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© 1999-2010 by Francis Edward Su

From the Fun Fact files, here is a Fun Fact at the Easy level:

Spherical Bands

 Figure 1

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:
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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.

Su, Francis E., et al. "Spherical Bands." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Keywords:    multivariable calculus
Subjects:    calculus, analysis
Level:    Easy
Fun Fact suggested by:   Michael Moody
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