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The Volume of the Unit n-Ball

Harold R. Parks
Mathematics Magazine
Vol. 86, No. 4 (October 2013), pp. 270-274
DOI: 10.4169/math.mag.86.4.270
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.4.270
Page Count: 5
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The Volume of the Unit n-Ball
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Abstract

Summary Two simple proofs are given for the fact that the volume of the unit ball in n-dimensional Euclidean space approaches 0 as n approaches ∞. (Some authors use the term “unit sphere” for what is here called the unit ball.) One argument involves covering the unit ball by simplices. The other argument involves covering the unit ball by rectangular solids.

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