|Name: _________________________||Period: ___________________|
This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.
Short Answer Questions
1. Carl Gauss referred to mathematics 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. Johannes Kepler used calculus to determine that planets had what, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?
4. The author states in Chapter 6, “Infinity’s Twin” that Carl Gauss realized that real and imaginary numbers could be what?
5. Georg Cantor is best known as the inventor of what fundamental theory in mathematics?
Short Essay Questions
1. Who was Carl Gauss? What discovery did he make regarding imaginary numbers?
2. What are differential equations? Who first developed differential equations?
3. The author states in Chapter 6, “Infinity’s Twin” that before imaginary numbers could be accepted, several developments had to occur. Which was the first?
4. What does the author say thermodynamics has taught us in Chapter 7, “Absolute Zeros”?
5. Who discovered “absolute zero”? How is absolute zero defined in Chapter 7, “Absolute Zeros”?
6. How were Georg Cantor’s mathematical principles applied to his theology? Who disagreed with his vision and why?
7. How did the field of quantum mechanics address the problem of zero in thermodynamics?
8. 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”?
9. What is expressed through the Rayleigh-Jeans law? How does this law relate to zero?
10. How did the discovery of imaginary numbers affect the study of algebra?
Write an essay for ONE of the following topics:
Essay Topic 1
Discuss the biography, works, and mathematical developments of Mohammed ibn-Musa al-Khowarizmi. When was his work, Compendious Book on Calculation by Completion and Balancing completed? What did this work entail?
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 advancements made in mathematics, music, and philosophy by Pythagoras. What is the Pythagorean Theorem? When was it developed? What were the beliefs of the Pythagoreans?
This section contains 823 words
(approx. 3 pages at 300 words per page)