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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 did Ferdinand Lindeman prove in 1882?

**2.** What was the same about Apollonius and Erosthanes?

**3.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

**4.** What is true about prime numbers?

**5.** What was Hippocrates famous for?

## Short Essay Questions

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

**2.** Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

**4.** Explain when the knowledge of ancient scholars was rediscovered.

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

**6.** What did Euclid state for his theory on prime numbers?

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

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

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

**10.** Explain what Neils Abel proved.

## 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

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

### Essay Topic 3

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

This section contains 827 words(approx. 3 pages at 300 words per page) |