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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. In what written work did Aristotle describe Zeno of Elea’s paradox of motion?

2. The ancient Egyptians are credited with creating what numerical system?

3. The author states in Chapter 3, “Nothing Ventured” that India adopted a Babylonian style number system around what century?

4. Approximately when was Zeno of Elea born?

5. The Italian word “zefiro,” meaning “west wind” derived from what Latin and Greek word?

Short Essay Questions

1. How does the author assert zero’s existence has been responsible for mathematical progress in Chapter 1, “Nothing Doing”?

2. How did zero enter into Indian mathematics, according to the author in Chapter 3, “Nothing Ventured”?

3. How did zero enter into Babylonian mathematics, according to the author in Chapter 1, “Nothing Doing”?

4. What mathematical developments was Pythagoras credited with in ancient Greece?

5. What mathematical properties of zero presented problems in the ancient world, according to the author in Chapter 1, “Nothing Doing”?

6. How does the author describe the relationship between early Christianity and zero in Chapter 2, “Nothing Comes of Nothing”?

7. Where does the author claim zero was “born” in Chapter 1, “Nothing Doing”? How was zero involved in early mathematics?

8. How did Aristotle approach the concept of zero, according to the author in Chapter 2, “Nothing Comes of Nothing”?

9. How does the concept of zero relate to the beliefs of Hinduism?

10. What paradox of Zeno of Elea’s is presented by the author in Chapter 2, “Nothing Comes of Nothing”?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Discuss the biography and the mathematical and philosophical contributions of Archimedes of Syracuse. How did Archimedes first encounter the infinite? How did this discovery influence his work and the work of mathematicians after him?

Essay Topic 2

Discuss the work of Sir Isaac Newton, Gottfried Wilhelm Leibniz, Johannes Kepler, and the origins and development of calculus. When did Newton and Leibniz independently create calculus? What conflict occurred between the two? When did this conflict end?

Essay Topic 3

Describe and discuss the advancements made in mathematics, music, and philosophy by Pythagoras. What is the Pythagorean Theorem? When was it developed? What were the beliefs of the Pythagoreans?

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