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 Subject: What is a triangle? Author: rabeldin Date: Jan 2 2005
The name "triangle" suggests a figure with three angles. This definition
excludes U shaped figures with two parallel sides since they have but two
angles. However, if you ask most people for the definition, they will respond in
terms like "a three sided polygon" or "a closed figure with three sides". We
seem to prefer a definition in terms of sides as easier than one in terms of
angles.

What we call triangles could legitimately be called "trigons", polygons with
three sides. Are triangles and trigons completely equivalent? If we generalize
to a non-plane space, they may be different. At least the question bears
investigation.

I suspect that there are subtle errors in school mathematics where we mentally
substitute an informal definition for the formal one and generalize improperly.
Has anyone spent any time on such issues?