Discussion:  All Topics 
Topic:  What is a triangle? 
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Subject:  RE: What is a triangle? 
Author:  proofpad 
Date:  Jan 4 2005 
In any case, I am more concerned with the general class
> of error involved in using informal definitions. This is but a
> single example of such an error.
Unless you mean the way we use the English language in our translations of
mathematics (where, for instance, corresponding angles means one thing when you
have a transversal and something similar yet different when discussing congruent
polygons), I too see no problem as long as you have given the formal definition
and then used the informal one to help clear up students that get confused by
the formal definitions. This is a tactic used more when we get to nice long
definitions (such as the definitions of certain theorems) rather than "triangle"
for example, but even then that is simply a matter of explaining.
Keeping the students clear on the formal definitions, though, is important once
they have a firm grasp on the informal ones. IMHO.
Gabriel Edge
 
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