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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 was one of Euclid's great theorems?

2. Besides being a mathematician, what else other work was Archimedes famous for?

3. Dunham showed that Heron's proof could also be used as which of the following?

4. What was Eratosthanes most famous for?

5. What was Euclid's definition of a prime number?

Short Essay Questions

1. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

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

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

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

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

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

7. How did Archimedes find a number value for pi?

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

9. Explain what Neils Abel proved.

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 a three part essay to compare Archimedes's and Newton's determination of a number value for pi.

Part 1) Explain what general approach each mathematician used in the determination of pi.

Part 2) What prior knowledge of mathematics is required to use each method?

Part 3) Which number determination for pi was more accurate, Newton's or Archimedes? 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

Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?

(see the answer keys)

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