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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. When did René Descartes live?

2. What does the author refer to as “zero’s twin” in the book?

3. Aristotle referred to Zeno of Elea as the inventor of what?

4. The Renaissance roughly spanned the period of what centuries?

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

Short Essay Questions

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

2. What reason does the author give for why the Greeks and Romans resisted using zero in their mathematical systems in Chapter 1, “Nothing Doing”?

3. What mathematical advancements were made by the ancient Egyptians?

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

5. What were Blaise Pascal’s theological beliefs? How was zero viewed in his beliefs?

6. What caused the USS Yorktown to have a computer meltdown in 1997, according to the author in Chapter 0, “Null and Void”? How is the ship described?

7. What theory was developed through Blaise Pascal’s mathematical approach to theology?

8. How does the author describe Islam’s history in the seventh century in Chapter 3, “Nothing Ventured”?

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Discuss Guillaume de l'Hôpital, Bishop Berkeley, and l'Hôpital's rule. How are derivatives used to evaluate limits involving indeterminate forms under l'Hôpital's rule? How did these advancements deal with the problem of zero?

Essay Topic 2

Discuss the mathematical influences of Copernicus and Nicholas of Cusa during the Renaissance. How did Copernicus’s model of the universe differ from the Aristotelian model? What became of Copernicus and Nicholas of Cusa?

Essay Topic 3

Discuss the origins, development, and contributions of Babylonian mathematics. How did the Babylonian numeral system differ from that of the ancient Egyptians? Where has most of our information of Babylonian mathematics been derived?

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