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xkcd #3125: Snake-in-the-Box Problem
(imgs.xkcd.com)
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What about goats in circular pens? A goat is tied to the fence of a circular pen. How long does the rope need to be so that the goat can reach exactly half of the pen's area? What sounds like a high school math problem was eventually solved in 2020 via complex analysis.
Here's the answer:
I feel like the answer should be much simpler than that equation salad.
Equation salad? It's elegant. Well, according to my father who was a math professor.
Deriving that monstrosity must be something out of a grad school horror novel.
What's really neat about this problem is that the 3D example, a bird in a cage, was solved sooner and is much simpler