this post was submitted on 14 Mar 2024
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Sure. And I mean the "sufficiently small" distance is exactly the question. I mean it's not really an interesting question to ask if they're still 12 nautical miles apart... The initial distance isn't really of concern. It just has to work for any given initial state. And the next question is, are we talking about entering a ship or using cannons? Then it's either can the distance become 0 or can it get less than something.
I agree they aren't practically interesting egde cases, because in order to hit them, they're no longer meaningful for realistically describing pirate ships. At very high turning speeds, it also ceases to matter that one is 3/4 than that the other either. But at that point, we're talking about pirate ships spinning like ballerinas across the seven seas.
Feel free to extend that problem to fighter jets or ballerinas playing tag ๐
However, I'm pretty sure it's already solved. Doesn't seem difficult to prove and has had applications for centuries already. And I've played the Robots Game when I was 12 or something...