Canada to Announce Vast New Park, from tomorrow's NYT.
The size of the park is referred to as "25.5 million acres", which seems kind of silly to me. The whole point of an acre is that it measures areas which are too large for, say, square feet and too small for square miles. I have no idea how large 25.5 million acres is, until I convert it to square miles -- 40,000 square miles. That's approximately the area of Pennsylvania, or five times the area of New Jersey. If the park were circular, it would have a radius of 112 miles -- that's kind of a useful way to picture it, since that says that if you were in the center of the park the borders would be over a hundred miles away. I have some idea what a hundred miles looks like.
But that relies on the fact that an area is the square of a distance. An acre is 43,560 square feet, or 1/640 of a square mile. What's the square root of an acre? 208.7 feet, which isn't any conventional length unit. The history is that an acre is a rectangle one furlong by one chain, or so Wikipedia says, so 208.7 feet is the geometric mean of a furlong (660 feet, or 1/8 mile) and a chain (66 feet, or 1/80 mile), or √10 chains. The weird definition is agricultural -- "[t]he acre was selected as approximately the amount of land tillable by one man behind an ox in one day", and it's easier to plow a long, narrow rectangle than a square. But haven't we moved past this?
Of course, in the end trying to rationalize the customary measurement system is silly. I suspect many of you are just saying "why don't you Americans use metric already?" In fact, one of my students, who is not American, actually wrote this once on a homework assignment, in his solution to a problem which applied calculus to physics where measurements were given in customary units.