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"
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?



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