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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. 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
Write a three part essay on the lives and work of both Euler and Gauss.
Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?
Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?
Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?
Essay Topic 2
Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.
Part 1) Describe what we know about geometry before Thales.
Part 2) In what ways were mathematics and geometry used before Thales?
Part 3) Explain what we know about Thales' work. How did it advance mathematics?
Essay Topic 3
Write a three part essay to compare Archimedes's and Newton's determination of a number value for pi.
Part 1) Explain what general approach each mathematician used in the determination of pi.
Part 2) What prior knowledge of mathematics is required to use each method?
Part 3) Which number determination for pi was more accurate, Newton's or Archimedes? Explain.
This section contains 1,760 words
(approx. 6 pages at 300 words per page)