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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 becomes an important definition in mathematics that was first presented in Elements?

2. What provided most of the content in the book Elements?

3. According to Euclid, when is a triangle a right triangle?

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

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

Short Essay Questions

1. Describe Lindeman's work on the square of a circle, and state what he discovered.

2. Describe how Cardano eventually publishes the solution to cubic equations.

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

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

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

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

7. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

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

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

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

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

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

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.

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