What's wrong with Japanese B paper sizes?

What's a gnomon? What does this have to do with geometrical progressions?

I hoped you'd ask that question. Suppose you want a range of paper sizes: the most obvious way to pick them is so that they increase linearly. You might decide you want paper for printing photographs with a 2:3 aspect ratio, from 2x3 cm to 20x30 cm. By "linearly" we mean simply that the sides of the paper increase by the same amount in each step, so the obvious set is extremely easy to calculate: 2x3, 4x6, 6x9, 8x12, ... 18x27, 20x30. The trouble is that although the steps look the same, the sizes are crowded at the large end, while customers designing postage stamps will keep asking for sizes between 2x3 and 4x6.

The answer is to make the step proportions the same. e.g. x1.25: This is a geometric series... Trouble is, working backwards is easy for an arithmetic series, cuz we divide. How to do geo - logs figure 2x3

../books/ogaf.htm


Then try logarithmic..

Perhaps inevitably, photo.net kept coming up as an example, naturally of a well designed site. As he says, somewhere, the trouble is that the websites you know the best are always the ones you built yourself. And this isn't egotism: photo.net (curious how I pronounce this "photo dot-net[rising tone]" while he seems to say "photodot[falling tone] net") is a fantastic resource for every decision you will ever have to make about buying camera equipment. Yet, again, its strength comes from a relatively subtle design point: the content is not just Immutable Truth written by an Expert, it's the collaborative suggestions of a community of contributors. (This is also why this "community" tag really is a useful description, and not just more hype.) Unfortunately, it seems impossible to describe the effectiveness of this approach to anyone who hasn't experienced it. In the questions afterwards, someone asked how you ensure that contributions are "correct", but of course this isn't the problem, since gross errors normally receive a barrage of correction. As Greenspun says, the real problem is keeping the questions in line.

And the paper?

Gnomons... working

A sizes

B sizes ...

And the Japanese version

Baffled by copier in Xerox ... answer speculation ...

