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 of the following is an example of a postulate that must be accepted in Elements?

2. How many sides did the pentadecagon have, as presented by Euclid?

3. Where was the modern number system developed?

4. What was Euclid's definition of a prime number?

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

Short Essay Questions

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

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

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

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

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

6. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

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

8. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

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

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 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 2

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 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)

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