Figure 1

Suppose that you have a rope around the equator of a
basketball. How much longer would you have to make the
rope so that it is 1 foot from the surface of the basketball
at all points? The answer is 2*Pi feet.
Now suppose you have the rope around the equator
of the earth. (Yes, a rope about 25,000 miles long!)
How much longer would you have to make the rope
so that it is 1 foot off the ground all the way around the
equator?
Surprise answer: it's 2*Pi feet also!
Presentation Suggestions:
Ask quickly so that students respond by intuition
rather than calculation.
Students are always amazed that the answer is
independent of the radius of the sphere!
The Math Behind the Fact:
Many will think that since 25,000 miles is so large,
you will need to add lots of rope to lift it off
of the equator. But extra circumference only scales as
2*Pi times the extra radius, which is 1 foot...
a somewhat surprising consequence
of simple geometry. See also Football Field.
How to Cite this Page:
Su, Francis E., et al. "Hugging the Equator."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
