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Paper size

Paper size standards govern the size of sheets of paper used as writing paper, stationery, cards, and for some printed documents.

The ISO 216 standard, which includes the commonly used A4 size, is the international standard for paper size. It is used across the world except in North America and parts of Central and South America, where North American paper sizes such as "Letter" and "Legal" are used. The international standard for envelopes is the C series of ISO 269.

International standard paper sizes

The international paper size standard is ISO 216. It is based on the German DIN 476 standard for paper sizes. Each ISO paper size is one half of the area of the next larger size in the same series. ISO paper sizes are all based on a single aspect ratio of the square root of 2, or approximately 1:1.41421. There are different series, as well as several extensions.

The following international paper sizes are included in Cascading Style Sheets (CSS): A3, A4, A5, B4, B5.

A series

There are 11 sizes in the A series, designated A0–A10, all of which have an aspect ratio of $$\frac{a}{b} = \sqrt{2} \approx 1.41421\ldots$$, where a is the long side and b is the short side.

Since A series sizes share the same aspect ratio $$(\sqrt{2}),$$ they can be scaled to other A series sizes without being distorted, and two sheets can be reduced to fit on exactly one sheet without any cutoff or margins.

The A0 base size is defined as having an area of 1 m$2$; given an aspect ratio of $$\sqrt{2}$$, the dimensions of A0 are:

 * $$\sqrt[4]2\,\mathrm{m}$$ by $$\frac1\sqrt[4]2\,\mathrm{m}$$.

or, rounded to the nearest millimetre, 1189 x.

A series sizes are related in that the smaller dimension of a given size is the larger dimension of the next smaller size, and folding an A series sheet in half in its larger dimension—that is, folding it in half parallel to its short edge—results in two halves that are each the size of the next smaller A series size. As such, a folded brochure of a given A-series size can be made by folding sheets of the next larger size in half, e.g. A4 sheets can be folded to make an A5 brochure. The fact that halving a sheet with an aspect ratio of $$\sqrt{2}$$ results in two sheets that themselves both have an aspect ratio of $$\sqrt{2}$$ is proven as follows:

 * $$\frac{a}{b} = \sqrt{2},$$

where a is the long side and b is the short side. The aspect ratio for the new dimensions of the folded paper is:

 * $$\frac{b}{\frac{a}{2}} = 2\frac{b}{a} = 2\frac{1}{\sqrt{2}} = \sqrt{2} = \frac{a}{b}.$$

The advantages of basing a paper size upon an aspect ratio of $$\sqrt{2}$$ were noted in 1786 by the German scientist and philosopher Georg Christoph Lichtenberg. He also observed that some raw sizes already adhered to that ratio so that when a sheet is folded, the length to width ratio does not change.

Briefly after the introduction of the metric system, a handful of new paper formats equivalent to modern ones were developed in France, having been proposed by the mathematician Lazare Carnot, and published for judicial purposes in 1798 during the French Revolution. These were never widely adopted, however:

 * grand registre (A2)
 * moyen papier (A3)
 * grand papier (B3)
 * petit papier (B4)
 * demi feuille (B5)
 * effets de commerce (half-B5)

Early in the 20th century, the ratio was used to specify the world format starting with 1 cm as the short edge of the smallest size. Walter Porstmann started with the largest sizes instead, assigning one an area of 1 m2 (A0) and the other a short edge of 1 m (B0). He thereby turned the forgotten French sizes (relatively few in number) into a logically-simple and comprehensive plan for a full range of paper sizes, while introducing systematic alphanumeric monikers for them. Generalized to nothing less than four series, this 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 A4" in everyday use in Germany and Austria.

The DIN 476 standard spread quickly to other countries. Before the outbreak of World War II, it had been adopted by the following countries in Europe:

 * Belgium (1924)
 * Netherlands (1925)
 * Norway (1926)
 * Finland (1927)
 * Switzerland (1929)
 * Sweden (1930) with later extensions
 * Soviet Union (1934) with custom extensions
 * Hungary (1938)
 * Italy (1939)

During World War II, the standard spread to South America and was adopted by Uruguay (1942), Argentina (1943) and Brazil (1943), and afterwards spread to other countries:

 * Australia (1974)
 * Austria (1948)
 * Bangladesh (1972)
 * Barbados (1973)
 * Chile (1968)
 * Colombia (1975)
 * Czechoslovakia (now Czechia and Slovakia) (1953)
 * Denmark (1953)
 * Ecuador (1974)
 * France (1967)
 * Greece (1970)
 * Iceland (1964)
 * India (1957) with custom extensions
 * Iran (1948)
 * Ireland (1959)
 * Israel (1954)
 * Japan (1951) with different B series
 * Kuwait (1975)
 * Mexico (1965)
 * New Zealand (1963)
 * Peru (1967)
 * Poland (1957)
 * Portugal (1954)
 * Rhodesia (now Zimbabwe) (1970)
 * Romania (1949)
 * Singapore (1970)
 * South Africa (1966)
 * Spain (1947)
 * Thailand (1973)
 * Turkey (1967)
 * United Kingdom (1971)
 * Venezuela (1962)
 * Yugoslavia (now Croatia, Serbia, Slovenia, Bosnia and Herzegovina, Montenegro, and North Macedonia) (1956)

By 1975, so many countries were using the German system that it was established as an ISO standard, as well as the official United Nations document format. By 1977, A4 was the standard letter format in 88 of 148 countries. Today the standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Costa Rica, Colombia, Venezuela, Chile, and the Philippines, the US letter format is still in common use, despite their official adoption of the ISO standard.

The weight of an A-series sheet of a given paper weight can be calculated by knowing the ratio of its size to the A0 sheet. For example, an A4 sheet is $1/undefined$ the size of an A0 sheet, so if it is made from 80-g/m$2$ paper, it weighs $1/undefined$ of 80 g, which is 5 g.

B series

The B series paper sizes are less common than the A series. They have the same aspect ratio as the A series:

 * $$\frac{a}{b}=\sqrt{2} = 1.41...$$

However, they have a different area. The area of B series sheets is in fact the geometric mean of successive A series sheets. B1 is between A0 and A1 in size, with an area of $$\frac{1}{\sqrt{2}}$$ m$2$, or about 0.707 m$2$. As a result, B0 is 1 metre wide, and other sizes of the series are a half, a quarter, or further fractions of a metre wide: in general, every B size has exactly one side of length $$\frac{1 \operatorname{m}}{2^n}$$ for $$n \in \mathbb{N}$$. That side is the short side for B0, B2, B4, etc., and the long side for B1, B3, B5, etc.

While less common in office use, the B series is used for a variety of applications in which one A-series size would be too small but the next A-series size is too large, or because they are convenient for a particular purpose.

 * B4, B5, and B6 are used for envelopes that will hold C-series envelopes.
 * B4 is quite common in printed music sheets.
 * B5 is a relatively common choice for books.
 * B7 is equal to the passport size ID-3 from ISO/IEC 7810.
 * Many posters use B-series paper or a close approximation, such as 50 cm × 70 cm ~ B2.

The B-series is widely used in the printing industry to describe both paper sizes and printing press sizes, including digital presses. B3 paper is used to print two US letter or A4 pages side by side using imposition; four pages would be printed on B2, eight on B1, etc.

C series
The C series is defined in ISO 269, which was withdrawn in 2009 without a replacement, but is still specified in several national standards. It is primarily used for envelopes. The area of C series sheets is the geometric mean of the areas of the A and B series sheets of the same number; for instance, the area of a C4 sheet is the geometric mean of the areas of an A4 sheet and a B4 sheet. This means that C4 is slightly larger than A4, and slightly smaller than B4. The practical usage of this is that a letter written on A4 paper fits inside a C4 envelope, and both A4 paper and C4 envelope fits inside a B4 envelope.

Some envelope formats with mixed sides from adjacent sizes (and thus an approximate aspect ratio of 2:1) are also defined in national adaptations of the ISO standard, e.g. DIN C6/C5 (also known as C65) is 114 mm × 229 mm where the common side to C5 and C6 is 162 mm. This format allows an envelope holding an A-sized paper folded in three, e.g. for the C65, an A4.

Overview of ISO paper sizes
The $$\alpha$$ variables are the distinct first terms in the three geometric progressions of the same common ratio equal to the square root of two. Each of the three geometric progressions (corresponding to the three series A, B, and C) is formed by all possible paper dimensions (length and width) of the series arranged in decreasing order. This interesting arrangement of dimensions is also very useful—not only does it form a geometric progression with easy-to-remember formulae, but also each consecutive pair of values (like a sliding window of size 2) will automatically correspond to the dimensions of a standard paper format in the series.

