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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. What was true about Heron's theorem as described by Dunham?

2. What was Hippocrates famous for?

3. What provided most of the content in the book Elements?

4. In what time period did mathematicians find a solution to cubic equations?

5. What did Dunham consider as Archimedes's "masterpiece"?

Short Essay Questions

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

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

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

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

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

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

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

8. Explain when the knowledge of ancient scholars was rediscovered.

9. What was already known about circles before Archimedes?

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a three part essay to describe third century Alexandra.

Part 1) Describe the geographic location of Alexandria. Why did its location affect its scholars?

Part 2) Name and describe the work of a few scholars in third century Alexandria.

Part 3) Who was Heron? How did his achievements improve mathematics?

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

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

(see the answer keys)

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