Clue to Puzzle #41: Rope Around the Earth

41. Suppose you tie a rope tightly around the Earth's equator. You add an extra 3 feet to the length. All around the Earth the rope is raised up uniformly as high as is possible to make it tight again. How high is that?

picture of the earth with a rope around it This puzzle is somewhat counter intuitive. If you have reasoned the answer and can't believe it, you are probably right. In the answer i give a rigorous mathematical proof for the general case, but you can do it without that.

The only equation you need to know it the relationship between the circumference of a circle and it's radius is given by R = C/2π

Another big clue might be that whilst I can tell you the radius of the earth is 20,902,231 feet you don't need to know it.

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