The tolerances specified in the standard are

 * ±1.5 mm (0.06 in) for dimensions up to 150 mm (5.9 in),
 * ±2 mm (0.08 in) for lengths in the range 150 to 600 mm (5.9 to 23.6 in) and
 * ±3 mm (0.12 in) for any dimension above 600 mm (23.6 in).

German original
The German standard DIN 476 was published on 18 August 1922 and is the original specification of the A, B and C sizes. In 1991, it was split into DIN 476-1 for the A and B formats and 476-2 for the C series. The former has been withdrawn in 2002 in favor of adopting the international standard as DIN EN ISO 216, but part 2 has been retained and was last updated in 2008.

The first and the second editions of DIN 476 from 1922 and 1925 also included a D series.

The smallest formats in the original specifications for each series were A13, B13, C8, and D8. Sizes A11 through A13 were no longer listed in the 1930 edition, nor were B11 through B13. C9 and C10 were added in the 1976 revision for compatibility with photography sizes: C8 closely matches 6×9 photos, and C9 and C10 closely match 7×7 and 5×5 slides, respectively.

DIN 476 provides for formats larger than A0, denoted by a prefix factor. In particular, it lists the formats 2A0 and 4A0, which are twice and four times the size of A0 respectively. However, ISO 216:2007 notes 2A0 and 4A0 in the table of Main series of trimmed sizes (ISO A series) as well: "The rarely used sizes [2A0 and 4A0] which follow also belong to this series."

DIN 476 also used to specify slightly tighter tolerances than ISO 216:

 * ±1 mm (0.04 in) for dimensions up to 150 mm (5.9 in),
 * ±1.5 mm (0.06 in) for lengths in the range 150 mm to 600 mm (5.9 to 23.6 in) and
 * ±2 mm (0.08 in) for any dimension above 600 mm (23.6 in).

There used to be a standard, DIN 198, that was just a table of recommended A series formats for a number of business applications. The 1976 edition of this standard introduced a size $1/2$ A4 and suggested it for some forms and slips.

Swedish extensions

The Swedish standard SIS 01 47 11 generalized the ISO system of A, B, and C formats by adding D, E, F, and G formats to it. Its D format sits between a B format and the next larger A format (just like C sits between A and the next larger B). The remaining formats fit in between all these formats, such that the sequence of formats A4, E4, C4, G4, B4, F4, D4, *H4, A3 is a geometric progression, in which the dimensions grow by a factor $$\sqrt[16]{2}$$ from one size to the next. However, this SIS standard does not define any size between a D format and the next larger A format (called *H in the previous example).

Of these additional formats, G5 (169 × 239 mm) and E5 (155 × 220 mm) are popular in Sweden and the Netherlands for printing dissertations, but the other formats have not turned out to be particularly useful in practice. They have not been adopted internationally and the Swedish standard has been withdrawn.

The Swedish and German D series basically contain the same sizes but are offset by one, i.e. DIN D4 equals SIS D5 and so on.

Japanese variation
The Japanese standard JIS P 0138 defines two main series of paper sizes. The JIS A-series is identical to the ISO A-series except that it has slightly different tolerances. The area of B-series paper is 1.5 times that of the corresponding A-paper (instead of the factor $$\sqrt{2} = 1.414...$$ for the ISO B-series), so the length ratio is approximately 1.22 times the length of the corresponding A-series paper. The aspect ratio of the paper is the same as for the A-series paper. Both A- and B-series paper are widely available in Japan, Taiwan and China, and most photocopiers are loaded with at least A4 and either one of A3, B4, and B5 paper.

Cascading Style Sheets (CSS) only supports the most popular of the Japanese sizes, JIS-B4 and JIS-B5.

A popular size for books, dubbed AB, combines the shorter edges of A4 and B4. Another two with an aspect ratio approximating 16:9 are 20% narrower variants of A6 and B6, respectively, the latter resulting from cutting JIS B1 into sheets (thus "B40").

There are also a number of traditional paper sizes, which are now used mostly by printers. The most common of these old series is the Shiroku-ban and the Kiku paper sizes.

Chinese extensions
The Chinese standard GB/T 148–1997, which replaced GB 148–1989, documents the standard ISO series, A and B, but adds a custom D series. This Chinese format originates from the Republic of China (1912–1949). The D series is not identical to the German or Swedish D series. It does not strictly follow the same principles as ISO paper sizes: The aspect ratio is only very roughly $$\sqrt{2}$$. The short side of the size is always 4 mm longer than the long side of the next smaller size. The long side of the size is always exactly – i.e. without further rounding – twice as long as the short side of the next smaller size.

Indian variants
The Bureau of Indian Standards recommends the "ISO-A series" size of drawing sheet for engineering drawing works. The Bureau of Indian Standards specifies all the recommendations for engineering drawing sheets in its bulletin IS 10711: 2001.

The Bureau extended the ISO-A series with a Special Elongated Sizes (Second Choice). These sizes are achieved by increasing the shorter dimensions of a sheet of the ISO A series to lengths that are multiples of the shorter dimensions of the chosen basic sheet; in effect, all of the Indian elongated sizes emulate having several regular-size sheets joined on their long edge.

There is also a Exceptional Elongated Sizes (Third Choice). These sizes are obtained by increasing the shorter dimensions of a sheet of the ISO-A series to lengths that are multiples of the shorter dimensions of the chosen basic sheet. These sizes are used when a very large or extra elongated sheet is needed.

Soviet variants
The first standard of paper size in the Soviet Union was OST 303 in 1926. Six years later, it was replaced by OST 5115 which generally followed DIN 476 principles, but used Cyrillic lowercase letters instead of Latin uppercase, had the second row shifted so that б0 (B0) roughly corresponded to B1 and, more importantly, had slightly different sizes:

The general adaptation of ISO 216 in the Soviet Union, which replaced OST 5115, was GOST 9327. In its 1960 version, it lists formats down to A13, B12 and C8 and also specifies $1/4$, $1/2$ and $3/4$ prefixes for halving the shorter side (repeatedly) for stripe formats, e.g. $1 1/2$A4 = 105 mm × 297 mm.

A standard for technical drawings from 1960, GOST 3450, introduces alternative numeric format designations to deal with very high or very wide sheets. These 2-digit codes are based upon A4 = "11": The first digit is the factor the longer side (297 mm) is multiplied by and the second digit is the one for the shorter side (210 mm), so "24" is 2×297 mm × 4×210 mm = 594 mm × 840 mm.

GOST 3450 from 1960 was replaced by ESKD GOST 2301 in 1968, but the numeric designations remained in popular use much longer. The new designations were not purely numeric but consisted of the ISO label followed by an 'x', or possibly the multiplication sign '×', and the factor, e.g. DIN 2A0 = GOST A0×2, but DIN 4A0 ≠ GOST A0×4, also listed are: A0×3, A1×3, A1×4, A2×3–A2×5, A3×3–A3×7, A4×3–A4×9. The formats ...×1 and ...×2 usually would be aliases for existing formats.

Elongated sizes
ISO 5457, last updated in 1999, introduces elongated sizes that are formed by a combination of the dimensions of the short side of an A-size (e.g. A2) with the dimensions of the long side of another larger A-size (e.g. A0). The result is a new size, for example with the abbreviation A2.0 we would have a mm size.

These drawing paper sizes have been adopted by ANSI/ASME Y14.1M for use in the United States, alongside A0 through A4 and alongside inch-based sizes.

International envelope and insert sizes
DIN 5008 (previously DIN 676) prescribes, among many other things, two variants, A and B, for the location of the address field on the first page of a business letter and how to fold the A4 sheet accordingly, so the only part visible of the main content is the subject line.

International raw sizes
ISO 5457 specifies drawing paper sizes with a trimmed size equal to the A series sizes from A4 upward. The untrimmed sizes are 3 to 4 cm larger and rounded to the nearest centimetre. A0 through A3 are used in landscape orientation, while A4 is used in portrait orientation. Designations for preprinted drawing paper include the base sizes and a suffix, either T for trimmed or U for untrimmed sheets.

The withdrawn standard ISO 2784 did specify sizes of continuous, fan-fold forms based upon whole inches as was common for paper in continuous lengths in automatic data processing (ADP) equipment. Specifically, 12 inches (304.8 mm) were considered an untrimmed variant of the A4 height of 297 mm.

PA4 or L4
A transitional size called PA4 (210 ×), sometimes dubbed L4, was proposed for inclusion into the ISO 216 standard in 1975. It has the height of Canadian P4 paper (215 mm × 280 mm, about $1 3/4$ in × 11 in) and the width of international A4 paper (210 ×), i.e. it uses the smaller value among the two for each side. The table shows how this format can be generalized into an entire format series.

