2. Absolute zero has no energy and is unattainable for what reason?
(a) Any attempt to get a space to absolute zero exerts energy.
(b) Any attempt to get a space to absolute zero requires a black hole.
(c) Any attempt to get a space to absolute zero requires string distribution.
(d) Any attempt to get a space to absolute zero requires infinity.

3. During what years did Georg Cantor live?
(a) 1811-1878.
(b) 1777-1836.
(c) 1845-1918.
(d) 1689-1759.

4. What refers to the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics?
(a) Microquasar theory.
(b) Gravitational theory.
(c) Special relativity.
(d) General relativity.

5. Bernhard Riemann was able to show how to generate the geometry for what, according to the author in Chapter 6, “Infinity’s Twin”?
(a) Non-Euclidean spaces.
(b) Differential equations.
(c) Sound waves.
(d) Light waves.

Short Answer Questions

1. Calculus allowed Newton to combine the known natural laws of physics into one grand set of laws that could be expressed as what?

2. The Rayleigh–Jeans law revealed an important error in physics theory of its time. The law predicted an energy output that diverges towards infinity as wavelength approaches what?

3. The Leibniz–Newton calculus controversy was an argument between Sir Isaac Newton and Gottfried Leibniz over what?

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

5. According to the author in Chapter 7, “Absolute Zeros,” Max Planck came up with a new equation that solved the ultraviolet catastrophe but implied that energy was released in discrete packets that have come to be called what?

Short Essay Questions

1. What does the author say thermodynamics has taught us in Chapter 7, “Absolute Zeros”?

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

3. How did the discovery of imaginary numbers affect the study of algebra?

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

5. What discovery did Georg Cantor make regarding different types of infinities? How are these types defined?

6. 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”?

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

8. What was discovered by Albert Einstein’s solution to the photoelectric effect?

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

10. How did Max Planck address the problem of the ultraviolet catastrophe?

(see the answer keys)

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