My actual problem with those definitions is not that they are difficult to deal with. In my honest opinion these definitions are unmathematical in the sense that mathematics generalizes things.
The trapezoid is a weaker form of a rectangle (which is a weaker form of a square), and as such theorems on geometric properties of trapezoids naturally include rectangles (and squares). I am afraid that if one teaches pupils to be precise on these exclusive definitions, one teaches them to focus on the wrong things, and perhaps forget the important concept of generalization.
We wouldn't like to use exclusive definitions for number sets like Natural numbers, Integers, Rational numbers, Real numbers and Complex numbers, do we? It's so good that those include each other! The use of exclusive definitions of - for example - trapezoids, is rather the same.
Kind regards, Floor van Lamoen.
John Conway wrote: > > On Tue, 8 Aug 2000, Floor van Lamoen wrote: > > > No, No!! > > > > One must call it the "Trapezoid-Rectangle-or-Square Rule" of course, if > > one really wants to use exclusive definitions. > > Thanks, Floor! This just goes to illustrate my point that it's > so hard to work with the exclusive definitions that even the best of > us (as I modestly term myself) can't actually manage to do it! > > John Conway