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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3 Responses to “A cute puzzler”

  1. Paul Landsberg Says:

    Cute! I had 3 kids go through high schools over the past 8 years and each of them would have solved it by end of 10th grade, if not by 9th grade. While I know it is in vogue to bash millennials and the core curriculum, it is scary what they have to learn, when they have to learn it, and at what pace. This year one of their schools actually let 9th graders take calculus.

  2. Lee Says:

    If you had a dress that covered the surface of the earth snugly and then added a square meter of fabric … and you assume that the fabric is stretchy in a way that the added square meter gets distributed evenly over the whole surface of the earth … how high above the ground would the expanded dress then be?

  3. rationaloptimist Says:

    16 cm! Same problem.

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