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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

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

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Floor van Lamoen

Posts: 183
Registered: 12/3/04
Re: The trapezoid-triangle-line rule?
Posted: Aug 9, 2000 6:20 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Jon Marshall wrote:
>
> Beating a dead horse, not even the accepted inclusive definition of
> trapezoid saves us from degenerate cases in the integration rule. If
> one or more of the endpoints of a subinterval of the partition is a
> zero of the function, you get a triangle or a horizontal line for the
> representative area. The benefits of an inclusive definition
> generally seem to be for mathematical or organizational elegance,
> whereas an exclusive definition can afford quick, concise
> communication. Both are worthy goals in their own situations.

And for particularly quick, concise communication one can use words like
nondegenerate, nonrectangular, etc., if really needed. After all
degenerate cases are often nonproblematic.

Floor van Lamoen.

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