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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. According to the author in Chapter 2, “Nothing Comes of Nothing,” the Pythagorean view tied numbers to what?

2. What word did the Indians use for zero during Muhammad ibn Ahmad al-Khwarizmi’s time?

3. What 12 Century rabbi sought to reconcile Greek philosophy with the Semitic Bible?

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

5. What was the fifth element that Aristotle proposed, in addition to earth, water, fire, and air?

Short Essay Questions

1. How are ancient Babylonian mathematics described in Chapter 1, “Nothing Doing”?

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

3. How was zero dealt with in the Pythagorean view, according to the author in Chapter 2, “Nothing Comes of Nothing”?

4. How does the author describe the ancient Greek and Roman mathematical systems in Chapter 1, “Nothing Doing”?

5. How are multiplication and division involving zero described in Chapter 1, “Nothing Doing”?

6. What inventions is Blaise Pascal credited with, according to the author in Chapter 4, “The Infinite God of Nothing”?

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

8. 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?

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Describe and discuss the biography and works of Leonardo Fibonacci during the Middle Ages, and Fibonacci’s influence in spreading the Hindu–Arabic numeral system in Europe. What is the Fibonacci number sequence? What works did Fibonacci write?

Essay Topic 2

Describe and discuss the development of mathematics within Jewish culture and society, as well as the Jewish relationship with the Aristotelian world view and the work of Maimonides. Why did the Aristotelian viewpoint contradict Jewish belief? How did Maimonides approach this problem?

Essay Topic 3

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?

(see the answer keys)

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