It doesn't mean anything unless you specify the maximum allowed distance to the coast (or the average distance to the coast along your ride, or the median distance to the coast). Notice that you probably want to define the distance of each point of the coast to some point in your traject, and not the other way round (which would make your endeavor trivial).
Really, it seems a very complicated concept to define precisely, and it would entail a lot of seemingly arbitrary parameters.
Wait, isn't this Hacker news? I want to be given a definition and analyze it deeply.
For instance, looking at the wikipedia page it seems that the closest that De Brune got to Cape York Tip (the northernmost point of Australia) was about one thousand kilometers. If this "counts" as a complete tour, he might as well had walked consistently 1000km inland for a much shorter tour (but maybe harder, due to the desert?).
Mathematics is pretty much on topic here. I made a valid point, just for fun, that giving a precise mathematical definition of "walking around an island" is a tricky issue. Of course everybody knows what does it mean roughly, but making that point, about a mathematical definition cannot be construed as anti-social. Unless you consider mathematics anti-social.
> Of course everybody knows what does it mean roughly
So you know this goes against
> Please respond to the strongest plausible interpretation of what someone says
But you've generated such a strong negative reaction that you've been flagged and the comment has been removed, so it's a lot of people saying it, not just my random opinion!
I like this definition. Not sure that the "non-intersecting" condition is necessary. I was thinking about a different one, given by the condition that the path never goes farther than d meters from the sea (while encircling the part of the land that is farther than d meters).
Really, it seems a very complicated concept to define precisely, and it would entail a lot of seemingly arbitrary parameters.