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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. How did Archimedes demonstrate his theory of pi?

2. What instruments did the Greeks use to square a shape?

3. After Hippocrates, what shape did the Greeks attempt to square without success?

4. Exactly what limit is reached at a quartic equation?

5. What were the proofs in Elements based on?

Short Essay Questions

1. What was already known about circles before Archimedes?

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

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

4. Explain what Neils Abel proved.

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

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

7. Describe what is quadrature and why it was useful in the time of Hippocrates.

8. Explain some puzzles suggested by Euclid's theories.

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

10. Who was Luca Pacioli, and what controversy was sparked over his writings?

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

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 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 874 words (approx. 3 pages at 300 words per page) View a FREE sample