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

[faithhopetricks.livejournal.com]

Ah, now that explains why Russell Hoban is always talking about A4 (I think) yellow paper. Once again, the Rest of the World has a sensible easily understood universally applied measuring system the US just won't buy. ((sighs heavily))

[trochee.livejournal.com]

now come on. 5280 feet per mile is a nice round number, as long as you're using base 5280.

[xaosenkosmos.livejournal.com]

Not just base 5280, but in many different ones: 5280 = 2⁵*3*5*11.

The best compromise between convenience and practicality, in my opinion, is EZ!₃₀, with digits { !, A-Z, 0, 1, 2 }.

[trochee.livejournal.com]

now this starts to sound like InterCal.

[trochee.livejournal.com]

now that I think about it, I think maybe the system of English units is a sort of pre-computational Intercal, anyway. I mean, come on: a rod is 16.5 feet? a furlong is 40 rods? gills? drams? pennyweight? bushel? peck?

[marnanel.livejournal.com]

I've always loved the A-series. Letter, pschah.

[boobirdsfly.livejournal.com]

Ben oui bien sur : format A4 !

[several-bees.livejournal.com]

Ha to a slightly odd sort of insularity - it never occurred to me that Americans might have to have this explained to them; sure, they might seem to use this odd 'letter paper' thing, but they must all know really, mustn't they, and just be being awkward for the fun of it, and out of habit? Surely?

[trochee.livejournal.com]

hah. the difference in reaction between my international friends (you, marnanel, imtboo) and my American friends (including some here in my lab) is amusing.

But yes, I swear, I didn't know about the fancy ratio properties of the A-series. That's pretty neat, believe it or not.

And there's a certain stubbornness to American attitudes towards international standards. I'm not defending it -- we also don't have sensible health care programs or intelligent foreign policy -- but there it is.

America -- the world's biggest case of Not Invented Here syndrome.

[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.