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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. How is zero represented in Roman numerals?

2. Copernicus developed what kind of model of the universe?

3. What term refers to the religious or philosophical concept that the soul is reborn after biological death?

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

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

Short Essay Questions

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

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

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

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

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

6. How did Filippo Brunelleschi introduce the concept of zero to the Italian Renaissance?

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Discuss the biography and work of Filippo Brunelleschi and the introduction of linear perspective. What did paintings look like before the invention of the vanishing point? How did Brunelleschi discover the concept of the vanishing point? How did this concept involve zero?

Essay Topic 2

Describe and discuss the origins and history of mathematics within Islamic culture. When was the House of Wisdom built? Who first coined the term “algebra”? When was the term coined?

Essay Topic 3

Describe and discuss the biography and the philosophical, artistic, and mathematical contributions of Aristotle. How influential were Aristotle’s ideas in the formation of Western culture? How does the concept of zero impact Aristotle’s view?

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