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

 Messages: [ Previous | Next ]
 NealAgMan@nyc.rr.com Posts: 26 Registered: 12/4/04
Re: Is a rectangle a square?
Posted: Sep 28, 2004 4:09 PM

On 28 Sep 04 05:21:38 -0400 (EDT), Kit wrote:
>Pamela Paramour wrote:
>>Is a square a rectangle? ...
>> If you refer to Webster, ...

>
>Here is a nice story realy happend in german tv, sorry for my bad
>english.
>
>In the german quiz-show "Wer wird MillionÃ¤r" (Who becomes a
>millionaire) from January, 31 2003 the 8000-Euro question was:
>Every rectangle is:
>(a) a rhombus
>(b) a square
>(c) a trapezoid
>(d) a parallelogram.
>
>In this show _allways_ exactly one answer is (has to be) correct.
>The candidate was so confused, she didn't know if c or d is thw right
>answer, so she skipped the question and went home (with "just" 4000
>Euro). In the following days the broadcast station got tons of mails,
>letters and phone calls. Nearly all "mathematicians" regarded c _and_
>d as correct. The broadcast station told, that they looked up in

three
>different encyclopaedias, all three saying that trapezoids have only
>one pair of parallel sides. Taking this definition only d is correct.
>
>That's the problem. Who is right: More than 90 percent of the
>mathematicians saying a parallelogram is also an trapezoid or three
>
>The Solomonian solution. In the next week the candidate got a "new"
>8000-Euro-question.

You can't really say "who's right." It's just a question of how one
defines "trapezoid." In all American textbooks (except the University
of Chicago geometry textbook), a trapezoid is defined as a
quadrilateral with exactly one (or at most one) pair of parallel
sides. A parallelogram is defined as a quadrilateral with 2 pairs of
parallel sides.

Professor Conway, on the other hand, defines a trapezoid as a
quadrilateral with "at least" on pair of parallel sides. Using that
definition, the set of parallelograms is clearly a subset of the set
of trapezoids. Thus, using that definition, every rectangle is a
trapezoid, and also a parallelogram (as is the case with the usual
definition).

A similar problem exists with the definition of the kite. Most
writers say it is a quadrilateral in which AT MOST one diagonal is the
perpendicular bisector of the other. Conway would say that it is a
quadrilateral in which AT LEAST one diagonal is the perpendicular
bisector of the other. So using Conway's definition, every rhombus is
a kite.

There have been many, many message threads here on this issue.
Logically, there is a great deal to be said for Prof. Conway's
position.

Date Subject Author
8/7/00 John Benson
8/8/00 John Conway
8/8/00 Floor van Lamoen
8/8/00 John Conway
8/9/00 Floor van Lamoen
8/9/00 mary krimmel
8/9/00 Lee Rudolph
10/17/02 Julio Albornoz
10/18/02 Walter Whiteley
10/18/02 G.E. Ivey
10/28/03 Pamela Paramour
10/28/03 Walter Whiteley
10/28/03 John Conway
10/29/03 Mary Krimmel
10/29/03 John Conway
10/30/03 Rick Nungester
9/28/04 Kit
9/28/04 David W. Cantrell
9/28/04 NealAgMan@nyc.rr.com
9/28/04 Mary Krimmel
10/7/04 Donna W.
10/7/04 Donna W.
10/23/02 Ken.Pledger@vuw.ac.nz
10/25/02 Pat ballew
8/9/00 Jon Marshall
8/9/00 Floor van Lamoen
8/10/00 John Conway