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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 did Dunham claim about Archimedes's determination of a number value for pi?

2. Which city was the center of thinking and learning in Third century BC?

3. Who was Heron?

4. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

5. In Elements, how many postulates must be accepted as given?

Short Essay Questions

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

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

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

4. Explain what Neils Abel proved.

5. 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.

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

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

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

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

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

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 2

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

Essay Topic 3

Write a three part essay to compare the work of Euclid to the work of Gauss.

Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.

Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.

Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?

(see the answer keys)

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