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

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David W. Cantrell

Posts: 3,395
Registered: 12/3/04
Re: Is a rectangle a square?
Posted: Sep 28, 2004 10:38 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply (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 Millionär" (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
> encyclopeadias saying the opposite?
> The Solomonian solution. In the next week the candidate got a "new"
> 8000-Euro-question.

This is actually rather complicated.

First, we should know precisely which German word was used for (c). Was it
Trapez or Trapezoid? One of my German-English dictionaries says

Trapez means trapezoid or trapezium

and that

Trapezoid (German) means quadrilateral.

Of course, I can't say for sure that my dictionary is correct. But I can
tell you that the English words "trapezoid" and "trapezium" have different
meanings on different sides of the Atlantic. One of my mathematics
dictionaries (which happens to have editors from both Canada and the UK)
says that

(1) A quadrilateral having two parallel sides of _unequal_ length is
called a trapezium in the UK and a trapezoid in North America.

and that

(2) A quadrilateral with neither pair of sides parallel is called a
trapezoid in the UK and a trapezium in North America.

I must add that, as a North American mathematician myself, I disagree
with (1). For me, a trapezoid is simply a quadrilateral having two parallel
sides. Those sides need not be of unequal length. Furthermore, note that
I only said "two", _not_ "exactly two". Thus, for me, both (c) and (d) are

[BTW, I also question the correctness of (2), but I don't often use the
word "trapezium".]

But if (1) and (2) are used precisely as given above, then regardless of
which side of the Atlantic an English speaker resides on, (c) must be

David Cantrell

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