rectangle vs. square

[Robin Hamilton]

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> Sender:       American Dialect Society <ADS-L at LISTSERV.UGA.EDU>
> Poster:       victor steinbok <aardvark66 at GMAIL.COM>
> Subject:      Re: rectangle vs. square
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>
> I disagree in the strongest possible terms with at least one of these
> assertions. To be honest, I have no idea what "oblong" is--in all my
> mathematical education, I have never heard this even remotely
> approaching any technical meaning. More precisely, I have never heard
> it used to any mathematical object or property. But I've also never
> have heard of anyone seriously contesting that a square is a
> rectangle.

Yeah, I think "oblong" is the crunch (or one of the crunches) in this
brouhaha.

{Apropos of nothing, thinking about Victor's "What is an oblong?" it struck
me that I'd term the shape of a coffin "oblong" rather than "rectangular".
For what that's worth.}

But coming back to ....

        Polygon > Quadrilateral > Rectangle > square + oblong.

A Quadrilateral is a subset of the set:  Polygon
A Rectangle is a subset of the set:  Quadrilateral
A Square is a subset of the set:  Rectangle
An Oblong is (also) a subset of the set:  Rectangle -- *but it's defined as
"All those members of the set:  Rectangle which are not members of the set:
Square."

So "oblong" is where it goes drifty.  Inelegant to say the least, whether or
not it makes sense in the domain of mathematics or symbolic logic.

Except that we need the word in general language usage, even if only to
apply to a coffin.

Robin

> But a circle is an extreme or a degenerate case of an ellipse and
> there are reasons to classify circles as a special subset. There are
> obvious dynamic implications when looking at conic sections. In a
> sense, a circle is also a transitional point between an ellipse and a
> hyperbola, but I am not going to get into details why this is the
> case. The transformational properties of ellipses are also represented
> in a circle, although somewhat trivially so.
>
> Squares are a subset of rectangles, and, in fact, the justification
> for classifying them this way is even stronger. Mathematically,
> pretending that these are distinct categories makes no sense at all.
> That is, they are semantically distinct--the definition of a square is
> not the same as a definition of a rectangle. On the other hand,
> logically, they are not distinct--every definition that describes all
> rectangle also describes all squares.
>
> A square is a rectangle for which the two pairs of edges have the same
> length. To make matters even more fun, it's also a rhombus. And these
> two descriptions are very informative--they specify that a square has
> all the properties of a rectangle and all the properties of a
> rhombus--something that the remaining rectangles and rhombuses cannot
> claim. The reason I stated that the square-rectangle relationship is
> somewhat stronger is because the only distinguishing characteristic of
> squares compared to the other rectangles is the congruence of adjacent
> edges. The distinction between a circle and an ellipse is a bit more
> robust--the two foci of the ellipse collapse at the center of the
> circle, so there are some distinct properties there.
>
> The bizarre recategorization occurs because of elementary school text
> written by illiterates (some of whom also teach in their spare time).
> For this reason one may find new quadrilateral poseurs in textbooks,
> such as "diamonds", "kites", etc. These are given formal but
> meaningless definitions (diamonds are really just rhombuses, excluding
> the squares, kites are two isosceles triangles joined at the base,
> but, again, not including the squares, i.e., those with the two
> triangles non-congruent). But these definitions are mathematically
> vacuous, just as the definition of a rectangle that does not include
> the square (i.e., the usual definition with an additional proviso that
> the two pairs of edges are not congruent to each other). Generally,
> you will find few exclusions in traditional definitions--you're more
> likely to find /additional/ definitions that define special cases. The
> goal is to generalize, not to exclude.
>
> VS-)
>
> On Sat, Jun 26, 2010 at 8:17 PM, Dan Goncharoff <thegonch at gmail.com>
> wrote:
>>
>> First, when did "rectangle" ever include "oblong"?
>>
>> Second, what would be the justification for using "ellipse" when
>> describing
>> a circle, or rectangle for square? It may be correct, but it's not
>> informative.
>>
>> DanG
>
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