From our Dr. Math archives:
The Goat in the Field Problem
A farmer owns a circular field of grass (radius = r). He tethers a goat via a length of rope (R) to the circumference of the field. What ratio r/R must the farmer choose so that the goat can only eat half the area of grass?
The problem looks simple, but calculus must not be used.
. . .This problem is germane to communications physics, for instance determining the optimum siting of mobile telephone base stations (you can imagine the circles as the coverage areas of the radio signals). It is also useful in determining the optimum placement for a jammer transmitter so as to cause maximal disruption...
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