Number Theory and Algebra Summary
Monday, July 8, 2002
Monday brought with it a good problem, if not a perfect solution. We looked at what should be a very nice problem... how do we choose integer sides of a triangle so that the area is also an integer.
Now, as we've found, choosing the obvious answer is never sufficient (right triangle, one leg even). So, we brought in Heron's formula and spent the better part of two hours determing criteria so that we could find three sides! We've found a few properties and defined a subset of possible solutions... the general answer eludes us (for now!).
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.