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UK usage[edit]

The UK definition here is obsolete. A trapezoid in the UK is either a synonym of UK trapezium or refers to a solid which has a cross-section with two parallel sides. I am collecting citations before altering the disputed definition. Dbfirs 21:30, 22 January 2008 (UTC)

I have marked the disputed UK usage as obsolete because it was last used with this sense in 1851 (R F Burton, Goa). The US websites which state that British usage is the reverse of US usage are either referring back to obsolete usage or are thinking of German and French usage which does appear sort of reversed, though of course the words are different. I would be interested to know if anyone can find British usage of Trapezoid meaning irregular quadrilateral since 1851. I am compiling a lits of recent citations to prove that current usage, though rare, is closer to that in the US, with the possible extension to prisms with a cross-section having two parallel sides. I am still working on this. If I succeed, and find no recent contradictory usage, then I will adjust both this definition and the article in Wikipedia, both of which I believe to be confusing and inaccurate. What does anyone else think? I would be especially interested in opinion from outside America. Research of US websites seems to support the error, but such sites give no references or sources except old US dictionaries which probably base their definitions on obsolete usage. Dbfirs 21:56, 22 January 2008 (UTC)

So far I have found about twenty current UK uses of trapezoid and not a single one of them is a synonym for the US trapezium. I will edit the definition when I have categorised the citations. Dbfirs 23:18, 22 January 2008 (UTC)
I've put the web-site citations on the citations page. I've still to search for citations in print, but don't know how to restrict a search to UK publications. I am editing the entry to reflect current usage. Dbfirs 07:21, 14 April 2008 (UTC)
So how can you explain the fact that, of all the other dictionaries I've checked (both dead tree and online)
  • not one of them states that the UK-specific meaning of trapezoid is even dated, let alone obsolete?
  • those I can make out to be British-made unanimously give the meaning corresponding to UK trapezium as being an Americanism?
-- Smjg 12:39, 15 June 2008 (UTC)
Please see the citation page for my evidence. Despite extensive searching, I have not found a single current usage in the sense given in old dictionaries (though I agree that this was, for a short time in the past, British usage). Dbfirs 10:04, 20 July 2008 (UTC)
To answer the specific (and valid) points made by Smjg:
  • Dictionary definitions quickly become obsolete as usage changes. Most on-line dictionaries just copy the hundred-year-old definitions from Merriam-Webster without checking if that usage is still current.
  • "Americanisms" very quickly become standard usage in Britain. I could find thousands of other words that started out as "Americanisms" and are now considered standard English in Britain.
I am quite happy to be proved wrong if you can find one current usage to support Merriam-Webster's claim (though it was no doubt true at the time it was compiled). The best I could come up with was one Wiktionarian who knew someone who remembered this usage from long ago. The term trapezoid is rare in the UK anyway, perhaps because it has had different meanings in various centuries. Dbfirs 19:53, 20 July 2008 (UTC)

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[UK usage]

The last usage in the obsolete sense given in the definition is in 1851. I am compiling a list of modern citations. France, Spain, and Italy may use similar words with this meaning, but not the UK or Australia. Can anyone else confirm this? Dbfirs 13:29, 23 January 2008 (UTC)

I've taught in the US, where we say "trapezoid" and in AU where we say "trapezium". I don't know about GB. It's a quadrilateral, which has one pair of opposite sides that are parallel to each other and another that aren't (usually). I mean both rhombi/rhombuses & rectangles are parallelograms & may be squares, but squares are always rectangular rhombi. Do you say "flying trapeze"? :)--Thecurran 14:45, 24 January 2008 (UTC)
Sense one is obsolete in the UK, although current in the US. In Britain we call it a trapezium now. No idea why. Widsith 09:59, 25 January 2008 (UTC)
From my research so far (about 20 independent definitions clearly implied) the UK and Commonwealth usage of trapezoid is very close to the US usage, with an extension to 3-D. Has anyone ever heard a modern usage of trapezoid to mean a general quadrilateral with no special properties? Dbfirs 10:09, 25 January 2008 (UTC)
A trapezoid (in UK) does have special properties: specifically, no two of its sides are parallel. Widsith 10:16, 25 January 2008 (UTC)
So a kite is a trapezoid? Dbfirs 19:49, 25 January 2008 (UTC)

Here is the OED's fascinating note on how the terms came about (subbed down slightly): Widsith 10:26, 25 January 2008 (UTC)

With Euclid, τραπέζιον included all quadrilateral figures except the square, rectangle, rhombus, and rhomboid; into the varieties of trapezia he did not enter. But Proclus retained the name τραπέζιον only for quadrilaterals having two sides parallel, subdividing these into the τραπέζιον ἰσοσκελές "isosceles trapezium", having the two non-parallel sides (and the angles at their bases) equal, and σκαληνὸν τραπέζιον "scalene trapezium", in which these sides and angles are unequal. For quadrilaterals having no sides parallel, Proclus introduced the name τραπεζοειδές = trapezoid. This nomenclature is retained in all the continental languages, and was universal in England till late in the 18th century, when the application of the terms was transposed, so that the figure which Proclus and modern geometers of other nations call specifically a trapezium (F. trapèze, Ger. Trapez, Du. trapezium, It. trapezio) became with most English writers a trapezoid, and the trapezoid of Proclus and other nations a trapezium. This changed sense of trapezoid is given in Hutton's Mathematical Dictionary, 1795, as ‘sometimes’ used – he does not say by whom; but he himself unfortunately adopted and used it, and his Dictionary was doubtless the chief agent in its diffusion. Some geometers however continued to use the terms in their original senses, and since c 1875 this is the prevalent use.

Thanks for the clarification. We obviously must blame Proclus for introducing another word to add to the confusion. As far as I can see, almost everyone except the French use trapezoid in modern usage (as opposed to definitions in old dictionaries) in the US sense of a quadrilateral with exactly two sides parallel, or to refer to one of two solids with some faces having this property (trapezoidal prism or frustrum of right square-based pyramid). I am collecting citations specific to the UK for this modern usage. Only the word trapezium currently has a different meaning in the US. Have you come across any modern usage of trapezoid to mean a quadrilateral with no sides parallel (e.g. a kite????) Dbfirs 19:49, 25 January 2008 (UTC)