Posted by: Alexandre Borovik | June 25, 2008

## Andean Architecture: The power of the trapezoid

From John Baldwin:

You may be intrigued by the short essay and photos I have posted at

http://www2.math.uic.edu/~jbaldwin/pub/incaarch.htm

It suggests the mathematical problem. How you state and prove the statement: A trapezoid is stronger than a rectangle.

## Responses

1. It is a rather annoying fact that the Americans use “trapezoid” for that which the British call a “trapezium”, and “trapezium” for a quadrilateral with no special form.

2. Dr. Rick, I’ve never heard an American say “trapezium” for a generic quadrilateral. In fact, I’ve only ever heard an American say it to point out that the Brits use a different word. Do you have a citation to the corpus?

3. http://en.wikipedia.org/wiki/Trapezoid says “In North America, the term trapezium is used to refer to a quadrilateral with no parallel sides. The term trapezoid was once defined as a quadrilateral without any parallel sides in Britain and elsewhere, but this usage is now obsolete.” and cites Merriam-Webster for the American usage of trapezium. If it is now also obsolete, I am delighted.

Mathworld also provides the “American definition” of trapezium: http://mathworld.wolfram.com/Trapezium.html

4. I still see no citation to the corpus. This is a linguistic question. You say that Americans say “trapezium” in that case. Neither I nor anyone I know has ever heard anyone using the term in that sense.

Mathworld cites no source for its assertion. Wikipedia cites Merriam-Webster’s definition from 1913 American usage. The Oxford English Dictionary has similarly-dated British uses in the more general sense.

So what we have here is that the term “trapezium” meant a generic quadrilateral other than a paralellogram. It did so until shortly after the turn of the 20th century. At that point, British usage restricted the term to those quadrilaterals with one pair of sides parallel, and American usage adopted the term “trapezoid” for that figure. I have found only one citation of the more general usage of “trapezium” since that era.

Just accept that you really don’t know what terms Americans actually use, and stop getting all uppity over how horrendously confusing it is.

5. John, I seem to have upset you, for which I apologise. If the sources I quoted are wrong, I am – as I said – delighted that an extra source of potential confusion has been removed. I rather thought that Mathworld might know what it was talking about with respect to American mathematical usage; if you find that an unforgivable assumption, so be it. I am obviously not going to argue with an American about what American usage is, I’m not an idiot.

No implication that the (alleged or actual) American usage was in any sense wrong or inferior was made or intended; I know there are some Englishmen who like nothing better than knocking American usage for the sin of not being English, but I am not one of them. I have no idea why you think I was being “uppity”. I know you’re avowedly unapologetic, but this time I think you owe me one, too.

6. I know there are some Englishmen who like nothing better than knocking American usage for the sin of not being English, but I am not one of them.

And yet in a recent thread you were very opinionated about the differences in usage. Here the only comment you make is how “annoying” you find the American usage (which isn’t even accurate) when that wasn’t even the point of the post.

You come saying (unprovokedly) that American usage is annoying due to an inaccurate second-hand report on it and I owe you an apology?

7. John, I really don’t know what you mean. The only thread I can think of in which I talked at all about American or English teminology was http://micromath.wordpress.com/2008/05/25/first-tremors-of-a-tectonic-shift/ , in which I attempted to explain the (bizarre and confusing) English usage to somebody who asked about it, on Sasha’s request. If you mean something else and I’ve forgotten about it, please remind me.

I called the fact that the two usages differ, and that – according to credible sources – actually contradict each other (if you tell me these sources are wrong, I am prepared to accept your unsubstantiated word) annoying. I can see how it could be misunderstood, if you were feeling defensive, but it really wasn’t intended to say that. I am not aware of anywhere on this blog (or anywhere else, for that matter) that I’ve criticised American usage; as anybody who knows me knows, it would be severely out of character to do so.

I’ve apologised for being wrong, since you tell me I am, and for upsetting you. You have been the one doing the name-calling, unless you somehow meant “uppity” kindly, and so yes, I do think you owe me an apology. Never mind.

8. My word is substantiated by the Oxford English Dictionary, and by one of your very own sources, which states that the usage you complain about was the standard British one through the 19th century.

You attacked American usage, I did the legwork to show that you don’t know what you’re talking about. That’s all.

9. As I’ve said, I didn’t attack the usage, or complain about it, only regretted the difference; even if you don’t think that’s completely clear in my first post, it is in every subsequent one. I accepted as soon as it was raised the possibility that I had been misled by my sources. I didn’t call you any names, or accuse you of opinionated attacks on usage elsewhere (which you have yet to substantiate, probably because you can’t). Nor do I intend to, because I believe in being civil, especially on the blogs of my friends. Good day.