics in the 1860s and 1870s?

Part 3) Explain how Cantor's philosophy and mathematical theorems fit with the new artistic and philosophic ideas of the time.

Essay Topic 3

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

(see the answer keys)

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