ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today, although not in Canada, the United States, Mexico, Colombia, or the Dominican Republic. The standard defines the "A" and "B" series of paper sizes, including A4, the most commonly available paper size worldwide. 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 (except some envelopes) have the same aspect ratio, √:1, within rounding to millimetres. This ratio has the unique property that when cut or folded in half widthways, the halves also have the same aspect ratio. Each ISO paper size is one half of the area of the next larger size in the same series.
|Size||A series formats||B series formats||C series formats|
|0||841 × 1189||33.1 × 46.8||1000 × 1414||39.4 × 55.7||917 × 1297||36.1 × 51.1|
|1||594 × 841||23.4 × 33.1||707 × 1000||27.8 × 39.4||648 × 917||25.5 × 36.1|
|2||420 × 594||16.5 × 23.4||500 × 707||19.7 × 27.8||458 × 648||18.0 × 25.5|
|3||297 × 420||11.7 × 16.5||353 × 500||13.9 × 19.7||324 × 458||12.8 × 18.0|
|4||210 × 297||8.3 × 11.7||250 × 353||9.8 × 13.9||229 × 324||9.0 × 12.8|
|5||148 × 210||5.8 × 8.3||176 × 250||6.9 × 9.8||162 × 229||6.4 × 9.0|
|6||105 × 148||4.1 × 5.8||125 × 176||4.9 × 6.9||114 × 162||4.5 × 6.4|
|7||74 × 105||2.9 × 4.1||88 × 125||3.5 × 4.9||81 × 114||3.2 × 4.5|
|8||52 × 74||2.0 × 2.9||62 × 88||2.4 × 3.5||57 × 81||2.2 × 3.2|
|9||37 × 52||1.5 × 2.0||44 × 62||1.7 × 2.4||40 × 57||1.6 × 2.2|
|10||26 × 37||1.0 × 1.5||31 × 44||1.2 × 1.7||28 × 40||1.1 × 1.6|
In 1786, the German scientist Georg Christoph Lichtenberg described the advantages of basing a paper size on an aspect ratio of √ in a letter to Johann Beckmann. The formats that became ISO paper sizes A2, A3, B3, B4, and B5 were developed in France. They were listed in a 1798 law on taxation of publications that was based in part on page sizes.
The main advantage of this system is its scaling. Rectangular paper with an aspect ratio of √ has the unique property that, when cut or folded in half midway between its shorter sides, each half has the same √ aspect ratio and half the area of the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets paper with an aspect ratio of √ side-by-side along their longer side, they form a larger rectangle with the aspect ratio of √ and double the area of each individual sheet.
The ISO system of paper sizes exploits these properties of the √ aspect ratio. In each series of sizes (for example, series A), the largest size is numbered 0 (for example, A0), and each successive size (for example, A1, A2, etc.) has half the area of the preceding sheet and can be cut by halving the length of the preceding size sheet. The new measurement is rounded down to the nearest millimetre. A folded brochure can be made by using a sheet of the next larger size (for example, an A4 sheet is folded in half to make a brochure with size A5 pages. An office photocopier or printer can be designed to reduce a page from A4 to A5 or to enlarge a page from A4 to A3. Similarly, two sheets of A4 can be scaled down to fit one A4 sheet without excess empty paper.
This system also simplifies calculating the weight of paper. Under ISO 536, paper's grammage is defined as a sheet's weight in grams (g) per area in square metres (abbreviated g/m2 or gsm). Since an A0 sheet has an area of 1 m2, its weight in grams is the same as its grammage. One can derive the grammage of other sizes by arithmetic division in g/m2. A standard A4 sheet made from 80 g/m2 paper weighs 5 g, as it is 1/ (four halvings, ignoring rounding) of an A0 page. Thus the weight, and the associated postage rate, can be easily approximated by counting the number of sheets used.
ISO 216 and its related standards were first published between 1975 and 1995:
Paper in the A series format has an aspect ratio of √ (≈ 1.414, when rounded). A0 is defined so that it has an area of 1 square metre before rounding to the nearest millimeter. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the area of the preceding paper size and rounding down, so that the long side of A(n+1) is the same length as the short side of An. Hence, each next size is roughly half of the prior size. So, an A1 page can fit 2 A2 pages inside the same area.
The most used of this series is the size A4, which is 210 mm × 297 mm (8.27 in × 11.7 in) and thus almost exactly 0.0625 square metres (96.9 sq in) in area. For comparison, the letter paper size commonly used in North America (8 1⁄2 in × 11 in, 216 mm × 279 mm) is about 6 mm (0.24 in) wider and 18 mm (0.71 in) shorter than A4. Then, the size of A5 paper is half of A4, as 148 x 210 mm (5.8 x 8.3 in). 
