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 was known about pi, during Archimedes' time?

2. In what century did Archimedes live?

3. Which shapes as described by Euclid, inspired the Greek philosopher Plato?

4. That properties of specific shapes were early Egyptians aware of?

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

Short Essay Questions

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

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

3. Describe Lindeman's work on the square of a circle, and state what he discovered.

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

5. Describe what Gauss discovered according to Dunham.

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

7. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite 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. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

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

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.

Essay Topic 2

Explain the accuracy of Archimedes determination of pi. How did he determine the number value of pi? How accurate is Archimedes's measurement of pi? What other mathematician was able to determine a number value, though more accurate, for pi?

Essay Topic 3

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.

(see the answer keys)

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