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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. Johannes Kepler used calculus to determine that planets had what, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

2. According to the author in Chapter 6, “Infinity’s Twin,” geometry shows that mathematically the north and south poles of spheres do what?

3. Bernhard Riemann was able to show how to generate the geometry for what, according to the author in Chapter 6, “Infinity’s Twin”?

4. What rule in calculus uses derivatives to help evaluate limits involving indeterminate forms?

5. What term refers to an elementary particle, the quantum of light and all other forms of electromagnetic radiation?

Short Essay Questions

1. What problems were encountered in calculus with zero? How did zero apply to the physical world, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

2. How many dimensions are required for string theory to work? How are these dimensions described in Chapter 8, “Zero Hour at Ground Zero”?

3. How were Georg Cantor’s mathematical principles applied to his theology? Who disagreed with his vision and why?

4. What is expressed through the Rayleigh-Jeans law? How does this law relate to zero?

5. Who was Carl Gauss? What discovery did he make regarding imaginary numbers?

6. How is string theory described by the author in Chapter 8, “Zero Hour at Ground Zero”?

7. Who discovered “absolute zero”? How is absolute zero defined in Chapter 7, “Absolute Zeros”?

8. How are electrons described in Chapter 8, “Zero Hour at Ground Zero”?

9. How did the field of quantum mechanics address the problem of zero in thermodynamics?

10. Who created calculus? How did calculus differ from the other mathematical fields, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

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

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 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?

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