Why yes, that is the square root of 2, thanks for noticing. Do you want to know the really odd thing about it? It is one of the things I miss about living in Europe. Why is that you ask? Does math work differently in North America? Is this another Common Core critique? No, it has to do with paper.
For some reason, the United States is saddled with strange measurement systems. Inches, feet, miles. Gallons, pints, tablespoons. AM and PM. Most of these units are the equivalent of organizing the Library of Congress by the book’s color and height. You can do that, but it isn’t a very efficient way to organize a library.
The metric system works because it is not arbitrary. Consider the following:
“In metric, one milliliter of water occupies one cubic centimeter, weighs one gram, and requires one calorie of energy to heat up by one degree centigrade—which is 1 percent of the difference between its freezing point and its boiling point. An amount of hydrogen weighing the same amount has exactly one mole of atoms in it.”
Josh Bazell, Wild Thing
Don’t even think about trying that with Imperial units.
What does this have to do with paper? Europe, as with most of the rest of the world, uses International Paper Sizes. (It seems we led Canada astray as well.) If you’ve ever looked closely at your printer, scanner, or copier, you may have noticed marks on it that say A4. You may or may not have realized that it is a paper size, the “normal” sized paper in most of the world. It is not an equally random size like our “letter” size is.
What does this have to do with the square root of 2? It just so happens that the square root of 2 is the ratio of length/width for all A-format paper. Why does this matter? It is the only thing that does matter about the international sizes as far as I’m concerned. It means if you take any sheet of international A-series paper and cut it in half horizontally, you suddenly have two sheets of the next smaller size and they have the same aspect ratio. Stay with me.
Have you ever printed or copied a document but wanted to conserve space or paper and decided to place two pages side-by-side horizontally on a sheet? Have you noticed when doing that you always end up with extra margin at the bottom? It’s because our letter sized paper doesn’t have a length/width ratio of 1.4142. It’s 1.2941, but for “half sheet” of 5.5″ x 8.5″ it’s 1.5454.
Perform the same operation with any A-sized paper to any other A-sized paper and the margins will all scale properly. You will have an actual reduced size page. It’s a beautiful system. Have an A4 document you want to reduce to fit in your A5 or A6 notebook? No problem. And C-sized envelopes coordinate with it all. (American envelope sizes make even less sense than our paper sizes, which is a truly startling achievement.)
Does my passion about paper sizes make me a lunatic? Possibly. But it all works so beautifully, as one site I discovered notes:
Technical drawing pens follow the same size-ratio principle. The standard sizes differ by a factor sqrt(2): 2.00 mm, 1.40 mm, 1.00 mm, 0.70 mm, 0.50 mm, 0.35 mm, 0.25 mm, 0.18 mm, 0.13 mm. So after drawing with a 0.35 mm pen on A3 paper and reducing it to A4, you can continue with the 0.25 mm pen. (ISO 9175-1)
I understand why we haven’t changed and it’s the same reason will still use feet and fahrenheit. It is what we are used to and in order to change we’d have to change all sorts of things, like the size of our filing cabinets. As a country that likes to deride those who say, “We’ve always done it that way,” it is surprising that we cling to this so vehemently. We throw away all of our music every 20 years and switch to a new format. Vinyl, cassette, CD, MP3. We’ve changed from analog to digital TV. We transitioned from VHS to DVD. Would it really be that much worse to get on board with the rest of the world on paper?