The Goat Problem, Now Solved

I had no idea this existed. But this infamous goat problem is more difficult than the ‘how many milk bottles’ will one have after a certain number of conditions. This one has baffled mathematicians for quite some time. The problem is this: ‘for a goat to be able to eat grass in a circle with an area of exactly one half acre, how much rope does it need?’ Now this may look simple, but the answer actually has only been approximations for centuries, as Popular Mechanics detailed: 

The goat problem is a living example of what it means to round off your answer. Steve Nadis at Quanta explains the distinction:

“To illustrate the difference, consider the equation x2 − 2 = 0. One could derive an approximate numerical answer, x = 1.4142, but that’s not as accurate or satisfying as the exact solution, x = √2.”

With a few moments of thought, the goat problem quickly turns into an exercise in many intersecting approximations. This is why every answer offered since the 1700s has been an approximation as well.

And now, finally, there’s an exact solution for the first time. Mathematician Ingo Ullisch took a cue from the previous researchers who made progress on the problem. He introduced complex analysis, which is kind of like algebra with an optional imaginary-number add-on. 

Check Popular Mechanics’ full piece on the solution to the problem here. 

Image via Popular Mechanics