The PA formats did not end up in ISO 216, because the committee decided that the set of standardized paper formats should be kept to the minimum necessary. However, PA4 remains of practical use today. In landscape orientation, it has the same 4:3 aspect ratio as the displays of traditional TV sets, some computer displays (e.g. the iPad) and data projectors. PA4, with appropriate margins is, therefore, a good choice as the format of presentation slides.

As a compromise between the two most popular paper sizes globally, PA4 is used today by many international magazines, because it can be printed easily on equipment designed for either A4 or US Letter. That means (in practice) it has turned out to be not so much a paper size as a page format. Apple, for instance, requires this format for digital music album booklets.

The size 210 mm × 280 mm was documented in the Canadian standard CAN2-200.2-M79 "Common Image Area for Paper Sizes P4 and A4".

F4
A non-standard F4 paper size is common in Southeast Asia. It is a transitional size with the shorter side of ISO A4 (210 mm, $2 1/2$ inch) and the longer side of British Foolscap (13-inch, 330 mm). ISO A4 is exactly 90% the height of F4. This size is sometimes also known as (metric) 'foolscap' or 'folio'.

In some countries, the narrow side of F4 is slightly broader: 8.5 inches (216 mm) or 215 mm. It is then equivalent to the US Government Legal and Foolscap Folio sizes. In Indonesia, where it is the legally-mandated paper size for use in the printing of national legislation, it is sometimes called Folio or HVS (from houtvrij schrijfpapier, "wood-free writing paper"). In Philippines, it is commonly called long bond as opposed to short bond which refers to the US Letter paper size.

A sheet of F4 can be cut from a sheet of SRA4 with very little wastage. The size is also smaller than its Swedish equivalent SIS F4 at 239 mm × 338 mm.

Weltformat
The Weltformat (world format) was developed by German chemist Wilhelm Ostwald in 1911 as part of Die Brücke, around the same time DIN 476 was first discussed. It shares the same design primitives, especially the aspect ratio, but is based upon 1 cm as the short edge of the smallest size. Sizes were designated by roman numerals. The result, for the fourth through fourteenth size, is close to the DIN/ISO C series.

The sizes have been used for some print products in the early 20th century in central Europe but got replaced by DIN sizes almost entirely. However, it was successfully adopted from 1913 onwards for posters and placards in Switzerland. Even today, the default size for posters in Swiss advertisements, F4, is colloquially known as Weltformat, although it measures 895 mm × 1280 mm, i.e. 1 cm less than size XIV. This poster size goes alongside F12 "Breitformat" 2685 mm × 1280 mm (3 × F4) and F24 "Großformat" 2685 mm × 2560 mm (2 × 3 × F4, ) as well as F200 "Cityformat" 1165 mm × 1700 mm.

A0a
Although the movement is towards the international standard metric paper sizes, on the way there from the traditional ones there has been at least one new size just a little larger than that used internationally.

British architects and industrial designers once used a size called "Antiquarian", 31 ×, as listed above, but given in the New Metric Handbook (Tutt & Adler 1981) as 813 × for board size. This is a little larger than ISO A0, 841 mm × 1189 mm. So for a short time, a size called A0a of 1000 × was used in Britain, which is actually just a slightly shorter version of ISO B0 at 1414 mm.

Pliego
The most common paper sizes used for commercial and industrial printing in Colombia are based upon a size referred to as pliego that is ISO B1 (707 mm × 1000 mm) cut to full decimetres. Smaller sizes are derived by halving as usual and just get a vulgar fraction prefix: $2 3/4$ pliego and $3 1/2$ pliego.

K
In East Asia, i.e. Japan, Taiwan, and China in particular, there is a number of similar paper sizes in common use for book-making and other purposes. Confusingly, a single designation is often used with slightly different edge measures: The base sheet is labeled 1K (or 1开, where K stands for ; or 1切/1取 in Japanese); all smaller sizes derived by halving have the power of two number, i = 2n, in front of the uppercase letter K. The number in ISO designations, in contrast, is the exponent n that would yield the number of sheets cut from the base sizes.

The sizes of such folios depend on the base sheet. Pre-metric standards include:

 * The imperial 菊判 (kiku-ban), named after the Chrysanthemum watermark on imperial paper, measuring 636mm × 939mm.
 * The four-by-six 四六判 shi-roku-ban (4×6 or 4/6), where the final size at 32K was measured 4 by 6 sun in Japan, c. mm, or slightly more,  mm i.e.  sun.
 * In Taiwan, the traditional base size 1K inherited from Japan is sometimes quoted as measuring inches exactly, which is off by c. 1 millimeter from the commonly quoted metric base size of  mm, which is directly derived from  sun or  shaku.
 * The three-by-five 三五判 (3×5 or 3/5), where the final size at 32K is slightly less than 3 by 5 sun, often given as mm which would be c.  sun.

The 4/6 standard has given rise to newer metric book-size standards, including:

 * The modern Japanese size for books, simply labeled B and is specified as millimeters. It is not directly related to the similar JIS B series, where B1 is slightly smaller.
 * The Chinese SAC D series.

Inch-based loose sizes
The United States, Canada, and the Philippines primarily use a different system of paper sizes from the rest of the world. The current standard sizes are unique to those countries, although due to the size of the North American market and proliferation of both software and printing hardware from the region, other parts of the world have become increasingly familiar with these sizes (though not necessarily the paper itself). Some traditional North American inch-based sizes differ from the Imperial British sizes described below.

Common American loose sizes
Letter, Legal and Ledger/Tabloid are by far the most commonly used of these for everyday activities, and the only ones included in Cascading Style Sheets (CSS).

The origins of the exact dimensions of Letter size paper are lost in tradition and not well documented. The American Forest and Paper Association argues that the dimension originates from the days of manual papermaking and that the 11-inch length of the page is about a quarter of "the average maximum stretch of an experienced vatman's arms." However, this does not explain the width or aspect ratio.

Outside of North America, Letter size may also be known as "American Quarto". If one accepts some trimming, the size is indeed one quarter of the old Imperial paper size known as Demy, 17+1/2 ×. Manufacturers of computer printers, however, recognize inch-based Quarto as $3 3/4$ or 10.83 inch long.

Usage and adoption
US paper sizes are currently standard in the United States and are the most commonly used formats at least in the Philippines, most of Mesoamerica and Chile. The latter use US Letter, but their Legal size is 13 inches tall (recognized as Foolscap by printer manufacturers, i.e. one inch shorter than its US equivalent.

Mexico and Colombia, for instance, have adopted the ISO standard, but the US Letter format is still the system in use throughout the country. It is rare to encounter ISO standard papers in day-to-day uses, with Carta (Letter), Oficio (Government-Legal), and Doble carta (Ledger/Tabloid) being nearly universal. Printer manufacturers, however, recognize Oficio as 13.4 inch long.

In Canada, select US paper sizes are a de facto standard.

Variant American loose sizes
There is an additional paper size, 8 ×, to which the name Government-Letter was given by the IEEE Printer Working Group (PWG). It was prescribed by Herbert Hoover when he was Secretary of Commerce to be used for US government forms, apparently to enable discounts from the purchase of paper for schools, but more likely due to the standard use of trimming books (after binding) and paper from the standard letter size paper to produce consistency and allow "bleed" printing. In later years, as photocopy machines proliferated, citizens wanted to make photocopies of the forms, but the machines did not generally have this size of paper in their bins. Ronald Reagan therefore had the US government switch to regular Letter size, which is half an inch both longer and wider. The former government size is still commonly used in spiral-bound notebooks, for children's writing and the like, a result of trimming from the current Letter dimensions.

By extension of the American standards, the halved Letter size, 5+1/2 ×, meets the needs of many applications. It is variably known as Statement, Stationery, Memo, Half Letter, Half A (from ANSI sizes) or simply Half Size, and as Invoice by printer manufacturers. Like the similar-sized ISO A5, it is used for everything from personal letter writing to official aeronautical maps. Organizers, notepads, and diaries also often use this size of paper; thus 3-ring binders are also available in this size. Booklets of this size are created using word processing tools with landscape printing in two columns on letter paper which are then cut or folded into the final size.

A foot-long sheet with the common width of Letter and (Government) Legal, i.e. 8+1/2 x, would have an aspect ratio very close to the square root of two as used by international paper sizes and would actually almost exactly match ISO RA4 (215 mm × 305 mm). This size is sometimes known as European Fanfold.

While Executive refers to 7+1/4 × in America, the Japanese organization for standardization specified it as 216 ×, which is elsewhere known as Government Legal or Foolscap.

Standardized American paper sizes

In 1996, the American National Standards Institute adopted ANSI/ASME Y14.1 which defined a regular series of paper sizes based upon the de facto standard 8+1/2 × Letter size which it assigned "ANSI A", intended for technical drawings, hence sometimes labeled "Engineering". This series is somewhat similar to the ISO standard in that cutting a sheet in half would produce two sheets of the next smaller size and therefore also includes Ledger/Tabloid as "ANSI B". Unlike the ISO standard, however, the arbitrary base sides forces this series to have two alternating aspect ratios. For example, ANSI A is less elongated than A4, while ANSI B is more elongated than A3.

