"Parametrise" or "parameterise" a curve?
In British English, which one is correct? Does one parameterise a curve or parametrise it?
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.
Both parameterize and parametrize are acceptable according to the ODO.
Both parameterise and parametrise are acceptable in BE as per Collins.
For consistency, I agree with MW above. Although one cannot necessarily argue on the basis of consistency in English, it is nice to try to keep things consistent. Thus, metrizable -> parametrizable -> parametrize, etc.
It depends on what you think "correct" means. If the majority of people on Google prefer parameterize, to me, that simply means that the majority of people do not think about it. The English language is too precious and wonderful an invention to be left for majority vote.
The same holds for the -ize vs -ise spelling. Although I am not American, I write -ize because it is more etymologically correct (Greek). Even Groves says so. The =ise spelling comes via French, and so has little to do with what one should write in English.