Gareth, Ohhh, now *I* see what you mean by the metric inherited from R^2, which of course *does* depend on the embedding. I'm so used to thinking about Riemannian metrics, that this is wha I was referring to on simple closed curves (but without saying so). (Sorry about that. At least I had the wisdom not to post it to the group.) But all's well that ends well, right? Regards, Dan << Ohhh, I see. I entirely misunderstood. I thought you meant the metric induced by the obvious embedding of G in R^2. With the clarification you've now provided, I agree that that's a fine definition, not least because it's equivalent to the one I prefer :-).

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