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Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to exactly half an acre?
Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.
It sounds like high school geometry, but mathematicians and math enthusiasts have been pondering this problem in various forms for more than 270 years. And while they’ve successfully solved some versions, the goat-in-a-circle puzzle has refused to yield anything but fuzzy, incomplete answers.