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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
mary@krimmel.net
you several wrote what's below and much more:
>Hi,
>
>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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