The Canadian standard CAN2 9.60-M76 and its successor CAN/CGSB 9.60-94 "Paper Sizes for Correspondence" specified paper sizes P1 through P6, which are the U.S. paper sizes rounded to the nearest 5 mm. All custom Canadian paper size standards were withdrawn in 2012.

With care, documents can be prepared so that the text and images fit on either ANSI or their equivalent ISO sheets at a 1:1 reproduction scale.

Other, informal, larger sizes continuing the alphabetic series illustrated above exist, but they are not part of the series per se, because they do not exhibit the same aspect ratios. For example, Engineering F size is 28 × with ca. 1.4286:1; it is commonly required for NAVFAC drawings, but is generally less commonly used. Engineering G size is 22+1/2 inch high, but it is a roll format with a variable width up to 90 inch in increments of 8+1/2 inch. Engineering H through N sizes are also roll formats.

Such huge sheets were at one time used for full-scale layouts of aircraft parts, automotive parts, wiring harnesses, and the like, but are slowly being phased out, due to widespread use of computer-aided design (CAD) and computer-aided manufacturing (CAM). Some visual arts fields also continue to use these paper formats for large-scale printouts, such as for displaying digitally painted character renderings at life-size as references for makeup artists and costume designers or to provide an immersive landscape reference.

Architectural sizes
In addition to the system as listed above, there is a corresponding series of paper sizes used for architectural purposes defined in the same standard, ANSI/ASME Y14.1, which is usually abbreviated "Arch". This series also shares the property that bisecting each size produces two of the size below, with alternating aspect ratios. It may be preferred by North American architects because the aspect ratios (4:3 and 3:2) are ratios of small integers, unlike their ANSI (or ISO) counterparts. Furthermore, the aspect ratio 4:3 matches the traditional aspect ratio for computer displays.

The size Arch E1 has a different aspect ratio because it derives from adding 6 inches to each side of Arch D or subtracting the same amount from Arch E. Printer manufacturer recognize it as wide-format. An intermediate size between Arch C and D with a long side of 30 inch does not exist.

Demitab
The demitab or demi-tab (a portmanteau of the French word 'demi' [half] and 'tabloid') is 8 x, i.e. roughly one half of a sheet of 11 x tabloid-size paper.

"Demitab", "broadsheet" or "tabloid" format newspapers are not necessarily printed on paper measuring exactly their nominal size.

Notebook sizes
The sizes listed above are for paper sold loose in reams. There are many sizes of tablets of paper, that is, sheets of paper bound at one edge, usually by a strip of plastic or hardened PVA adhesive. Often there is a pad of cardboard (also known as paperboard or greyboard) at the bottom of the stack. Such a tablet serves as a portable writing surface, and the sheets often have lines printed on them, usually in non-repro blue, to make writing in a line easier. An older means of binding is to have the sheets stapled to the cardboard along the top of the tablet; there is a line of perforated holes across every page just below the top edge from which any page may be torn off. Lastly, a pad of sheets each weakly stuck with adhesive to the sheet below, trademarked as "Post-It" or "Stick-Em" and available in various sizes, serve as a sort of tablet.

"Letter pads" are 8+1/2 x, while the term "legal pad" is often used by laymen to refer to pads of various sizes including those of 8+1/2 x. Stenographers use "steno pads" of 6 x. The steno pad size is also used by Scholastic Corporation as the textblock size of their hardcover editions of the Harry Potter novels, with paperback editions using DIN D6.

Envelope sizes
This implies that all postcards have an aspect ratio in the range from = 1.18 to  = 1.71, but the machinable aspect ratio is further restricted to a minimum of 1.30. The only ISO 216 size in the US postcard range is A6. The theoretical maximum aspect ratio for enveloped letters is = 3.29, but is explicitly limited to 2.50.

Grain
Most industry standards express the direction of the grain last when giving dimensions (that is, 17 × 11 inches is short grain paper and 11 × 17 inches is long grain paper), although alternatively the grain alignment can be explicitly indicated with an underline ( 11 × 17 is a short grain) or the letter "M" for "machine" (11M × 17 is a short grain). Grain is important because the paper will crack if folded across the grain: for example, if a sheet 17 × 11 inches is to be folded to divide the sheet into two 8.5 × 11 halves, then the grain will be along the 11-inch side. Paper intended to be fed into a machine that will bend the paper around rollers, such as a printing press, photocopier or typewriter, should be fed grain edge first so that the axis of the rollers is along the grain.

Traditional inch-based paper sizes

Traditionally, a number of different sizes were defined for large sheets of paper, and paper sizes were defined by the sheet name and the number of times it had been folded. Thus a full sheet of "royal" paper was 25 × 20 inches, and "royal octavo" was this size folded three times, so as to make eight sheets, and was thus 10 × $4 1/2$ inches. Royal sizes were used for posters and billboards.

Imperial sizes were used in the United Kingdom and its territories and some survived in US book printing.

Traditional British paper sizes
Traditional British paper sizes are referred to by the number of sheets that can be cut from a sheet of uncut paper. The standard Imperial uncut paper sizes used in offices and schools were "foolscap", "post", and "copy". Each uncut sheet can then be halved into folios, quartered into quartos, or eighthed into octavos.

Traditional French paper sizes
Before the adoption of the ISO standard system in 1967, France had its own paper size system. Raisin format is still in use today for artistic paper. All are standardized by the AFNOR. Their names come from the watermarks that the papers were branded with when they were handcrafted, which is still the case for certain art papers. They also generally exist in double versions where the smallest measure is multiplied by two, or in quadruple versions where both measures have been doubled.

Business card sizes
The international business card has the size of the smallest rectangle containing a credit card rounded to full millimeters, but in Western Europe, it is rounded to half centimetres (rounded up in Northern Europe), in Eastern Europe to full centimetres, in North America to half inches. However, credit card size, as defined in ISO/IEC 7810, also specifies rounded corners and thickness.

Newspaper sizes
Newspapers have a separate set of sizes.

 * Compact: AR 1.54
 * Berliner: aspect ratio is 1.5
 * Rhenish: AR 1.4–1.5
 * Tabloid 1.34
 * Broadsheet: aspect ratio 1.25

In a recent trend many newspapers have been undergoing what is known as "web cut down", in which the publication is redesigned to print using a narrower (and less expensive) roll of paper. In extreme examples, some broadsheet papers are nearly as narrow as traditional tabloids.

title: Paper size


text:
Elvenking

Elvenking may refer to:

 * Elvenking (Middle-earth), a character in J. R. R. Tolkien's legendarium
 * Elvenking (band), an Italian folk/power metal band
 * Erlking, a german/danish folklore fairy
 * Erlkönig, a poem by Goethe

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Elvenking


text:
Talk:Smithsonian Institution

Untitled
How about affiliated institutions like Blackhawk Museum in Danville, California, where the Smithsonian's Tucker automobile is parked? Ortolan88

Needs a section on the associated record label of historical and cultural recordings of world music. heidimo 15:06, 9 Mar 2004 (UTC)

chancellor
May want to note the chancellor is the chief justice of the supreme court (odd fact): http://www.cnn.com/interactive/law/0507/chief.justice.duties/content4.html RAccettura

Smithsonian museums template?
Might it be a good idea to create a template that lists all the different Smithsonian museums and other buildings, so that they all could appear on the museums' respective pages and allow for quick browsing?

Folkways
Where to put Smithsonian Folkways Recordings?

Smithsonian Press
In 2005 Smithsonian Press folded owing to financial and administrative ineptitude. Most authors (including me) were told nothing of the impending collapse, and some had to approach their congressmen to obtain the barest of facts. Thousands of unsold books were remaindered with no possibility of authors recovering royalties on those volumes. Clearly the regents and congress were asleep at the switch, and apparently there has been no accountability at any level. Lacking further contacts in the DC area, I cannot pursue the matter but it should be addressed in this article. How a government-funded business goes broke should make illuminating reading.

B. Tillman, May 2007

 * How is this "Smithsonian Press" different from the Smithsonian Institution Scholarly Press which per the web page seems to be going strong?--2606:A000:131D:4413:AD7B:3D15:F242:D462 (talk) 20:56, 28 December 2018 (UTC)

A talk by Michael Edson
An interesting talk by Michael Edson, Smithsonian Institution's Director of Web and New Media Strategy

museum guide
As I understand it, the Smithsonian has a document that gives suggested usage for museums. I was told about this by a (non-Smithsoniam) museum curator regarding the units for jet engine thrust. It might be that it is only available to museum curators, but I suspect not. I am interested in it, as it might also be useful for some questions related to WP pages, though not necessarily this one. I don't even know what to call it, which complicates doing a web search. Gah4 (talk) 10:19, 19 April 2020 (UTC)

title: Talk:Smithsonian Institution


text:
Cunard (disambiguation)

Cunard usually refers to Cunard Line, a shipping company founded by Samuel Cunard.