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=========================================================================== Date: 01-08-95 (17:17) Number: 5085 P.& A. BBS From: BRIAN CHANDLER Refer#: NONE To: DAVID PARRY Recvd: NO Subj: Mirroring Conf: (16) Q&A --------------------------------------------------------------------------- I'll remember to think of you next time the German "Wetter" (vy alvays vetter?) report precedes the BBC news. Happy New Year, and Frohliche vossname! [Dave Parry lives in Dusseldorf] BTW: I wonder if you could satisfy my curiosity about "B" paper sizes. At least the Japanese versions are "wrong", in that they (just) fail to be geometrically between the "A" sizes. Perhaps next time you're in a stationers you could just measure something labelled "DIN Bsomething"? --- SLMR 1.05 Do not flush used batteries down the toilet. =========================================================================== Date: 01-10-95 (05:44) Number: 5086 P.& A. BBS From: ANDREAS BRAEM Refer#: 5085 To: BRIAN CHANDLER Recvd: YES Subj: Paper formats Conf: (16) Q&A --------------------------------------------------------------------------- BC>BTW: I wonder if you could satisfy my curiosity about "B" paper sizes. BC>At least the Japanese versions are "wrong", in that they (just) fail to BC>be geometrically between the "A" sizes. I couldn't find any info in this mess called "mein Zimmer" (Still Living In The Sixties) regarding the origin or logic of the Japanese B type paper formats. To clarify the issue for my gaijin friends: a sheet of A0 paper covers 1 square meter, is 841 mm wide and 1189 mm long; don't ask why. All A type as well as B type sizes have the same ratio of "1 unit wide by square-root-of-2 long" (blush; how do I write this more simply without using the root symbol?), i.e. roughly 1:1.41. The Japanese A type paper formats match the German DIN values exactly -- but not the B formats. Why not? And: are the German B values followed elsewhere in Europe? Paper formats, type B, in mm German Japanese B0 1,000 x 1,414 1,030 x 1,457 B1 707 x 1,000 728 x 1,030 B2 500 x 707 515 x 728 B3 353 x 500 364 x 515 B4 250 x 353 257 x 364 B5 176 x 250 182 x 257 B6 125 x 176 128 x 182 P.S. Sorry, I couldn't find any subject drier than this. Elsewhere, recently, Louise B. pointed a finger at me: "And why don't you write something good yourself?" Sigh. =========================================================================== Date: 01-10-95 (23:34) Number: 5092 P.& A. BBS From: BRIAN CHANDLER Refer#: 5086 To: ANDREAS BRAEM Recvd: NO Subj: Paper formats Conf: (16) Q&A --------------------------------------------------------------------------- AB>BC>BTW: I wonder if you could satisfy my curiosity about "B" paper sizes. AB>BC>At least the Japanese versions are "wrong", in that they (just) fail to AB>BC>be geometrically between the "A" sizes. AB>Paper formats, type B, in mm AB> German Japanese AB>B0 1,000 x 1,414 1,030 x 1,457 Right!! Wrong!! (they, not you) A thousand smackeroos to you, my boy! (Don't take this too seriously.) But a long-agonised mystery resolved. AB>paper formats. To clarify the issue for my gaijin friends: a sheet of A0 AB>paper covers 1 square meter, is 841 mm wide and 1189 mm long; don't ask AB>why. Follows from elementary maths, that's why. When you cut a piece of An in half, you get two pieces of A(n+1), and the two sizes are the same shape. Suppose A(n+1) is L by W, then An must be 2W by L, putting the length first. And the sizes are in the same ratio, so: L/W = 2W/L Cross-multiplying gives: L^2 = 2 W^2 So L/W = root(2) But if A0 has an area of 1 sqUare metre, then L * W = 1 (in metres) Or L * L/root(2) = 1 Or L^2 = root(2) (L^4 = 2) Or L = fourth-root-of-2, which you can check in an instant on your calculator agrees with the figure above. Now it is obvious to the meanest intelligence (what does that _really_ mean?) that the B sizes should be geometrically in between these sizes: i.e. the linear multiplying factor from an A-size to the B-size above should equal the factor from this B-size to the next A-size. Since the A-sizes are root(2) apart, it is now extremely easy to see that the two steps via the B-size will be fourth-root(2), and fairly immediate that the width of B0 should be exactly 1 metre. AB>The Japanese A type paper formats match the German DIN values exactly -- AB>but not the B formats. Why not? And: are the German B values followed AB>elsewhere in Europe? "DIN-ah-fear" is now officially "ISO A4", and I bet that the same goes for "ISO B5". I have in the past "corrected" paper sizes from "JIS B5" to "ISO B5", but for the time being I'll guess that was a mistake. Where on earth the Japanese 1.03 factor came from, goodness only knows. Question: Can I get a CD-ROM stuffed with the texts of every ISO publication I'm likely to want to access (for a reasonable price)? AB>P.S. Sorry, I couldn't find any subject drier than this. Huh? Perhaps I'd better start another message. --- SLMR 1.05 Do not flush used batteries down the toilet. =========================================================================== Date: 01-11-95 (00:21) Number: 5093 P.& A. BBS From: BRIAN CHANDLER Refer#: NONE To: ANDREAS BRAEM Recvd: NO Subj: More paper formats Conf: (16) Q&A --------------------------------------------------------------------------- I spent most of today on one train or another, in the pursuit of a rather pointless meeting. In the process, I finished "On Growth and Form", by Wentworth D'Arcy Thompson (1860-1948), in the Canto reprint (=cost reasonable) 1991 with a foreword by Stephen Jay Gould, of the 1961 edition abridged by John Tyler ("slime-mould") Bonner to 330 pages, from the first edition of 793 pages in 1917 and second enlarged edition of 1116 pages in 1942. THIS IS A WONDERFUL BOOK. READ IT! It is a bit hard in places, because D'AT was a classics scholar on the side, so he leaves bits of Latin and Greek in, plus quite a few slabs of French, and smidgens of German and Italian. But like (SJ) Gould, he can use difficult words yet basically make his meaning clear and simple. (It's quite a relief though to see that he obviously can't read Russian.) I read today about "spirals" (i.e. helical spirals) and gnomons. How a ram's horn is shaped, and why it is like umpteen molluscs and bits of plant construction. I bought a in Shiojiri, and there was a demonstration: the coiled-up shoot of a young Bryophyte. [This is an error. I meant Pteridophyte.] A gnomon is a shape which, added to shape A makes shape A', where A' is just an enlarged form of A. So in a snail's shell, the last glump, or last bit of growth, is a gnomon which, added to last year's shell makes this year's shell, *and*both*shells*are*similar*figures*. D'AT sadly did not see the full glory of Churman-thinking-applied-to-the-world. Here he is... There are other gnomonic figures more curious still. For example, if we make a rectangle (Fig. 77) such that the two sides are in the ratio of 1 : root(2), it is obvious that, on doubling it, we obtain a similar figure; for 1 : root(2) :: root(2) : 2; and each half of the figure, accordingly, is now a gnomon to the other. Were we [ah!!!] to make our paper of such a shape (say, roughly, 10 in. x 7 in.), we might fold and fold it, and the shape of folio, quarto and octavo pages would be all the same. Three books lead me back to this one: the biography of Turing, who towards the very end of his life became very interested in embryonic development, and the two engineering books (also wonderful reads) by J.E. Gordon. Authors can only be inspired by earlier authors, and I now find myself wanting to know more about Oliver Wendell Holmes who, my Conc. Ox. Comp. to Eng. Lit tells me, was an American writer and physician (1809- 94) and famous contributor to the Atlantic Monthly. --- SLMR 1.05 Do not fire used batteries from a cannon.