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Name: _________________________ | Period: ___________________ |

This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

## Short Answer Questions

**1.** Absolute zero has no energy and is unattainable for what reason?

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

**4.** What mathematical term refers to a function that preserves distinctness by never mapping distinct elements of its domain to the same element of its codomain?

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

## Short Essay Questions

**1.** Who devised the concept of a limit in calculus? What problems did the limit solve?

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

**3.** What are differential equations? Who first developed differential equations?

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

**5.** What discovery did Friedrich Riemann make in the field of projective geometry?

**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 did l’Hopital address the problem of zero, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

**8.** What problem do black holes present in physics, according to the author in Chapter 8, “Zero Hour at Ground Zero”?

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

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

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

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 2

Describe and discuss the origins and development of mathematics in Indian society. From whom did India adopt the concept of zero? How did the beliefs of Hinduism deal with the concept of zero? Why and how was this different than Christianity’s viewpoint of the void?

### Essay Topic 3

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?

This section contains 897 words(approx. 3 pages at 300 words per page) |