# “Parametrise” or “parameterise” a curve?

In British English, which one is correct? Does one parameterise a curve or parametrise it?

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I have been using parametrize – Santosh Linkha Aug 28 '12 at 8:36
The main heading in the Oxford English Dictionary says "parameterize"; the other possibilities are also recorded: "parameterise", "parametrise", "parametrize". – Zhen Lin Aug 28 '12 at 9:49
@ZhenLin Please post this as an answer instead of a comment. – MετάEd Aug 29 '12 at 6:18
I would assume then that parametise is dead wrong ? – user68654 Mar 12 '14 at 19:58

Both parameterize and parametrize are acceptable according to the ODO.

Both parameterise and parametrise are acceptable in BE as per Collins.

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True that. I'd go with parameterize, ordinarily, because parameter is the root word, making it more clear. If I were feeling lazy, I'd go with parametrize. – Wolfpack'08 Sep 2 '12 at 8:14

This depends a bit on how one defines "correct". Various dictionaries might accept either or both uses. If you go by the scientific literature, both seem to be widely used.

On the other hand, if you are looking for a spelling that is suggestive of the correct meaning, then you should go with "parametrize" (or "parametrise").

You are not transforming the curve into a parameter, nor are you making it like a parameter. You are making the curve into a parametric curve (not a "parameteric" curve).

Similarly, one does not "meterize" a topological space to make it into a metric space, and likewise, Thurston didn't pose a "geometerization" conjecture that one can turn certain topological 3-manifolds into living, breathing geometers.

Also, for what little it's worth, as far as mathscinet is concerned, "parametriz*" is almost twice as frequent as "parameteriz*" (13961 hits vs 7720). Not to mention that the earliest use of "parametriz*" in that database is from 1933:

McShane, E. J. Parametrizations of saddle surfaces, with application to the problem of plateau. Trans. Amer. Math. Soc. 35 (1933), no. 3, 716–733. 53A10 (49Q05)

predating the first recorded use of "parameteriz*" by 3 years:

Morse, Marston; A special parameterization of curves. Bull. Amer. Math. Soc. 42 (1936), no. 12, 915–922.

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A difference of three years is not really significant. It's possible both where in common usage in non-published text concurrently and one just happened to get published a few years earlier. If it were a much longer duration that might be a better indicator of what was common at the time. – Huckle Mar 7 at 1:38
"a spelling that is suggestive of the correct meaning" It seems this is the crux. Apparently parametri[s/z]e comes from math circles re parametric curves; parameteri[s/z]e seems borrowed to talk about applying parameters to something in general to modify the outcome. Programmers as a matter of course apply parameters to a display to show/hide/add/subtract or otherwise alter what a user sees depending on applicable parameters, so it seems both are valid based on context? – gordon Jul 15 at 15:36

For what it's worth, parameterize has 1,100,000 search results on Google, while parametrize has 500,000. I would take that as evidence that both are acceptable and in widespread usage.

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Given the various complex strategies for query expansion used by Google Search, I wouldn't assume it's worth very much to count hits for variants like this. – Will May 5 at 13:14
I would expect the words "parametrization" and "parameterization" to be just as commonly used as their verb counterparts. – user3932000 May 13 at 5:46
Perhaps huge demand for coders tilts the ratio of them vs mathematicians so no surprise the Google hits are favoring parameteri[s/z]e over time? (see my comment above re difference of usage/context) – gordon Jul 15 at 15:42