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. Which is one of the common notions presented in Elements?

2. How did Archimedes arrive at a number value for pi?

3. What were the proofs in Elements based on?

4. Which of the following could NOT be included as a step in Euclid's great theorem?

5. Which of the following was NOT one of Gauss' discoveries?

Short Essay Questions

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

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

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

4. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

5. Who was Luca Pacioli, and what controversy was sparked over his writings?

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

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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 2

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 3

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.

(see the answer keys)

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