Blogtrek

Square Root of an Acre

A long time ago I heard of a book with the title "The Square Root of Tuesday". It was a book about mathematics education, although I remember little else about it, except for the title, which is nonsensical. Square roots apply only to numbers, and only to non-negative real numbers at that, usually. The square root of 4 is 2, and the square root of 3 is 1.732. . . But such things as the square root of one of my cats or of a democratic state constitution or of Tuesday doesn't make sense, nor does, it seems, the square root of an acre.

But wait. Google has a great new service. It used to be that if you type 2 + 3 in Google, you get sites containing 2 + 3; usually mathematics sites but maybe a few others who are trying to demonstrate simple arithmetic. But now when you try it, you get 2 + 3 = 5, and a comment to click here to find sites containing "2 + 3". In other words, Google is now a calculator! If you have access to the Internet, you don't need a calculator. Just type in what you want to compute and get the answer. For example, try 3/7. You get 0.428571428 or something like that. sin(pi/6) gets you 0.5. Sqrt(2) gets you 1.41421356. Sqrt(-1) gets you i. That's right, Google does complex arithmetic. Now here it is on shaky ground. Minus one has two square roots which are negative of each other, and you can't tell which is which, but Google states unequivocally that it is i. This leads into trouble with other expressions as it makes unwarranted selections of answers in those cases where the answer is ambiguous. But Google has done it again!

It even works with units. For example, "1 inch in centimeters" yields "1 inch = 25.4 centimeters". "(60 mph) * (9 hours)" yields "540 miles". But sqrt(Tuesday) gets you a list of web sites containing sqrt and Tuesday. No, that does not make sense. Even "1/0" yields merely a list of sites containing 1/0; it does not show the calculator, for you can't divide by zero. But if you try sqrt(acre), you get "sqrt(acre) = 63.6149072 meters". Google can take the square root of an acre! But does it make sense? It sure does. An acre is a unit of area, 43,560 square feet. The square root of a square foot is a foot. Even though a foot is not a number, it can be squared to yield square feet, and so the square root of a square foot does make sense. And so does the square root of an acre. Further, you get results when you try "gallon^(1/3)" (i.e., the cube root of a gallon), "2 inches^3 in teaspoons", and even "(1 gallon)^(2/3)" as you can demonstrate by entering them in Google - the latter is an area.

So although many people don't recognize that it makes sense to talk about the square root of an acre, Google certainly does, and I will remember that every time I go to work and walk from my car to my building - that is about the square root of an acre.