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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 could NOT be included as a step in Euclid's great theorem?

2. Who asked Tartaglia for his solution to cubic equations?

3. What did Dunham discuss for many pages in this chapter?

4. Where was the modern number system developed?

5. What did Gauss set out to prove?

Short Essay Questions

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

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

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

4. Explain what Neils Abel proved.

5. Describe what Gauss discovered according to Dunham.

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

7. What was already known about circles before Archimedes?

8. What did Dunham explain about the shift in learning from the West to the East?

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

In Dunham's book, there were many descriptions of mathematicians and their personal lives. Write an essay to describe the common elements or characteristics that seem to be shared among these historically famous mathematicians. Also, explain what personal characteristics made them all excellent mathematicians.

Essay Topic 2

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

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)

This section contains 849 words (approx. 3 pages at 300 words per page) View a FREE sample