Hm, it doesn't seem problematic for the area to be lower than expected for a given perimeter. You could do the same thing by having a triangle (an actual triang

Hm, it doesn't seem problematic for the area to be lower than expected for a given perimeter. You could do the same thing by having a triangle (an actual triangle), but then at some random point have the bounding line shoot off in some random outward direction, then come back (increasing the perimeter without enclosing any area at all). It's no more or less a triangle than your fractally jagged triangle, and it has the same perimeter and area. I think the lesson for me is that any part of any line, if you zoomed into it enough, could actually be found to be all wadded up and much longer than you would otherwise expect. A line from point A to point B must be at least as long as the straight line from A to B, but could be any length greater than that. The only thing that makes your jaggy line special is that the distance from any point along it to the nearest point on the straight (triangle's) line is zero.