Mid-Book Test - Hard
|Name: _________________________||Period: ___________________|
This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.
Short Answer Questions
1. What was the bases of Hippocrates's proof ?
2. Which of the following best describes Cardano's character?
3. After working on pi, what did Archimedes continue with in his study of mathematics?
4. What instruments did the Greeks use to square a shape?
5. Which is one of the common notions presented in Elements?
Short Essay Questions
1. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.
2. Describe the connection between Fermat and Euler's work.
3. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?
4. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?
5. How did Heron find the area of a triangle, and what did Dunham state about Heron's work?
6. Describe the great theorem explained by Dunham in this chapter.
7. Describe who was Archimedes and how Dunham described his character.
8. Who was Heron, and what is known about him today?
9. Who was Luca Pacioli, and what controversy was sparked over his writings?
10. Describe what Gauss discovered according to Dunham.
Essay Topic 1
Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?
Essay Topic 2
Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?
Essay Topic 3
Explain the accuracy of Archimedes determination of pi. How did he determine the number value of pi? How accurate is Archimedes's measurement of pi? What other mathematician was able to determine a number value, though more accurate, for pi?
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