Cunard may also refer to:

 * Cunard Building in Liverpool, the former headquarters of Cunard Line
 * Cunard (surname)
 * Cunard (coachbuilder), London-based supplier of car bodies.

title: Cunard (disambiguation)


text:
RMS Queen Mary

RMS Queen Mary is a retired British ocean liner that sailed primarily on the North Atlantic Ocean from 1936 to 1967 for the Cunard Line. Built by John Brown & Company in Clydebank, Scotland, she was subsequently joined by RMS Queen Elizabeth in Cunard's two-ship weekly express service between Southampton, Cherbourg and New York. The Queens were a British response to the express superliners built by German, Italian and French companies in the late 1920s and early 1930s.

Queen Mary sailed on her maiden voyage on 27 May 1936 and won the Blue Riband that August; she lost the title to SS Normandie in 1937 and recaptured it in 1938, holding it until 1952, when it was taken by the new SS United States. With the outbreak of World War II, she was converted into a troopship and ferried Allied soldiers during the conflict. On one voyage in 1943, she carried over 16,600 people, the still-standing record for the most people on a vessel.

Following the war, Queen Mary was refitted for passenger service and along with Queen Elizabeth commenced the two-ship transatlantic passenger service for which the two ships were initially built. The pair dominated the transatlantic passenger transportation market until the dawn of the jet age in the late 1950s. By the mid-1960s, Queen Mary was ageing and was operating at a loss.

After several years of decreased profits for Cunard Line, Queen Mary was officially retired from service in 1967. She left Southampton for the last time on 31 October 1967 and sailed to the port of Long Beach, California, United States, where she was permanently moored. The City of Long Beach bought the ship to serve as a tourist attraction featuring restaurants, a museum and a hotel. The city contracted out management of the ship to various third-party firms over the years. It took back operational control in 2021.

Construction and naming
With Weimar Germany launching SS Bremen (1928) and SS Europa (1930) into service, Britain did not want to be left behind in the shipbuilding race. White Star Line began construction on their 80,000-ton Oceanic in 1928, while Cunard planned a 75,000-ton unnamed ship of their own. Construction on the ship, then known only as "Hull Number 534", began in December 1930 on the River Clyde by the John Brown & Company shipyard at Clydebank in Scotland. Work was halted in December 1931 due to the Great Depression and Cunard applied to the British Government for a loan to complete 534. The loan was granted, with enough money to complete the unfinished ship, and also to build a running mate, with the intention to provide a two ship weekly service to New York.

One condition of the loan was that Cunard merge its operations with the White Star Line, another struggling British shipping company, which was Cunard's chief British rival at the time and which had already been forced by the depression to cancel construction of its Oceanic. Both lines agreed and, on 10 May 1934, the companies created a third company, Cunard-White Star Line, to manage their newly combined fleet. Work on Queen Mary resumed immediately and she was launched on 26 September 1934. Completion ultimately took $3 1/2$ years and cost 3.5 million pounds sterling, then equal to $17.5 million (equivalent to $ in ). Cunard's Chief Naval Architect, George Mcleod Paterson, was the principal designer. Prior to the ship's launch, the River Clyde had to be specifically deepened to cope with her size, this being undertaken by the engineer D. Alan Stevenson.

The ship was named after Mary of Teck, consort of King George V. Until her launch, the name was kept a closely guarded secret. Legend has it that Cunard intended to name the ship Victoria, in keeping with company tradition of giving its ships names ending in "ia", but when company representatives asked the King's permission to name the ocean liner after Britain's "greatest Queen", he said his wife, Mary of Teck, would be delighted. And so, the legend goes, the delegation had, of course, no other choice but to report that No. 534 would be called Queen Mary.

This story has always been denied by company officials, and traditionally the names of royal family members have only been used for capital ships of the Royal Navy. This anecdote has been widely contested ever since Frank Braynard published it in his 1947 book, Lives of the Liners. Some support for the story was provided by Washington Post editor Felix Morley, who sailed as a guest of the Cunard Line on Queen Mary's 1936 maiden voyage. In his 1979 autobiography, For the Record, Morley wrote that he was placed at a table with Sir Percy Bates, chairman of the Cunard Line. Bates told him the story of the naming of the ship "on condition you won't print it during my lifetime." The story was finally proven in 1988 when Braynard attended the same dinner party as Eleanor Sparkes, daughter of Sir Ashley Sparkes, who'd been with Bates during the conversation with George V. She confirmed the "favourite ship story" to him, telling the exact anecdote that Braynard had published in his book.

Despite this, Cunard still denies the name change. It is also possible the name Queen Mary was decided upon as a compromise between Cunard and the White Star Line, as both lines had naming traditions. White Star used names ending in "ic", while Cunard used names ending in "ia".

The name had already been given to the Clyde turbine steamer TS Queen Mary, so Cunard made an arrangement with its owners and this older ship was renamed Queen Mary II.

Queen Mary was fitted with 24 Yarrow boilers in four boiler rooms and four Parsons turbines in two engine rooms. The boilers delivered 400 pounds per square inch (28 bar) steam at 700 °F (371 °C) which provided a maximum of 212,000 shp to four propellers, each turning at 200 RPM.

Pre-Second World War
In 1934 the new liner was launched by Her Majesty Queen Mary as RMS Queen Mary. On her way down the slipway, Queen Mary was slowed by eighteen drag chains, which checked the liner's progress into the River Clyde, a portion of which had been widened to accommodate the launch.

24 March 1936, leaving Clydebank she ran aground on the River Clyde but with the help of tugboats she was refloated.

Queen Mary achieved 32.84 knots on her acceptance trials in the spring of 1936.

When she sailed on her maiden voyage from Southampton on 27 May 1936, she was commanded by Sir Edgar Britten, who had been the master designate for Cunard White Star whilst the ship was under construction at the John Brown shipyard. Queen Mary measured, making her the world's largest passenger ship. Her rival SS Normandie, only measured 79,280 GRT. However, CGT modified the Normandie to increase her size to 83,243 GRT, reclaiming the title of world's largest passenger ship. Queen Mary sailed at high speed for most of her maiden voyage to New York, until heavy fog forced a reduction of speed on the final day of the crossing, arriving in New York Harbor on 1 June 1936.

Queen Mary design was criticised for being too traditional, especially when Normandie hull was revolutionary with a clipper-shaped, streamlined bow. Except for her cruiser stern, she seemed to be an enlarged version of her Cunard predecessors from the pre-First World War era. Her interior design, while mostly Art Deco, seemed restrained and conservative when compared to the ultramodern French liner. Nonetheless Queen Mary proved to be the more popular vessel than her rival, in terms of passengers carried.

In August 1936, Queen Mary captured the Blue Riband from Normandie, with average speeds of 30.14 kn westbound and 30.63 kn eastbound. In 1937, Normandie received a new set of propellers and reclaimed the Blue Riband. However, in 1938, under the command of Robert B. Irving, Queen Mary took back the Blue Riband in both directions, with average speeds of 30.99 kn westbound and 31.69 kn eastbound, records which stood until lost to SS United States in 1952.

Interior
Among facilities available on board Queen Mary, the liner featured two indoor swimming pools, beauty salons, libraries and children's nurseries for all three classes, a music studio and lecture hall, telephone connectivity to anywhere in the world, outdoor paddle tennis courts and dog kennels. The largest room on board was the cabin class (first class) main dining room (grand salon), spanning three stories in height and anchored by wide columns. The ship had many air-conditioned public rooms on board. The cabin-class swimming pool facility spanned over two decks in height. This was the first ocean liner to be equipped with her own Jewish prayer room – part of a policy to show that British shipping lines avoided the antisemitism evident in Nazi Germany.

The cabin-class main dining room featured a large map of the transatlantic crossing, with twin tracks symbolising the winter/spring route (further south to avoid icebergs) and the summer/autumn route. During each crossing, a small motorised model of Queen Mary would travel along the mural to indicate the vessel's progress en route.

As an alternative to the main dining room, Queen Mary featured a separate cabin-class Verandah Grill on the Sun Deck at the upper aft of the ship. The Verandah Grill was an exclusive à la carte restaurant with a capacity of approximately eighty passengers and was converted to the Starlight Club at night. Also on board was the Observation Bar, an Art Deco-styled lounge with wide ocean views. Arthur Joseph Davis of Messrs, Mewes and Davis, and Benjamin Wistar Morris designed the Queen Mary's interior spaces. The Bromsgrove Guild constructed much of the ship's interior, while H.H. Martyn & Co. built the staircases, foyers, and entrances.

