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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 NOT one of the basic definitions in Elements?

2. Which of the following is true about pi, as described by Dunham.

3. Which of the following is false about the modern implications of Euclid's number theory?

4. Which of the following was NOT defined by Euclid?

5. Who was Eratosthanes?

Short Essay Questions

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

2. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

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

4. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

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

6. Who was Heron, and what is known about him today?

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

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

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

10. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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?

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

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

(see the answer keys)

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