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?