Woods from different regions of the British Empire were used in her public rooms and staterooms. Accommodation ranged from fully equipped, luxurious cabin (first) class staterooms to modest and cramped third-class cabins. Artists commissioned by Cunard in 1933 for works of art in the interior include Edward Wadsworth and A. Duncan Carse.

Second World War
In late August 1939, Queen Mary was on a return run from New York to Southampton. The international situation led to her being escorted by the battlecruiser HMS Hood (51). She arrived safely and set out again for New York on 1 September. By the time she arrived, war had been declared and she was ordered to remain in port alongside Normandie until further notice.

In March 1940, Queen Mary and Normandie were joined in New York by Queen Mary new running mate RMS Queen Elizabeth, fresh from her secret voyage from Clydebank. The three largest liners in the world sat idle for some time until the Allied commanders decided that all three ships could be used as troopships. Normandie was destroyed by fire during her troopship conversion. Queen Mary left New York for Sydney, Australia in March 1940, where she, along with several other liners, was converted into a troopship to carry Australian and New Zealand soldiers to the United Kingdom.

In the conversion, the ship's hull, superstructure, and funnels were painted navy grey. As a result of her new colour, and in combination with her great speed, she became known as the "Grey Ghost". To protect against magnetic mines, a degaussing coil was fitted around the outside of the hull. Inside, stateroom furniture and decoration were removed and replaced with triple-tiered (fixed) wooden bunks, which were later replaced by "standee" (fold-up) bunks.

A total of 6 mi of carpet, 220 cases of china, crystal and silver services, tapestries, and paintings were removed and stored in warehouses for the duration of the war. The woodwork in the staterooms, the cabin-class dining room, and other public areas were covered with leather. Queen Mary and Queen Elizabeth were the largest and fastest troopships involved in the war, often carrying as many as 15,000 men in a single voyage, and often travelling out of convoy and without escort. Indeed, only a handful of ships, such as the Polish destroyer ORP Blyskawica, could even provide an escort. The Queens high speed and zigzag courses made it virtually impossible for U-boats to catch them, although one attempted to attack the ship. On 25 May 1944, U-853 spotted Queen Mary and submerged to attack, but the ship outran the U-boat before it could do so. Because of their importance to the war effort, Adolf Hitler offered a bounty of 1 million Reichsmarks and Oak Leaves to the Knight's Cross, Germany's highest military honor, to any U-boat captain that sank either ship.

The Queen Mary was not so lucky throughout the war. On 2 October 1942, she accidentally sank one of her escort ships, slicing through the light cruiser HMS Curacoa (D41) off the Irish coast with a loss of 338 lives. Queen Mary was carrying thousands of Americans of the 29th Infantry Division to join the Allied forces in Europe. Due to the risk of U-boat attacks, Queen Mary was under orders not to stop under any circumstances and steamed onward with a fractured stem. Some sources claim that hours later, the convoy's lead escort, consisting of HMS Bramham (L51) and one other ship, returned to rescue 99 survivors of Curacoa crew of 437, including her captain John W. Boutwood. This claim is contradicted by the liner's then Staff Captain Harry Grattidge, who recorded that Queen Mary Captain, Gordon Illingsworth, immediately ordered the accompanying destroyers to look for survivors within moments of Curacoa sinking.

Later that year, from 8–14 December 1942, Queen Mary carried 10,389 soldiers and 950 crew (total 11,339). During this trip, on 11 December, while 700 mi from Scotland during a gale, she was suddenly broadsided on her starboard side by a rogue wave that might have reached a height of 28 m. An account of this crossing can be found in Carter's book. As quoted in the book, Carter's father, Dr. Norval Carter, part of the 110th Station Hospital on board at the time, wrote in a letter that at one point Queen Mary "damned near capsized... One moment the top deck was at its usual height and then, swoom! Down, over, and forward she would pitch." It was calculated later that the ship rolled 52 degrees, and would have capsized had she rolled another three degrees.

From 25 to 30 July 1943, Queen Mary carried 15,740 soldiers and 943 crew (total 16,683), a standing record for the most passengers ever transported on one vessel. This was only possible in summer as passengers had to sleep on deck.

During the war, Queen Mary carried British Prime Minister Winston Churchill across the Atlantic three times for meetings with fellow Allied forces officials. He was listed on the passenger manifests as "Colonel Warden". On one crossing in 1943, Churchill and his staff planned the Normandy Invasion and he signed the D-Day Declaration aboard. Churchill later stated that the Queens, "challenged the fury of Hitlerism in the battle of the Atlantic. Without their aid, the day of final victory must unquestionably have been postponed.” By the war's end, Queen Mary had carried over 800,000 troops and traveled over 600,000 miles across the world's oceans.

After World War 2

After delivering war brides to Canada, Queen Mary made her fastest ever crossing, returning in early 1946 to Southampton in only three days, 22 hours and 42 minutes at an average speed of 31.9 knots. From September 1946 to July 1947, Queen Mary was refitted for passenger service, adding air conditioning and upgrading her berth configuration to 711 first class (formerly called cabin class), 707 cabin class (formerly tourist class) and 577 tourist class (formerly third class) passengers. Following their refit, Queen Mary and Queen Elizabeth dominated the transatlantic passenger trade as Cunard White Star's two-ship weekly express service through the latter half of the 1940s and well into the 1950s. They proved highly profitable for Cunard (as the company was renamed on 31 December 1949).

On 1 January 1949, Queen Mary ran aground off Cherbourg, France. She was refloated the next day and returned to service.

In 1952, Queen Mary lost the Blue Riband she held for 14 years to the SS United States during her maiden voyage.

In 1958, the first commercial transatlantic flights by jet began a completely new era of competition for the Cunard Queens. With a London–New York travel time of just 7–8 hours now possible with the new aircraft, demand for a sea crossing of the ocean fell away markedly. On some voyages, winters especially, Queen Mary sailed into harbour with more crew than passengers, though both she and Queen Elizabeth still averaged over 1,000 passengers per crossing into the middle 1960s. By 1965, the entire Cunard fleet was operating at a loss.

Hoping to continue financing Queen Elizabeth 2 which was under construction at Brown's shipyard, Cunard mortgaged the majority of the fleet. Due to a combination of age, lack of public interest, inefficiency in a new market and the damaging after-effects of the national seamen's strike, Cunard announced that both Queen Mary and Queen Elizabeth would be retired from service and sold off. Many offers were submitted, and the bid of $3.45m/£1.2m from Long Beach, California surpassed the Japanese scrap merchants. Queen Mary was featured in the film Assault on a Queen (1966) starring Frank Sinatra. That August, Queen Mary made her fastest eastbound passage since August 1938, crossing in 4 days, 10 hours and 6 minutes at an average speed of 29.46 knots (54.56 km/h).

Queen Mary was retired from service in 1967. On 27 September, she completed her 1,001st and last crossing of the North Atlantic having carried 2,112,000 passengers over 3792227 mi. Under the command of Captain John Treasure Jones, who had been her captain since 1965, she sailed from Southampton for the last time on 31 October with 1,093 passengers and 806 crew. After a voyage around Cape Horn, she arrived in Long Beach on 9 December. Queen Elizabeth was withdrawn in 1968 and Queen Elizabeth 2 took over the transatlantic route in 1969.

Post-retirement

Queen Mary is permanently moored as a tourist attraction, hotel, museum and event facility in Long Beach.

Conversion
Queen Mary, bought by Long Beach in 1967, was converted from a seafaring vessel to a floating hotel. The plan included clearing almost every area of the ship below "C" deck (called "R" deck after 1950, to lessen passenger confusion, as the restaurants were located on "R" deck) to make way for Jacques Cousteau's new Living Sea Museum. This increased museum space to 400000 sqft.

It required the removal of all the boiler rooms, the forward engine room, both turbo generator rooms, the ship stabilisers and the water softening plant. The ship's empty fuel tanks were filled with local mud to keep the ship's centre of gravity and draft at the correct levels, as these critical factors had been affected by the removal of the various components and structure. Only the aft engine room and "shaft alley", at the stern of the ship, was spared. The remaining space was used for storage or office space.

One problem that arose during the conversion was a dispute between land-based and maritime unions over conversion jobs. The United States Coast Guard had the final say. Queen Mary was deemed a building, since most of her propellers had been removed and her machinery gutted. The ship was also repainted with its red water level paint at a slightly higher level than during her service years. During the conversion, the funnels were removed, as this area was needed to lift out the scrap materials from the engine and boiler rooms. Workers found that the funnels were significantly degraded and they were replaced with replicas. With all of the lower decks nearly gutted from R deck and down, Diners Club, the initial lessee of the ship, converted the remainder of the vessel into a hotel. In 1969, it was reported that the hotel would be operated by Sky Chefs, the catering and hospitality division of American Airlines. Diners Club Queen Mary dissolved and vacated the ship in 1970 after their parent company, Diners Club International, was sold, and a change in corporate direction was mandated during the conversion process. Specialty Restaurants, a Los Angeles-based company that focused on theme-based restaurants, took over as master lessee the following year.

