Have you ever considered snugly wrapping a string around the entire Earth? If you did that, and then you added merely one additional meter of string (which would then raise the string uniformly off the surface of the Earth), how much higher off the ground would that new string be (the original long string, plus one additional meter)? Here's a simple statement of the problem, allegedly first used by Ludwig Wittgenstein. Here the math. Wonderful problem and surprising solution.