The geometric rationale for using the square root of 2 is to maintain the aspect ratio of each subsequent rectangle after cutting or folding an A-series sheet in half, perpendicular to the larger side. Given a rectangle with a longer side, x, and a shorter side, y, ensuring that its aspect ratio, x/, will be the same as that of a rectangle half its size, y/, which means that x/ = y/, which reduces to x/ = √; in other words, an aspect ratio of 1:√.
The formula that gives the larger border of the paper size An in metres and without rounding off is the geometric sequence:
The paper size An thus has the dimension
and area (before rounding)
The measurement in millimetres of the long side of An can be calculated as
(brackets represent the floor function).
The B series is defined in the standard as follows: "A subsidiary series of sizes is obtained by placing the geometrical means between adjacent sizes of the A series in sequence." The use of the geometric mean makes each step in size: B0, A0, B1, A1, B2 … smaller than the previous one by the same factor. As with the A series, the lengths of the B series have the ratio √, and folding one in half (and rounding down to the nearest millimeter) gives the next in the series. The shorter side of B0 is exactly 1 metre.
The measurement in millimetres of the long side of Bn can be calculated as
There is also an incompatible Japanese B series which the JIS defines to have 1.5 times the area of the corresponding JIS A series (which is identical to the ISO A series). Thus, the lengths of JIS B series paper are √ ≈ 1.22 times those of A-series paper. By comparison, the lengths of ISO B series paper are 4√ ≈ 1.19 times those of A-series paper.
The C series formats are geometric means between the B series and A series formats with the same number (e.g., C2 is the geometric mean between B2 and A2). The width to height ratio is √ as in the A and B series. The C series formats are used mainly for envelopes. An A4 page will fit into a C4 envelope. C series envelopes follow the same ratio principle as the A series pages. For example, if an A4 page is folded in half so that it is A5 in size, it will fit into a C5 envelope (which will be the same size as a C4 envelope folded in half). The lengths of ISO C series paper are therefore 8√ ≈ 1.09 times those of A-series paper.
A, B, and C paper fit together as part of a geometric progression, with ratio of successive side lengths of 8√, though there is no size half-way between Bn and A(n − 1): A4, C4, B4, "D4", A3, …; there is such a D-series in the Swedish extensions to the system.
The measurement in millimetres of the long side of Cn can be calculated as
The tolerances specified in the standard are:
These are related to comparison between series A, B and C.
The ISO 216 formats are organized around the ratio 1:√; two sheets next to each other together have the same ratio, sideways. In scaled photocopying, for example, two A4 sheets reduced to A5 size fit exactly onto one A4 sheet, and an A4 sheet in magnified size onto an A3 sheet; in each case, there is neither waste nor want.
The principal countries not generally using the ISO paper sizes are the United States and Canada, which use North American paper sizes. Although they have also officially adopted the ISO 216 paper format, Mexico, Panama, Venezuela, Colombia, the Philippines, and Chile also use mostly U.S. paper sizes.
Rectangular sheets of paper with the ratio 1:√ are popular in paper folding, such as origami, where they are sometimes called "A4 rectangles" or "silver rectangles". In other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion 1:(1 + √), known as the silver ratio.
An important adjunct to the ISO paper sizes, particularly the A series, are the technical drawing line widths specified in ISO 128, and the matching technical pen widths of 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.40, and 2.0 mm, as specified in ISO 9175-1. Color codes are assigned to each size to facilitate easy recognition by the drafter. These sizes increase by a factor of √, so that particular pens can be used on particular sizes of paper, and then the next smaller or larger size can be used to continue the drawing after it has been reduced or enlarged, respectively. For example, a continuous thick line on A0 size paper shall be drawn with a 0.7 mm pen, the same line on A1 paper shall be drawn with a 0.5 mm pen, and finally on A2, A3, or A4 paper it shall be drawn with a 0.35 mm pen.
The earlier DIN 6775 standard upon which ISO 9175-1 is based also specified a term and symbol for easy identification of pens and drawing templates compatible with the standard, called Micronorm, which may still be found on some technical drafting equipment.