This second plan was based on converting most of her first- and second-class cabins on A and B decks into hotel rooms, and converting the main lounges and dining rooms into banquet spaces. On Promenade Deck, the starboard promenade was enclosed to feature an upscale restaurant and café named Lord Nelson's and Lady Hamilton's; it was themed in the fashion of early-19th century sailing ships. The famed and elegant Observation Bar was redecorated as a western-themed bar.

The smaller first-class public rooms, such as the Drawing Room, Library, Lecture Room and the Music Studio, was stripped of most of their fittings and converted to commercial use. This markedly expanded retail space on the ship. Two more shopping malls were built on the Sun Deck in separate spaces previously used for first-class cabins and engineers' quarters.

A post-war feature of the ship, the first-class cinema, was removed for kitchen space for the new Promenade Deck dining venues. The first-class lounge and smoking room were reconfigured and converted into banquet space. The second-class smoking room was subdivided into a wedding chapel and office space. On the Sun Deck, the elegant Verandah Grill was gutted and converted into a fast-food eatery, while a new upscale dining venue was created directly above it on Sports Deck, in space once used for crew quarters.

The second-class lounges were expanded to the sides of the ship and used for banqueting. On R deck, the first-class dining room was reconfigured and subdivided into two banquet venues, the Royal Salon and the Windsor Room. The second-class dining room was subdivided into kitchen storage and a crew mess hall, while the third-class dining room was initially used as storage and crew space.

Also on R deck, the first-class Victorian Turkish bath complex, the 1930s equivalent to a spa, was removed. The second-class pool was removed and its space initially used for office space, while the first-class swimming pool was open for viewing by hotel guests and visitors. Because of modern safety codes and the compromised structural soundness of the area directly below, the swimming pool could not be used for swimming after the conversion, although it was filled with water until the late 1980s. Today the pool can only be seen on guided tours and from the first class entrance on R deck. No second-class, third-class or crew cabins remain intact aboard the ship today.

Opening as a tourist destination

On 8 May 1971, Queen Mary opened her doors to tourists. Initially, only portions of the ship were open to the public as Specialty Restaurants had yet to open its dining venues and PSA had not completed work converting the ship's original First Class staterooms into the hotel. As a result, the ship was open only on weekends. On 11 December 1971, Jacques Cousteau's Museum of the Sea opened, with a quarter of the planned exhibits completed. Within the decade, Cousteau's museum closed due to low ticket sales and the deaths of many of the fish that were housed in the museum. On 2 November 1972, the PSA Hotel Queen Mary opened its initial 150 guest rooms. Two years later, with all 400 rooms finished, PSA brought in Hyatt Hotels to manage the hotel, which operated from 1974 to 1980 as the Queen Mary Hyatt Hotel.

By 1980, it had become apparent that the existing system was not working. The ship was losing millions each year for the city because the hotel, restaurants and museum were run by three separate concessionaires, while the city owned the vessel and operated guided tours. It was decided that a single operator with more experience in attractions was needed.

Jack Wrather, a local millionaire, had fallen in love with the ship because he and his wife, Bonita Granville, had fond memories of sailing on it numerous times. Wrather signed a 66-year lease with the city of Long Beach to operate the entire property. He oversaw the display of the H-4 Hercules, nicknamed the Spruce Goose, on long-term loan. The immense plane, which had been sitting in a hangar in Long Beach for decades unseen by the public, was installed in a huge geodesic dome adjacent to the liner in 1983, attracting increased attendance.

Wrather Port Properties operated the entire attraction after his death in 1984 until 1988, when his holdings were bought by the Walt Disney Company. Wrather had built the Disneyland Hotel in 1955, when Walt Disney had insufficient funds to construct the hotel himself. Disney had been trying to buy the hotel for 30 years. When they finally succeeded, they also acquired Queen Mary. This was never marketed as a Disney property. Through the late 1980s and early 1990s, Queen Mary struggled financially. Disney pinned their hopes for turning the attraction around on Port Disney, a huge planned resort on the adjacent docks. It was to include an attraction known as DisneySea, a theme park celebrating the world's oceans. The plans eventually fell through; in 1992 Disney gave up the lease on the ship to focus on building what would become Disney California Adventure Park. The DisneySea concept was recycled a decade later in Japan as Tokyo DisneySea, with a recreated ocean liner resembling Queen Mary named the SS Columbia as the centrepiece of the American Waterfront area.

1992 closure and reopening
With Disney gone, the Hotel Queen Mary closed on 30 September 1992. The owners of the Spruce Goose, the Aero Club of Southern California, sold the plane to the Evergreen Aviation & Space Museum in Oregon. The plane departed on barges on 2 October 1992. The Queen Mary remained open until 31 December 1992 when it closed.

During this period, the ship was nominated and listed on the National Register of Historic Places in 1993. Also the Port of Long Beach turned over control over the vessel to the city in 1993.

On 5 February 1993, RMS Foundation, Inc signed a five-year lease with the city of Long Beach to act as the operators of the property. The foundation was run by President and C.E.O. Joseph F. Prevratil, who had managed the attraction for Wrather. On 26 February 1993 the tourist attraction reopened completely, while the hotel reopened partially on 5 March with 125 rooms and the banquet facilities, with the remainder of the rooms coming online on 30 April. In 1995, RMS Foundation's lease was extended to twenty years, while the scope of the lease was reduced to operation of the ship. A new company, Queen's Seaport Development, Inc. (QSDI), was established in 1995 to control the real estate adjacent to the vessel. The dome was used extensively as a soundstage for film and television by taking advantage of the adaptable interior space that was larger than any sound stage in the Los Angeles area. In 1998, the city of Long Beach extended the QSDI lease to 66 years. Carnival Cruises repurposed a portion of the dome as a passenger terminal in 2001. The California State Lands Commission also issued a report in response to citizens' concerns about the use of public trust lands and mismanagement of public trust funds. The report determined that the uses were not barred by the granting statutes or the public trust doctrine, but may be considered necessarily incidental to the enjoyment of public tidelands. They found no evidence of mismanagement, a conclusion that was reviewed and affirmed by the State Attorney General.

In 2004, Queen Mary and Stargazer Productions added Tibbies Great American Cabaret to the space previously occupied by the ship's bank and wireless telegraph room. Stargazer Productions and Queen Mary transformed the space into a working dinner theatre complete with stage, lights, sound and scullery.

In 2005, QSDI sought Chapter 11 protection due to a rent credit dispute with the city. In 2006, the bankruptcy court requested bids from parties interested in taking over the lease from QSDI. The minimum required opening bid was $41M. The operation of the ship, by RMS Foundation, remained independent of the bankruptcy. In summer 2007, Queen Mary lease was sold to a group named "Save the Queen", managed by Hostmark Hospitality Group.

They planned to develop the land adjacent to Queen Mary, and upgrade, renovate and restore the ship. During their management, staterooms were updated with iPod docking stations and flatscreen TVs and the ship's three funnels and waterline area were repainted their original Cunard red colour. The portside Promenade Deck's planking was restored and refinished. Many lifeboats were repaired and patched, and the ship's kitchens were renovated with new equipment.

In late September 2009, management of Queen Mary was taken over by Delaware North Companies, who planned to continue the restoration and renovation of the ship and its property. They were determined to revitalise and enhance the ship as an attraction. But in April 2011, the city of Long Beach was informed that Delaware North was no longer managing Queen Mary. Garrison Investment Group said this decision was purely business. Delaware North continued to manage Scorpion, a Soviet submarine that has been a separate attraction next to Queen Mary since 1998. Evolution Hospitality, LLC. assumed operational control of Queen Mary on 23 September 2011, with Garrison Investments leasing Queen Mary. The dome was used as a venue for the Long Beach Derby Gals roller derby team and as an event venue.

2006 meeting of the two Queen Marys

On 23 February 2006, RMS Queen Mary 2 saluted her predecessor as she made a port of call in Los Angeles Harbor, while on a cruise from South Africa to Mexico.

In March 2011, Queen Mary was saluted by MS Queen Victoria and fireworks, and on 12 March 2013, MS Queen Elizabeth made a similar fireworks accompanied salute.

The salute was carried out with Queen Mary replying with her one working air horn in response to Queen Mary 2 sounding her combination of two brand new horns and an original 1934 Queen Mary horn, which is on loan from the City of Long Beach. Queen Mary originally had three whistles tuned to 55 Hz, a frequency chosen because it was low enough that the extremely loud sound of it would not be painful to human ears.

