# Return of the Grazing Goat in '$$n$$' Dimensions

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

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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