How paper sizes are fixed
The Sunday Nation
Nairobi,
06 March 2011
After the 1992 General Elections, Mr. John Harun Mwau filed a petition in the High Court of Kenya against the declaration of former President Daniel arap Moi as winner of the presidential race. Mwau’s argument was that Moi (and all the other candidates) had not been properly nominated for the polls since they had not given the supporting signatures in the prescribed format.
The Election Regulations required presidential candidates to give the names and signatures of 1,000 supporters in "forty standard sheets of foolscap papers". Mwau’s argued that he was the only candidate who had used foolscaps measuring 8inches-by-13inches: all the others, including Moi, presented A4 sheets which measure 210mm-by-297mm (approximately, 8.27” × 11.69”).
Mwau lost the case but the petition brought out an interesting question: how are paper sizes decided? Why do they have such awkward dimensions? The answer lies in a tricky geometrical problem.
The international “A” standard sizes have a special the special characteristic that when folded into two halves, the new sheet retains the same aspect ratio as the unfolded one.
For example, the aspect ratio of A4 is 297 divided by 210; that is, 1.414. When folded once we get A5 which measures 148.5mm by 210mm. Note that the width of A4 is now the height of A5. The new aspect ratio is 210 divided by 148.5; that is, 1.414. You can test this for your self using the dimensions of A6: 105mm-by-148.5mm.
This characteristic of retaining the aspect ratio after every subdivision is not common to all rectangular dimensions. Indeed, the standard foolscap size does not follow this rule: try it out and see. So; here is a challenge to all readers who are secondary school: what should the aspect ratio of the special rectangle that is used in the A-series sizes of paper?
I’m waiting…
OK: the answer is that the height divided by width must be equal to the square-root of 2. If the rectangle is cut to half its original height, the new one will still have an aspect ratio of sqrt2.
That’s the first step; the second step is to decide on a starting point. We commonly use A4 and A5 in our offices. On a few occasions we also use the very large A3. Going “backwards”, these numbers should end somewhere, shouldn’t they?
Yes they do. A0 is the starting point of the international A series. It is the sheet of paper whose area is one square metre and with an aspect ratio of sqrt2. Again I call upon the readers in secondary school to work out the dimensions for us… tap-tap-tap, we are waiting…
The answer is 0.841m-by-1.189m; or 841mm-by-1,189mm. These are the dimensions of A0. A1 is a half of A0, that is, 594.5mm-by-841mm… and so on for the other sizes.
Now, since it is difficult to measure decimals of millimetres using ordinary rulers, the fractions are rounded DOWN. Thus A1 is 594mm-by-841mm; and A2 is 420mm-by-594mm… and so on.
Now, wouldn’t it be nice if surveyors used the same aspect ratio for plots of land instead of the current 1:2?
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