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. How did Archimedes demonstrate his theory of pi?

2. Which of the following is true in modern math about twin primes?

3. What range of values did Archimedes determine for pi?

4. What allowed Cardano to justify publishing his book?

5. Which was true of Euclid's number theory?

Short Essay Questions

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

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

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

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

5. How many definitions were in Euclid's book? List some of the definitions he included.

6. Describe the contents of Cardano's book.

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

In Dunham's book, there were many descriptions of mathematicians and their personal lives. Write an essay to describe the common elements or characteristics that seem to be shared among these historically famous mathematicians. Also, explain what personal characteristics made them all excellent mathematicians.

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 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.

(see the answer keys)

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