A0, A-0, A0, or a0 may refer to:
101 A0 and 103 A0, two versions of the German Heinkel Tourist moped
A0 paper size, an international ISO 216 standard paper size (841 × 1189 mm), which results in an area very close to 1 m²
A0 highway (Zimbabwe), a highway which orbits Zimbabwe
A0, the lowest A (musical note) note on a standard piano
A0, a climbing grade
A00, Irregular chess openings code in the Encyclopaedia of Chess Openings
A-0 Geyser, a geyser in Yellowstone National Park
A-0 System, an early compiler related tool developed for electronic computers
L'Avion, IATA airline designator for the French airline
Characters of type A0, an older term for algebraic Hecke characters
a0, the accepted mathematical symbol for the Bohr radius
Haplogroup A00 and A0; see Y-chromosomal Adam and Haplogroup A (Y-DNA)
A0, a subdivision in stellar classification
A0, sometimes written as 0xA0, is the hexadecimal representation of non-breaking space in various character encoding standardsA3
A3, A03 or A.III may refer to:
A3 paper, a paper size defined by ISO 216A7
A7, A.7, A 7, A07 or A-7 may refer to:
A7 (bar), bar in New York City
Altec Lansing's A-7 speaker
ATC code A07 Antidiarrheals, intestinal anti-inflammatory/anti-infective agents, a subgroup of the Anatomical Therapeutic Chemical Classification System
Arrows A7, a 1984 British racing car
Audi A7, a mid-size coupé released in 2010
British NVC community A7 (Nymphaea alba community), a British Isles plant community
Route A7 (WMATA), a bus route operated by the Washington Metropolitan Area Transit Authority
Subfamily A7, a Rhodopsin-like receptors subfamily
Air Comet, its IATA airline designator
A7, an ISO 216, international standard paper size, 74×105 mm
A7, the A dominant seventh chord used in many rock songs, see dominant seventh chord
A (musical note)
A7 road, in several countries
Avenged Sevenfold, a hard rock/metal band
Arutz Sheva, an Israeli radio station meaning Channel Seven
A7, a type of stereoautograph
A type of Réti Opening code for Chess (A07)
Autobacs Seven, sports car manufacturer
ARM Cortex-A7, a processor in the ARM Cortex-A processor family
LNER Class A7, a class of British 4-6-2T steam locomotive
Apple A7, a system on a chip used first in the iPhone 5S
Samsung Galaxy A7, a smartphone
Noradrenergic cell group A7ANSI/ASME Y14.1
In 1992, the American National Standards Institute adopted ANSI/ASME Y14.1 Decimal Inch Drawing Sheet Size and Format which defined a regular series of paper sizes based upon the de facto standard 8 1⁄2 in × 11 in "letter" size which it assigned "ANSI A". This series also includes "ledger"/"tabloid" as "ANSI B". This series is somewhat similar to the ISO 216 standard in that cutting a sheet in half would produce two sheets of the next smaller size. Unlike the ISO standard, however, the arbitrary aspect ratio forces this series to have two alternating aspect ratios. ANSI/ASME Y14.1 has been revised or updated in 1995, 2005 and 2012. It has an accompanying standard ANSI/ASME Y14.1M that defines metric drawing paper sizes based upon ISO 216 and ISO 5457.With care, documents can be prepared so that the text and images fit on either ANSI or their equivalent ISO sheets at 1:1 reproduction scale.
Size F does not continue the alphabetic series, because it does not exhibit the same aspect ratios.
Sizes G, H, J and K are roll formats. G size is 22 1⁄2 in (571.5 mm) high, but variable width up to 90 in (2286 mm) in increments of 8 1⁄2 in. Such sheets were at one time used for full-scale layouts of aircraft parts, wiring harnesses and the like, but today are generally not needed, due to widespread use of computer-aided design (CAD) and computer-aided manufacturing (CAM).A series
A series may refer to:
ISO 216 A series paper sizes defined by the ISO 216 standard, including A4 paper size
A series and B series, two philosophical descriptions of the temporal ordering of events
A-series light bulb, the most common type of light bulbs used since the early 20th century
BMC A-Series engine, a small straight-4 automobile engine produced by the Austin Motor Company
Canon PowerShot A cameras
Fujifilm FinePix A series cameras
Honda A engine
QI (A series), the first series of the TV quiz show QI
Series A venture capital financing round for startups
Tool steel A series, air hardenedAspect ratio
The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side – the ratio of width to height, when the rectangle is oriented as a "landscape".
The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, 8⁄5 and 1.6 are all ways of representing the same aspect ratio.
In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.Business card
Business cards are cards bearing business information about a company or individual. They are shared during formal introductions as a convenience and a memory aid. A business card typically includes the giver's name, company or business affiliation (usually with a logo) and contact information such as street addresses, telephone number(s), fax number, e-mail addresses and website. Before the advent of electronic communication business cards might also include telex details. Now they may include social media addresses such as Facebook, LinkedIn and Twitter. Traditionally many cards were simple black text on white stock; today a professional business card will sometimes include one or more aspects of striking visual design.C0
C0 or C00 has several uses including:
C0, the IATA code for Centralwings airline
C0 and C1 control codes
a CPU power state in the Advanced Configuration and Power Interface
an alternate name for crt0, a library used in the startup of a C program
the differentiability class C0
a C0-semigroup, a strongly continuous one-parameter semigroup
c0, the Banach space of real sequences that converge to zero
a C0 field is an algebraically closed field
in physics, c0, the speed of light in a vacuum
%C0, the URL-encoded version of the character "À"
C0, a note-octave in music
an ISO 216 paper format size
C00, the ICD-10 code for oral cancerDatenschleuder
Die Datenschleuder. Das wissenschaftliche Fachblatt für Datenreisende, literally translated as The Data Slingshot: The scientific trade journal for data voyagers, is a German hacker magazine that is published at irregular intervals by the Chaos Computer Club (CCC).
