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!
Presentation Suggestions:
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. <https://www.math.hmc.edu/funfacts>.
Fun Fact suggested by:
Michael Moody