# 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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