Take any sphere
and slice it up by parallel knives 1 inch
apart. The areas of the spherical bands
between the cuts (on the surface
of the sphere) are exactly the same area!
Draw a suggestive picture!
The Math Behind the Fact:
This begins to make sense when you reflect on it. The
bands are wider near the top of the sphere because it
is more curved there, but the diameter is smaller there.
These effects cancel exactly! It is makes a
nice homework exercise in multivariable calculus.
How to Cite this Page:
Su, Francis E., et al. "Spherical Bands."
Math Fun Facts.