MAT 300-02L Midterm Exam
This part of the exam is due on Thursday, April 29, 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 answers for composition, not just content.
8. (20 points) Write an essay on the following topic. Your answer should be 250-500 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".
9. (20 points) Write an essay on one of the following topics. Your answer should be 250-500 words typed and double spaced.
a. Discuss the works of Archimedes. Your answer should include something about major themes in his work, and the effect and/or influence of his works. You should name several specific works and briefly discuss their contents.
b. Discuss the Archimedes palimpsest, its origin, and its mathematical and historical significance.
10. (8 points) Choose one of the following and write your solution on a clean sheet of white paper. You do not need to type the solution to this problem.
a. Give
a geometric interpretation or demonstration of the following statement using
the techniques of the Pythagoreans. You
should explain in words what the picture represents. Include any auxiliary
lines used to explain the reasoning in the proof.
A square number is the sum of two consecutive triangle numbers.
b.. For
the following proposition from
Book II, Proposition 1
If there be two straight lines, and one
of them be cut into any number of segments whatever, the rectangle contained by
the two straight lines is equal to the rectangles contained by the uncut
straight lines and each of the segments,
THE END!