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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. Who asked Tartaglia for his solution to cubic equations?

2. Where was the modern number system developed?

3. What were the proofs in Elements based on?

4. What was the same about Apollonius and Erosthanes?

5. Why did Cardano take an oath to secrecy?

Short Essay Questions

1. Describe the contents of Cardano's book.

2. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

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

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

5. Describe the ancient city Alexandria and name a few of its third century geniuses.

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

7. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

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

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

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

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

Summarize the parts of Euclid's Elements. Use the following questions to guide your writing. What were the basic components to Elements? What were the most important theorems and proofs in Elements? How did Elements change the future of mathematics. Name a few mathematicians after Euclid who used Elements in their own work.

Essay Topic 3

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?

(see the answer keys)

This section contains 936 words (approx. 4 pages at 300 words per page) View a FREE sample