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

3. Which of the following was an important proposition given by Euclid's number theory?

4. When was the work of these early thinkers rediscovered again in history?

5. Where was Archimedes born?

Short Essay Questions

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

2. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

4. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

5. Describe the contents of Cardano's book.

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

7. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

8. Describe who was Archimedes and how Dunham described his character.

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

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

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance 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

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?

(see the answer keys)

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