Topics include primarily political and technical aspects of the digital world (freedom of information, data privacy (data protection), closed-circuit television, personal privacy (personal rights), cryptography and many more).
Die Datenschleuder was first published in 1984 and also can be subscribed to independently of a membership in the CCC. The founder is Herwart Holland Moritz. All (more than 90) back issues are freely available on the Internet as well. The current print paper format is DIN A5 as per ISO 216. Its editorial process is carried out over the Internet, while the magazine itself is printed in and distributed from Hamburg.
Issue #92 from March 2008 contained a reproduction of a fingerprint from Wolfgang Schäuble, the interior minister of Germany at the time.The US phreaking magazine TAP – The Youth International Party Line (YIPL) (founded in 1971) has been described as a model for Datenschleuder.Deutsches Institut für Normung
Deutsches Institut für Normung e.V. (DIN; in English, the German Institute for Standardization) is the German national organization for standardization and is the German ISO member body. DIN is a German Registered Association (e.V.) headquartered in Berlin. There are currently around thirty thousand DIN Standards, covering nearly every field of technology.Envelope
An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter or card.
Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a short-arm cross or a kite. These shapes allow for the creation of the envelope structure by folding the sheet sides around a central rectangular area. In this manner, a rectangle-faced enclosure is formed with an arrangement of four flaps on the reverse side.ISO 128
ISO 128 is an international standard (ISO), about the general principles of presentation in technical drawings, specifically the graphical representation of objects on technical drawings.ISO 217
The ISO 217:2013 standard defines the RA and SRA paper formats.ISO 7200
ISO 7200, titled Technical product documentation - Data fields in title blocks and document headers, is an international technical standard defined by ISO which describes title block formats to be used in technical drawings.Letter (paper size)
Letter or ANSI Letter is a paper size commonly used as home or office stationery in the United States, Canada, Chile, Colombia, Costa Rica, Mexico, Panama, the Dominican Republic and the Philippines. It measures 8.5 by 11 inches (215.9 by 279.4 mm). US Letter-size paper is a standard defined by the American National Standards Institute (ANSI, paper size A), in contrast to A4 paper used by most other countries, and adopted at varying dates, which is defined by the International Organization for Standardization, specifically in ISO 216.Newspaper format
Newspaper formats vary substantially, with different formats more common in different countries. The size of a newspaper format refers to the size of the paper page; the printed area within that can vary substantially depending on the newspaper.
In some countries, particular formats have associations with particular types of newspaper; for example, in the United Kingdom, there is a distinction between "tabloid" and "broadsheet" as references to newspaper content quality, which originates with the more popular newspapers using the tabloid format; hence "tabloid journalism".Paper size
Many paper size standards conventions have existed at different times and in different countries. Today, the A and B series of ISO 216, which includes the commonly used A4 size, are the international standard used by almost every country. However, in many countries in the Americas as well as in the Philippines, the North American series of paper sizes such as 'Letter' and 'Legal' is more prevalent.Paper sizes affect writing paper, stationery, cards, and some printed documents. The international standard for envelopes is the C series of ISO 269Silver ratio
In mathematics, two quantities are in the silver ratio (also silver mean or silver constant) if the ratio of the sum of the smaller and twice the larger of those quantities, to the larger quantity, is the same as the ratio of the larger one to the smaller one (see below). This defines the silver ratio as an irrational mathematical constant, whose value of one plus the square root of 2 is approximately 2.4142135623. Its name is an allusion to the golden ratio; analogously to the way the golden ratio is the limiting ratio of consecutive Fibonacci numbers, the silver ratio is the limiting ratio of consecutive Pell numbers. The silver ratio is denoted by δS.
Mathematicians have studied the silver ratio since the time of the Greeks (although perhaps without giving a special name until recently) because of its connections to the square root of 2, its convergents, square triangular numbers, Pell numbers, octagons and the like.
The relation described above can be expressed algebraically:
The silver ratio can also be defined by the simple continued fraction [2; 2, 2, 2, ...]:
The convergents of this continued fraction (2/, 5/, 12/, 29/, 70/, ...) are ratios of consecutive Pell numbers. These fractions provide accurate rational approximations of the silver ratio, analogous to the approximation of the golden ratio by ratios of consecutive Fibonacci numbers.
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