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I Must Be Psychic
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ISO 216 specifies international standard (ISO) paper sizes
used in most countries in the world today. It defines the "A" and "B"
series of paper sizes, including A4, the most commonly available size. Two supplementary standards, ISO 217 and ISO 269, define related paper sizes; the ISO 269 "C" series is commonly listed alongside the A and B sizes.
All ISO 216, ISO 217 and ISO 269 paper sizes have the same aspect ratio, .
This ratio has the unique property that when cut or folded in half
lengthwise, the halves also have the same aspect ratio. Each ISO paper
size is one half of the area of the next size up.
The advantages of basing a paper size upon an aspect ratio of √2 were already noted in 1786 by the German scientist Georg Christoph Lichtenberg, in a letter to Johann Beckmann. The formats that became A2, A3, B3, B4 and B5 were developed in France, and published in 1798 during the French Revolution, but were subsequently forgotten.
Early in the twentieth century, Dr Walter Porstmann turned
Lichtenberg's idea into a proper system of different paper sizes.
Porstmann's system was introduced as a DIN standard (DIN 476) in Germany
in 1922, replacing a vast variety of other paper formats. Even today
the paper sizes are called "DIN Ax" in everyday use in Germany and
The main advantage of this system is its scaling: if a sheet with an
aspect ratio of √2 is divided into two equal halves parallel to its
shortest sides, then the halves will again have an aspect ratio of √2.
Folded brochures of any size can be made by using sheets of the next
larger size, e.g. A4 sheets are folded to make A5 brochures. The system
allows scaling without compromising the aspect ratio from one size to
another – as provided by office photocopiers, e.g. enlarging A4 to A3 or
reducing A3 to A4. Similarly, two sheets of A4 can be scaled down and
fit exactly 1 sheet without any cutoff or margins.
The weight of each sheet is also easy to calculate given the basis weight in grams
per square metre (g/m² or "gsm"). Since an A0 sheet has an area of 1
m², its weight in grams is the same as its basis weight in g/m². A
standard A4 sheet made from 80 g/m² paper weighs 5g, as it is one 16th
(four halvings) of an A0 page. Thus the weight, and the associated
postage rate, can be easily calculated by counting the number of sheets
ISO 216 and its related standards were first published between 1975 and 1995:
Paper in the A series format has a aspect ratio, although this is rounded to the nearest millimetre. A0 is defined so that it has an area of 1 square metre,
prior to the above mentioned rounding. Successive paper sizes in the
series (A1, A2, A3, etc.) are defined by halving the preceding paper
size, cutting parallel to its shorter side (so that the long side of A(n+1) is the same length as the short side of An, again prior to rounding).
The most frequently used of this series is the size A4 which is 210 × 297 mm (8.3 × 11.7 in). For comparison, the letter paper size commonly used in North America (8.5" x 11") is approximately 6 mm (0.24 in) wider and 18 mm (0.71 in) shorter than A4.
The geometric rationale behind the square root of 2
is to maintain the aspect ratio of each subsequent rectangle after
cutting the sheet in half, perpendicular to the larger side. Given a
rectangle with a longer side, x, and a shorter side, y, the following equation shows how the aspect ratio of a rectangle compares to that of a half rectangle: which reduces to or an aspect ratio of .
The formula that gives the larger border of the paper size An in metres and without rounding off is the geometric sequence: an = 21 / 4 − n / 2. The paper size An thus has the dimension an × an + 1.
The exact millimetre measurement of the long side of An is given by .
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Penelope McBagpipe wrote:
Do not get me started on manual feeders who do not show up to feed.DO NOT
01/23/12 02:08 PM
Penelope McBagpipe wrote:Do not get me started on manual feeders who do not show up to feed.
01/23/12 02:09 PM
01/23/12 02:11 PM
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