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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 is one of the common notions presented in Elements?

2. What did Euclid state about pi in Elements?

3. What did Apollonius work with in mathematics?

4. What did Hippocrates do that advanced mathematical methods?

5. What did Ferdinand Lindeman prove in 1882?

Short Essay Questions

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

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

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

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

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

6. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

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

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

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

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

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 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

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)

This section contains 992 words (approx. 4 pages at 300 words per page) View a FREE sample