Trapezoid — a 4-sided level shape with straight sides that has actually a pair of opposite political parties parallel.

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Trapezium — a 4-sided level shape with right sides and NO parallel sides.

The meanings of the 2 words are specifically reversed between the US and also British interpretations.

I don"t know exactly how relevant this is, but in general the -oid suffix (humanoid, android, asteroid) way "similar come (but not actually)", vice versa, -ium (consortium, auditorium, emporium) is a "noun-forming" suffix, sometimes having actually the sense of bigger or an ext complicated.

The brothers definitions therefore seem much more "logical" come me - ours trapezoid is superficially "like" a trapezium (it has 4 sides), but it"s no actually the exact same (no sides are parallel). It"s likewise tempting to think Brits were utilizing the indigenous first.

Is there any explanation for just how this US/UK distinction came about?


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The trapezium short article at MathWorld gives the adhering to explanation (referencing OED) of exactly how the U.S.- and U.K.-differing meanings arose:

According to the Oxford dearteassociazione.org Dictionary, the confusion of trapezium and also trapezoid between the United states and great Britain dates ago to an error in Hutton"s Mathematical dictionary in 1795, the very first work that its type in the united States, which directly reversed the welcomed meanings. Hutton assigned trapezium come "no sides parallel" and also trapezoid to "two political parties parallel" (Simpson and Weiner 1992, p. 2101).

After 1795 in the joined States, the Hutton definitions came to be standard, when in the brother empire, the Proclus interpretations remained standard. Two century later, the controversy remains. Nation by country, an ar by region, and also even teacher by teacher, the meanings of trapezoid and also trapezium are commonly swapped.

Note, "the Proclus definitions" were mentioned previously in the MathWorld article:

Proclus (also Heron and also Posidonius) split quadrilaterals right into parallelograms and also non-parallelograms. Because that the latter, Proclus assigned trapezium come "two sides parallel," and trapezoid come "no political parties parallel." Archimedes additionally defined a trapezium as having precisely two parallel political parties (Heath 1956, pp. 188-190).

Edit: about distinctions make by Euclid, Proclus, Archimedes and also others, ~ above pages 189 and 190 the volume ns of thomas L. Heath"s The Thirteen books of Euclid"s Elements (1956) us find:

As Euclid has actually not yet defined parallel lines and also does no anywhere specify a parallelogram, the is no in a position to do the an ext elaborate group of quadrilaterals attributed by Proclus to Posidonius and appearing also in Heron"s Definitions. It may be displayed by the complying with diagram, distinguishing seven types of quadrilaterals.

The diagram indigenous Heath (representing quadrilateral group per Posidonius, Proclus, and Heron) is shown below. One may compare this diagram through that shown in wikipedia"s quadrilateral taxonomy section. That taxonomy go not have the indigenous trapezoid in it, since it claims "trapezium here is ... British" and "inclusive definitions are provided throughout". (A british trapezoid is a convex quadrilateral the is no a brother trapezium. The only categories that the taxonomy that have the right to contain a convex brother trapezoid room the quadrilateral, simple, convex, tangential, cyclic, kite, and also bicentric categories.)

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Heath then continues:

It will be it was observed that, when Euclid in the above an interpretation classes as trapezia all quadrilaterals other than squares, oblongs, rhombi, and rhomboids, words is in this classification restricted to quadrilaterals having actually two sides (only) parallel, and also trapezoid is supplied to signify the rest. Euclid shows up to have actually used trapezium in the limited sense of a quadrilateral with two political parties parallel in his publication περι διαιρεσεων (on departments of figures). Archimedes offers it in the same sense, however in one place describes it more precisely together a trapezium with its 2 sides parallel.

I think the very first it in the last sentence describes trapezium yet don"t recognize what the second it refers to. Consequently, that is unclear come me even if it is MathWorld"s assertions re Archimedes" interpretations are correct.

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Edit: In a trapezium and also trapezoid article on The linguist List, we read the adhering to quote indigenous Oxford dearteassociazione.org dictionary (under feeling (c) the trapezium):

An rarely often, rarely quadrilateral having neither pair that opposite sides parallel. (The usual feeling in England indigenous c1800 come c1875. Now rare. This feeling is the one the is traditional in the U.S., however in practice quadrilateral is offered rather 보다 trapezium.)

This suggests that throughout the 80 years after Hutton (a much-published dearteassociazione.org mathematician, born 1737 in ~ Newcastle-on-Tyne, 1778 Copley Medal recipient) gave the definitions now in usage in the U.S., those same meanings were likewise in usage in England, later on falling into disuse (ie gift reversed or set aright) in England. The OED goes on to indicate that in the U.S., the all-encompassing ax quadrilateral quite than (U.S.) trapezium is used to describe quadrilaterals that carry out not loss into more-specific category such together squares, rectangles, parallelograms, (British) trapezia, etc.