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Topic: Classification of quadrilaterals
Replies: 17   Last Post: Jan 11, 1995 6:43 AM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Classification of quadrilaterals
Posted: Dec 21, 1994 6:09 AM
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I'm not quite sure why you (ckfan) WANT to include the general
trapezoid in your classification!

I don't know of any interesting theorems on the trapezoid that
don't work for more general quadrilaterals, and it's always rather
puzzled me why anyone ever thought it worth while to give this
particular kind of quadrilateral its own special name.

I now think I know the reason, and am not too impressed by it.
Proclus (who's the guy responsible) says that the area is the
mean of the lengths of the two parallel sides times the distance
between them, and I think this was the point - the trapezoid is
the most general quadrilateral with a simple area formula. So
it has some practical point - you can compute the area of a
polygon by dividing it up into trapezoids.

But there's not much theoretical point - this area formula
is trivially deducible from the one for a triangle by just
drawing a diagonal. Does anyone know of any more interesting
theorem about trapezoids?

John Conway






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