The Other Rope Around The Earth

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So in the "Rope Around the Earth" problem the chap with the rope goes all the way around the Earth again to distribute the excess equally. Personally, I'd be too lazy to go round the Earth again, and instead I'd just prop it up in one place, taking it as high as possible/necessary to take up the slack.

So the question then is how high that tent pole (or clothes prop) will be? Again, the rope is light (which means it doesn't sag) and inextensible (so it doesn't stretch).

The answer isn't as simple and elegant as the rope around the earth answer, but it is perhaps just as surprising, if not more so.

The solution is on the page:

One of the Big List of Topics.

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