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Re: Are squares rectangles?
Posted:
Oct 23, 2002 1:13 AM
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In article <vyhqqahgm1ei@legacy>, JCAlbornoz@aol.com (Julio Albornoz) wrote:
> .... In reference to rectangles and squares, weather a square can be
> defined as a "kind of rectangle" remains to be mathematically proven.
> ....
George Ivey has already pointed out that it's not a question for
mathematical proof.
However, the word "oblong" gives a perfectly good solution to this
particular problem. In the definitions in Euclid Book I, English
translators have used "oblong" for the Greek "heteromekes" from Simson
(18th century) to Heath (the standard 20th century translation). Heath
says: "Of quadrilateral figures, a square is that which is both
equilateral and right-angled; an oblong that which is right-angled but not
equilateral; ...."
Our modern word "rectangle" can most conveniently encompass both
cases, so every rectangle is either a square or an oblong.
This is regularly overlooked in two other contexts. The four-group
is very often called the group of a rectangle, ignoring the fact that some
rectangles are square (so have a bigger group). I always tell my students
that it's the group of an oblong. Even more blatant is the term
"rectangular matrix" which people use for a matrix which isn't square.
All matrices are rectangular. A non-square one is an oblong matrix.
(Now I dismount from that hobby-horse. :-)
Ken Pledger.
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