A Cute Puzzler

This came not from Car Talk but an essay I read. Imagine a ribbon girdling the Earth’s circumference. Then add just one meter to the ribbon’s length. So there’d be a little slack. How big is the gap between the ribbon and the Earth’s surface?

Most people would guess it’s extremely tiny — that was my intuitive answer — a mere meter being nugatory over such a huge distance. But the surprising answer is about 16 centimeters. If the ribbon was snug around the Equator before, how could an added meter make it that much less snug?

My wife and I puzzled over this and soon figured out the simple solution, without even using pencil and paper:

A circle’s diameter is the circumference divided by Pi (3.14+) — i.e., a bit less than a third. If two circumferences differ by a meter, then their diameters differ by almost 1/3 of a meter — say about 32 centimeters — or about 16 centimeters at each end.

The essay said only mathematicians and dressmakers get this right.

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