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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 provided most of the content in the book Elements?

2. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

3. Who wrote a treatise that supposed that cubic equations may be impossible to solve?

4. Which of the following was NOT defined by Euclid?

5. What did the Pythagorean Theorem accomplish for mathematics?

Short Essay Questions

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

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

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

4. Explain what Neils Abel proved.

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

6. Describe the contents of Cardano's book.

7. What was Euclid's definition of composite and perfect numbers?

8. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

9. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a three part essay to compare the work of Euclid to the work of Gauss.

Part 1) Explain what concepts both Euclid and Gauss worked with, and how they approached a similar problem.

Part 2) Compare what Euclid believed about triangles to what Gauss believed about triangles.

Part 3) How did both Gauss and Euclid advance mathematical understanding in their own time?

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

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

(see the answer keys)

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