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smyrlis
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What's a nice argument that shows the volume of the unit ball in $\mathbb R^n$ approaches 0?

Before you close for "homework problem", please note the tags.

Last week, I gave my calculus 1 class the assignment to calculate the $n$-volume of the $n$-ball. They had finished up talking about finding volume by integrating the area of the cross-sections. I asked them to calculate a formula for $4$ and $5$, and take the limit of the general formula to get 0.

Tomorrow I would like to give them a more geometric idea of why the volume goes to zero. Anyone have any ideas? :)

Comm wiki in case people want to add/modify this a bit.

B. Bischof
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