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Comment on Very Wrong Mathparent

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infinite, or at least highly dependent on the thickness of the rope

The latter. But that's only if it's not somewhat taut. Some tension brings it closer to a circle and makes the actual thickness pretty unimportant.

But I like the idea overall. It means that lifting up the string makes it smoother and it actually needs less length. How's that for being unintuitive?

Exactly, if you're only 1cm off the surface you follow every nook and cranny. If you're 10km off the surface only Everest is a blip.

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