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After centuries, a seemingly simple math problem gets an exact solution
by Steve Nadis, Contributing Writer
Quanta Magazine Translate This Article
9 December 2020
On 9 December 2020 Quanta Magazine reported:
Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now. 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?
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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.
Even after all this time, 'nobody knows an exact answer to the basic original problem,' said Mark Meyerson, an emeritus mathematician at the U.S. Naval Academy. 'The solution is only given approximately.'
But earlier this year, a German mathematician named Ingo Ullisch finally made progress, finding what is considered the first exact solution to the problem -- although even that comes in an unwieldy, reader-unfriendly form.
... Of course, it won't upend textbooks or revolutionize math research, Ullisch concedes, because this problem is an isolated one. 'It's not connected to other problems or embedded within a mathematical theory.' But it's possible for even fun puzzles like this to give rise to new mathematical ideas and help researchers come up with novel approaches to other problems.
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