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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. Where was the modern number system developed?

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?

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

4. What did Heron's advances put into historical perspective for Dunham?

5. According to Euclid, when is a triangle a right triangle?

Short Essay Questions

1. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

2. Describe how Cardano eventually publishes the solution to cubic equations.

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

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

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

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

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

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

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

10. Describe the ancient city Alexandria and name a few of its third century geniuses.

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 on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

Essay Topic 3

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?

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