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

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?

Old Node ID:
758
Author(s):
Mark D. Meyerson (U. S. Naval Academy)
Publication Date:
Wednesday, August 3, 2005
Original Publication Source:
College Mathematics Journal
Original Publication Date:
November, 1984
Subject(s):
Calculus
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Publish Page:
Furnished by JSTOR:
File Content:
Rating Count:
28.00
Rating Sum:
84.00
Rating Average:
3.00
Author (old format):
Mark D. Meyerson
Applicable Course(s):
4.11 Advanced Calc I, II, & Real Analysis
Modify Date:
Wednesday, February 1, 2006