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Return of the Grazing Goat in '\(n\)' Dimensions

by Mark D. Meyerson (U. S. Naval Academy)

This article originally appeared in:
College Mathematics Journal
November, 1984

Subject classification(s): Calculus | Advanced Calculus
Applicable Course(s): 4.11 Advanced Calc I, II, & Real Analysis

Generalizations of the problem: A goat is tethered to the edge of a disc shaped field of radius \(r\). The goat's rope is of length \(kr\). If the field is \(n\)-dimensional, what fraction of it can the goat reach, and what happens as \(n\) approaches infinity?

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