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

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G.E. Ivey

Posts: 3,857
Registered: 12/3/04
Re: Are squares rectangles
Posted: Oct 18, 2002 12:38 PM
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Julio Albornoz wrote:

>Hello fellow math fanatics,

>The arguments about inclusive and exclusive definitions can go on for
>ever especially when one tries to make one point over another. In
>reference to rectangles and squares, weather a square can be defined
>as a "kind of rectangle" remains to be mathematically proven.

No, that's not true. Since it is a question of which definition is
better, it's not something one can prove mathematically.

It is, however, a fact, that one can "prove", not mathematically,
but by examining math book and journals, that the "inclusive"
definitions are the ones generally accepted.

>However, let's take the real fact:

>Suppose a problem reads: The perimeter of a "rectangle" is 48 ft.
>Using whole numbers only, what is the dimensions that would give the
>greatest area?

>If we are inclusive we can say that is a 12 ft by 12 ft = 144 sq ft.
>If we are exclusive we can say that is a 13 ft by 11 dt = 143 sq ft.


>But what would the "correct" answer be in the real test-answer world?

>Wouldn't you agree that since the problem stated "rectangle" the
>exclusive way would be the correct answer?

>Your comments will be appreciated.

How in the world is that a "real fact" and what do you mean by
"the real test-answer world"? (My experience is that the "test-answer
world" has little to do with the "real" world!)

To me the crucial point is that, dropping that artificial "whole
number" condition, using the "exclusive" definition, there is no
solution while using the "inclusive" definition there is.

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