applied math with sensible units

[trochee]

Apparently, European non-American international paper sizes are all of the ratio √2:1 , with A0 being defined to have a 1m² area. Thus A1 has 0.5m² area, and A2 has 0.25m² area, etcetera. Thus A6 is a postcard and A10 is (at least in principle) 26-by-37mm -- the size of a large postage stamp. In addition, a sheet of Ai paper can be exactly covered by two sheets of Ai+1 paper. (This is a special property of this ratio.) The relatively well-known A4 letter paper is a member of this class, and thus has an area of 2^-4 = 1/16 m².

Thus you can compute the dimensions of any Ai paper by solving the system of equations:

l * w = 2^-i
l = √2 w

This neat interlocking relationship would be really handy (as the link suggests) for easy reductions with a photocopier. American paper sizes, o my foreign reader, have no such elegant relationship to each other known to this author.

[update: unbelievably geeky, but cool: the B series is the geometric means between adjacent A values, and even the C-series (envelopes) follow the same pattern.]

Also, there's a rather tongue-in-cheek (one hopes) explanation for other interesting properties of the A4 paper.

[this post brought to you by trying to print the B5 paper size Computational Linguistics two-up onto American letter paper.]

Comments

[boobirdsfly.livejournal.com]

Not to mention inches. INCHES?!!!!

[xaosenkosmos.livejournal.com]

12 is actually a very good candidate for a construction standard: it has 2, 3, and 4 as factors. The 3 is the killer one: you can precisely space two objects along a distance fairly simply, which isn't something you can do with a tape in centimeters.

The modern belief that everything should be base-10 is falls apart when you consider that the single most utilized unit is a bizarro mess of base ten mixed with to levels of base sixty mixed with two 12s (or, if you're in a marginally saner part of the world, a single 24). Swatch introduced "internet time," a decimal time standard, in 1998. You can see how well it's caught on ;^)

In any case, arguing about units is like arguing about numeric bases or languages, in my view. Sure, America should get in line with the rest of the world, but, quite frankly, there's a reason the British still use feet when doing construction: they're damned handy units.

[boobirdsfly.livejournal.com]

Well, I *was* kidding, not arguing.
I see your point though.