I added a puzzle to my Pi Day post. For clarity, here’s the question:
Suppose you had a string that laid exactly on the surface completely around the Earth at the equator. The length of the string is immaterial. But suppose you add exactly three feet to the length of the string. How high would a string one earth’s circumference plus three feet stand off the surface?
And how how would a string one Earth’s circumference plus three feet stand off the surface, if a string were stiff enough to stand off the surface at all?
About six inches.
That is, the radius of the circle described by the rule will be about six inches longer than the radius of the can.
You can try the experiment with anything handy. A steel rule and a garbage can makes a convenient setup. Wrap the rule snugly around the top of the can. Let out three more feet, and see what you get. You will get the same result with any round object, from a molecule to a universe.
Now, the joker is this. This puzzle originally appeared in the American Mathematical Society Journal, where the answer was given as a foot. They were wrong.