Q&A #1664

Teachers' Lounge Discussion: Group research project in geometry for students

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From: George Zeliger, Ph.D.

To: Teacher2Teacher Public Discussion
Date: 2001012112:04:14
Subject: Geometry project

I am not a big fan of group learning. Mathematics in general is a field where individual efforts are crucial. Neither Euclides, nor Gauss, Bolyai, Lobachevsky or Riemann worked in groups. Nonetheless, a discussion in a group of the results obtained individually can be a useful experience, since peer review is a necessary part of the contemporary scientific research. I would suggest a topic rather than an Internet site or a book. The generic concept of area is intuitively rather simple. The most fundamental, "defining" properties of the concept are: 1) It is a non-negative number; 2) It does not change when the figure is moved around as a "solid" piece; 3) The area of the combination of two non-overlaping figures is the sum of the areas of the original pieces. The fourth, less fundamental, property is that we assign the value 1 to a square, which sides have unit lengths. Now comes the question -- what if we choose as a unit the area of another figure, say, the equilateral triangle with unit sides? How will the formulas for caculating areas of popular figures change? Regards, George

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