Number Theory and Algebra Summary
Monday, July 1, 2002
After a brief round of introductions, we dove into our work. Our goal: to look at situations that teachers run into on a daily basis and determine routines that would allow them to develop problems with "nice" (meaning integer or perhaps terminating decimal) answers.
Our first example was in finding the distances between three points on a plane -- how do we place the points so as to guarantee integer values. This was related very closely to our discussion of Gaussian integers in the morning session and ended up consuming most of of our time.
Our second, briefer, example was finding an angle in a triangle using the cosine law -- how do we choose the sides so that the angle is "nice", in this case, 60 degrees.
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.