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Topic: Trapezoid definition
Replies: 26   Last Post: Oct 7, 2004 11:51 PM

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mary krimmel

Posts: 74
Registered: 12/4/04
Re: Trapezoid definition
Posted: Aug 9, 2000 10:02 AM
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To Floor van Lamoen and John Conway especially, and to all who contributed
questions, opinions, complaints, concerns,

This discussion of exclusive/inclusive definition has been - is - highly
interesting and educational.

Thank you.

Now: it seems undisputable that the concept of counting numbers precedes
the concepts of rationals, integers, and so on both in individual
development and in social/mathematical history, but what about the
geometric figures?

I think that a circle comes first (and I see it not as a disk although
that's what's usually presented to toddlers being prematurely tutored in
"shapes") both for an individual and society? Then what?

Mary Krimmel

you several wrote what's below and much more:

>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


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