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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 INCORRECT, and not used in Archimedes proof of his theory?

2. Heron devised which of the following methods?

3. How many definitions were stated in Elements?

4. What was the title of Cardano's book which contained the solution to the cubic?

5. What was Eratosthanes most famous for?

Short Essay Questions

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

2. Describe what Gauss discovered according to Dunham.

3. What was Euclid's definition of composite and perfect numbers?

4. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

5. 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.

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

7. What did Dunham describe in the epilogue of the chapter?

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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?

Essay Topic 2

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?

Essay Topic 3

Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?

(see the answer keys)

This section contains 965 words (approx. 4 pages at 300 words per page) View a FREE sample