Copyright ©1997 by Paul Niquette. All rights reserved.
diagram shows that the length of the original band
can be calculated by multiplying the diameter of the earth (assumed to
be approximately 8,000 miles) by
+ 10 feet = (8,000 miles + x)
x = 10 feet / = 3.183 feet
...half of which (1.59 feet = 1 foot 7 inches) represents
the gap between the lengthened band and the surface of the earth.
oo-ha! That's the sound of a sophisticated puzzle solver making a discovery. In this case, he or she will observe that the diameter of the earth -- that the gap would be the same (1 foot 7 inches) whether the band were wrapped around the moon or a basketball or a marble.
The solution, in fact, is merely the radius of a circle
that has a 10-foot circumference.