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.
Reduce R to 0 and you have your basic circle with the circumference of 1m. Funny stuff this ;-).
Planeten: I did the same thing; the one meter circumference has the same radius as the Delta r based on any other size sphere. It surprised me that you get the same delta r, no matter how big the starting size of the sphere.
Excellent! What a fun little problem.
My first impression is that
r = C/(2 x π).
But I also know pre-calculus, so
Δr = ΔC/(2 x π)
So every Δ one adds to the circumference obviously adds 0.159 x Δ to the radius.
No need to work out the two separate answers.
Many counter-intuitive things become intuitive, once you know some math.