MAT 300-02L Test 2
This part of the exam is due on Tuesday, May 2, at the beginning of class. These questions are part of the midterm exam.. You may use only your text, your notes, and any other resources that have been assigned in class. You may not receive help from anyone else on these questions, except that you may ask Dr. Gingrich for clarifications. You also may not give help to anyone else in the class, and you may not talk to anyone else, whether in the class or not, about the test until it has been turned in. Note that I will be grading your essay answer for composition, not just content.
1. (20 points) Write an essay on the following topic. Your answer should be 300-500 words typed and double spaced.
A crisis was caused in Greek mathematics by the discovery of the square root of 2 and other irrational numbers. Explain why this might be called the “commensurability crisis”. Carefully explain the relationship of this problem to the theory of proportions and explain how the crisis was "resolved".
2. (8 points) Explain how the method of exhaustion is used by Archimedes in the proof of Proposition 1 in “On the Measurement of the Circle”. Write your solution on a clean sheet of white paper. You do not need to type the solution to this problem.
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