rectangle vs. square

[Tom Zurinskas]

Many years ago I asked folks to draw a 2-inch square on paper.  Came out on average about 3 parts high to 4 parts wide.  Like the aspect ratio of a TV.  I wonder if nowadays it'd be 9/16.

Tom Zurinskas, USA - CT20, TN3, NJ33, FL7+ 
see truespel.com phonetic spelling


 
 > 
> ---------------------- Information from the mail header -----------------------
> Sender: American Dialect Society <ADS-L at LISTSERV.UGA.EDU>
> Poster: victor steinbok <aardvark66 at GMAIL.COM>
> Subject: Re: rectangle vs. square
> -------------------------------------------------------------------------------
> 
> 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.
> 
> 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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