Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Hard

William Dunham (mathematician)
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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 Euclid state about pi in Elements?

2. What was the same about Apollonius and Erosthanes?

3. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

4. Where was Neil's Abel from?

5. Which words best describe how solid proofs were developed in Elements?

Short Essay Questions

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

2. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

3. Explain what Neils Abel proved.

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

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

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

7. What was already known about circles before Archimedes?

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

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

10. What did Euclid state for his theory on prime numbers?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

Essay Topic 2

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 3

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.

(see the answer keys)

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