Date: Sep 28, 2004 10:38 AM Author: David W. Cantrell Subject: Re: Is a rectangle a square? steinadler@gmx.de (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

> 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

correct.

[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

wrong.

David Cantrell