Origin of KITE
Pat Ballew
> > asked, "Was the geometric polygon named after the "toy", or the toy named after
> > the geometric polygon?" Does anyone know the origin of the geometric term?
> > Thanks for your help.
>
> I think the geometric usage is quite recent -- probably the result of
> someone noticing a hole in the traditional classification. The kite
> you fly is named after an Old English word for a predatory bird.
>
> --
>
>
> _
> | | Robert W. Hayden
> | | Department of Mathematics
> / | Plymouth State College
Actually, I think the shape of a kite(toy) that looks like the geometric
kite (and probably the bird) is relatively new also. I am desperatly trying
to think where I read that to check it.
Hakke Yoi
Pat Ballew
Edgren HS
Misawa, Japan
bal...@emh.misawa.af.mil
Don Luepke
question today in class that I couldn't answer. We are studying quadralaterals
and specifically "kites". (A quadralateral with two pairs of consecutive sides
conguent, but opposite sides not congruent)
His question is sort of a "chicken-egg" query. He
asked, "Was the geometric polygon named after the "toy", or the toy named after
the geometric polygon?" Does anyone know the origin of the geometric term?
Thanks for your help.
Don Luepke
Concordia Lutheran High School
Fort Wayne, IN
Michael Keyton
ortho-diagonal quadrialteral (a quadrialteral with perpendicular diagonals).
There are several good theorems for the orthodiagonal quadrilateral.
def.: the quad. formed by connecting consecutively the midpoints of a
quad. will be called a "varignon quadrilateral" (namd after its discoverer).
Theorem 1: The varignon quadrilateral of an orthodiagonal quad. is a
rectangle.
Theorem 2: If the varignon quad is a rectangle, then the quad. is an
orthodiagonal quad.
Theorem 3: Take any quadrilateral, construct squares on the sides of the
quad. in the exterior.Form a quadrilateral by connecting consecutively
the centers of these squares. This quadrilateral is ortho-diagonal.
Michael Keyton
St. Mark's School of Texas
On Wed, 10 Jan 1996, Bob Hayden wrote:
> > asked, "Was the geometric polygon named after the "toy", or the toy named after
> > the geometric polygon?" Does anyone know the origin of the geometric term?
> > Thanks for your help.
>
> I think the geometric usage is quite recent -- probably the result of
> someone noticing a hole in the traditional classification. The kite
> you fly is named after an Old English word for a predatory bird.
>
> --
>
>
> _
> | | Robert W. Hayden
> | | Department of Mathematics
> / | Plymouth State College
> | | Plymouth, New Hampshire 03264 USA
> | * | Rural Route 1, Box 10
> / | Ashland, NH 03217-9702
> | ) (603) 968-9914 (home)
> L_____/ hay...@oz.plymouth.edu
> fax (603) 535-2943 (work)
>
Michael Keyton
related to the German "kauz" which is a type of owl.
Here is the best instance of why quadrilaterals should be defined in
terms of their diagonals rather than their sides. Also using an
exclusive definition is poor from a mathematical point of view, for then
every theorem of a rhombus has to be restated.
Def. A kite is a quad. such that one diagonal is the perpendicular
bisector of the other.
Note: if diagonal means segment then the non-convex kite does not exist.
So when diagonal is used, it must be ambiguous as to whether it refers to
a segment of to the line containing the segment.
THis is not a difficulty, the same sort of construction occurs with a
radius and for a diameter.
Def. A rhombus is a quad.
such that each diagonal is the perpendicular bisector of the other.
Theorem 1: A rhombus is a kite.
Since the language for Kites is so deficient, this gives students a place
for great lee-way in naming the parts of a kite.
My best from students in the past.
The diagonal that is the perpendicular bisector, transdiagonal; or
symmetry diagonal.
The diagonal bisected, versdiagonal.
The angles of the versdiagonal, iso-angles.
THe angles of the transdiagonal, trans-angles.
Michael Keyton
On Wed, 10 Jan 1996, Don Luepke wrote:
> This is another first time message to the forum. I had a student who posed a
> question today in class that I couldn't answer. We are studying quadralaterals
> and specifically "kites". (A quadralateral with two pairs of consecutive sides
> conguent, but opposite sides not congruent)
> His question is sort of a "chicken-egg" query. He
> asked, "Was the geometric polygon named after the "toy", or the toy named after
> the geometric polygon?" Does anyone know the origin of the geometric term?
> Thanks for your help.
>
John Conway
On Wed, 10 Jan 1996, Don Luepke wrote:
> This is another first time message to the forum. I had a student who posed a
> question today in class that I couldn't answer. We are studying quadralaterals
> and specifically "kites". (A quadralateral with two pairs of consecutive sides
> conguent, but opposite sides not congruent)
> His question is sort of a "chicken-egg" query. He
> asked, "Was the geometric polygon named after the "toy", or the toy named after
> the geometric polygon?" Does anyone know the origin of the geometric term?
> Thanks for your help.
>
> Don Luepke
> Concordia Lutheran High School
> Fort Wayne, IN
The quadrilateral (note the spelling!) was named after the
toy. This name for a certain kind of quadrilateral has only come
into vogue quite recently - a few decades ago most authors would say
something like
a "kite-shaped" quadrilateral
leaving those quotation marks in to show that they felt a bit
uneasy about using this informal term in a technical sense.
The toy "kite" was in term named after the bird, and about
a century ago, people would have put explicit quote marks around
this word when using it for the toy!
By the way, the term "quadrilateral" only came into routine
use for a general four-sided polygon about a century ago,
although there are some isolated early instance of its use
in specialized senses. The older term was "trapezoid"; but (as
I said here some time ago) this got confused with "trapezium",
necessitating the introduction of a new word.
[I'll briefly repeat this story, because it may interest
more people than it reached before. Proclus introduced
the words whose English versions became "trapezium" and
"trapezoid" for
A quadrilateral with just 2 parallel sides (trapezium)
A quadrilateral with no parallel sides (trapezoid).
In a book published around 1800, Hutton reversed this
usage, and this reversed usage "stuck" for a time in both
Britain and America. Around 1870, the British managed to
get back to the original usage, but the American usage
stayed with the flipped version. The dictionaries still
tend to say that the words have the above senses in British
usage, but the reversed sense in American usage, but the
truth is that both words "trapezium" and "trapezoid"
now only mean the figure with two parallel sides; "trapezium"
being the preferred term in England, and "trapezoid" in the US.
So a separate word was needed for the arbitrary 4-sided figure,
and "quadrilateral" was gradually adopted from about 1850.
Of course modern mathematicians use the terms in the more
rational "exclusive" sense; but that's another story.
John Conway