Reader Ross Durland offers this:
Most countries have concave regions in their borders, where a neighboring country “bulges in.” For example, Canada bulges into the US up by the Great Lakes. If you wanted to fly from, say, Sault Ste. Marie, [MI], to Buffalo, NY, you could fly straight there going SE. That would only be about a 370 mile flight, but you’d have to pass over southern Ontario.
If you wanted to fly there while remaining in US airspace, you’d have to first go almost straight South to about Toledo, and then turn ENE to Buffalo, for a total distance of maybe 590 miles. That’s about 1.6 times as far. Let’s call that ratio the “concavity index.” More generally, for any two points within a single country, the concavity index is the shortest distance that is entirely within the country’s borders [counting bodies of water that are in between two points in a country as within the country’s borders -EV], divided by the absolute minimum distance.
Now to the puzzle. What two points exhibit the highest concavity index in the world?
Points located in non-contiguous portions of one country don’t count (e.g. Anchorage & Honolulu), although there is room to argue when that rule applies. Also, I think we can safely ignore changes in altitude when measuring distances. . . .
My apologies if my explanation isn’t as clear as I’d like. I always have trouble describing this in words.
Here’s the answer that my correspondent arrived at, and I independently reached as well:
If you have a provably better answer — not just an “I guess,” but a pointer to a map and a good approximation of the concavity index — please pass it along.
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