Modern IMO regulations specify ships' horn frequencies to be in the range 70–200 Hz for vessels that are over 200 m in length. Traditionally, the lower the frequency, the larger the ship. Queen Mary 2, being 345 m long, was given the lowest possible frequency (70 Hz) for her regulation whistles, in addition to the refurbished 55 Hz whistle on permanent loan. 55 Hz is the "A" note an octave above the lowest note of a standard piano keyboard. The air-driven Tyfon whistle can be heard at least 10 mi away.

2016 lease to Urban Commons
In 2016, Urban Commons, a real estate company, bought the lease, which extended to 2082, out of default. The lease obligated them to perform the ship's daily upkeep and long-term projects. Carnival Cruises took over the entire dome and made efficiency improvements under their management. The operator generated funds through its events, the hotel bookings, and passenger fees from the nearby Carnival cruise terminal, which was the largest source. Taxpayer funds were not being used to maintain the ship under the lease agreement. Urban Commons had plans to extensively renovate the liner and to redevelop the adjacent 45 acres of parking with a boutique hotel, restaurants, a marina, an amphitheater, jogging trails, bike paths and possibly a huge Ferris wheel, all at a cost of up to $250 million.

In July 2017, while making repairs to a bathroom, workers rediscovered the ship's forward gear room which had once controlled the ship's 16-ton anchors. The room was apparently sealed up during the 1960s conversion and was forgotten for decades.

In May 2019, Urban Commons formed Eagle Hospitality Real Estate Trust with the goal of generating up to $566 million for the Queen Mary along with its portfolio of 12 other hotel properties that it owns or manages. In December 2019, it was announced that the city was reviewing the finances of Urban Commons to determine whether the City of Long Beach had "received all revenues owed."

2017 condition
In 2017, a report on the ship's condition was issued. The report observed that, not only the hull, but also the supports for a raised exhibition area within the ship were corroding and that the ship's deteriorating condition left areas such as the engine room vulnerable to flooding. Repair costs were estimated at close to $300 million. In November 2016 the City of Long Beach had put $23 million toward addressing Queen Mary's most vital repairs. John Keisler, economic and property development director for Long Beach, said: "We have a timeline in which the engineers believe they can complete those immediate projects. These are major challenges we can only address over time; it can't all be done at once." Political leaders in Scotland, birthplace of Queen Mary, called for the then UK Prime Minister Theresa May to pressure the American government to fund a full repair of the liner in 2017.

In August 2019, Edward Pribonic, the engineer responsible for inspecting Queen Mary on behalf of the City of Long Beach, issued a report stating that the ship was in the worst condition he had seen in his 25 years on the job. Pribonic stated that the neglect of Queen Mary had grown worse under the management of Urban Commons, and concluded that "without an immediate and very significant infusion of manpower and money, the condition of the ship will likely soon be unsalvageable." Incidents of recent neglect include the flooding of the Grand Ballroom with sewage after a pipe which was flimsily patched with duct tape burst, significant amounts of standing water in the ship's bilge, and recently applied paint on the ship's funnels already peeling because of the poor way in which it was applied. The pessimistic conclusion of Pribonic was disputed by city officials, who called the warnings "hyperbolic" and pointed to the "significant" work that has already been undertaken towards repairing Queen Mary.

The $23 million apportioned for repairs ran out in 2018, with 19 out of the 27 urgent projects identified by a 2015 marine survey completed as of September 2019. There were significant cost overruns overall, with the cost of fire safety repairs increasing from the original estimate of $200,000 to $5.29 million. Two of the remaining eight issues identified in 2015 were considered "critical" – this includes the removal of the ship's lifeboats, which were rotted and in danger of collapsing.

In October 2019, the City of Long Beach warned Urban Commons that the company was failing to uphold its commitment to maintain and repair Queen Mary and that it was accordingly in danger of defaulting on its 66-year lease agreement. Urban Commons responded with an updated plan for repairs, including the removal of the lifeboats at a cost of between $5 and $7 million, and new paint work.

2020 closure and reopening
The Queen Mary ceased operations in May 2020, due to the COVID-19 pandemic. As overseer for several corporations that operated the Queen Mary, Eagle Hospitality Trust filed a motion in federal bankruptcy court on 9 March 2021 to auction off its lease. Court filings by the city claimed that Urban Commons' repair work was incomplete or not performed correctly and would likely have to be redone. Also, the current condition of the vessel was such that significant safety repairs needed to be performed before it could reopen to the public. In court filings, Eagle Hospitality Trust stated that the lease was their most valuable asset. There were no bidders on the lease after all of Eagle's other hotel properties were sold at a bankruptcy court auction. Eagle Hospitality Trust agreed to surrender its lease agreement back to the city, and Long Beach took back control in June 2021. To keep the ship running, the city approved a $2 million, six-month contract with Evolution Hospitality to cover monthly utility fees, security, landscaping and other costs. Simultaneously, the city contracted with Evolution Hospitality, a hotel management company that had been managing the daily operations of the ship since 2011, to act as caretaker.

An architecture and marine engineering firm hired by the city found that $23 million was needed for urgent safety repairs to keep the ship viable over the next two years. The report by Elliott Bay Design Group reported that the vessel was vulnerable to flooding or possibly even capsizing. On 21 September 2021, the Long Beach City Council voted to explore turning the Queen Mary and surrounding property over to the Harbor Department. Transfer of the ship and the surrounding land from city control to the port would include Pier H. An urgent removal of the deteriorated lifeboats was completed as they were putting stress on the side shell of the ship which has created cracks in the support system. Of the 22 lifeboats then on the ship, 15 were original while the remaining 7 were from other ships. Although the city offered the lifeboats to various groups, none were able to meet the city's removal requirements. Consequently, the city saved 11 of the original lifeboats for restoration and scrapped the remaining 11 (4 originals and 7 non-originals).

In June 2022, the city established a new agreement with Evolution Hospitality where company managed the ship for a portion of the revenues while the city controlled repair and restoration of the ship. By November, the city had spent $2.8 million for plumbing repairs, a new Wi-Fi connection, handrail restoration and energy-efficient lightbulbs. This also included beginning work on the ship's boilers and heat exchangers. The city approved $1 million to continue repairs to the ship's linoleum flooring and carpet, refrigerators, elevators, kitchen exhaust hoods, and guest room locks. After the ship opened for limited tours on 15 December 2022, a public opening was held on 1 April 2023. Later in the month, the city announced that the ship and Pier H would remain with the city with the port being a partner. The repairs, along with increased tourism, led the Queen Mary to earn over $3.5 million in operating profits from April - December 2023.

W6RO

Queen Mary's original professionally manned wireless radio room was removed when the ship was moored in Long Beach. In its place, an amateur radio room proposed by Long Beach resident and radio amateur Nate Brightman, K6OSC, was created one deck above the original radio reception room, with some of the discarded original radio equipment used for display purposes. The new Wireless Room was opened for operation on 22 April 1979. The amateur radio station, with the call sign W6RO ("Whiskey Six Romeo Oscar"), relies on volunteers from a local amateur radio club. They staff the radio room during most public hours. The radios can also be used by other licensed amateur radio operators.

In honour of his over forty years of dedication to W6RO and Queen Mary, in November 2007 the Queen Mary Wireless Room was renamed as the Nate Brightman Radio Room. This was announced on 28 October 2007, at Brightman's 90th birthday party by Joseph Prevratil, former president and CEO of Queen Mary.

Alleged hauntings

Following Queen Mary's permanent docking in California, claims were made that the ship was haunted. These claims began in earnest in the 1980s (possibly done by employees to increase business or spook guests) and have grown since then. For example, in 2008, Time magazine included the Queen Mary among its "Top 10 Haunted Places". One of the staterooms is alleged to be haunted by the spirit of a person supposedly murdered there. Other legends include a young girl who haunts the ship's former second class pool and a father who murdered his two daughters on board.

However, there is no historical record to support these claims as no person was murdered aboard the ship. In fact, most deaths aboard the ship were due to natural causes. Further, Center for Inquiry fellow Joe Nickell attributes the Queen Mary's haunting legends to pareidolia, illusory mental images triggered by subjective feelings, and daydreaming commonly experienced by workers doing repetitive chores.

Nevertheless, the Queen Mary operates a number of haunted attraction experiences, such as the "Haunted Encounters" and "Grey Ghost Project" tours. These tours, although focused on paranormal activity, counter many of the legends of the ship, with facts drawn from the ship's logs, such as records of documented fatalities. As such, the tours allow guests to experience the alleged hauntings of the ship without inventing fictitious stories.

title: RMS Queen Mary


text:
Nobukazu Takemura

Nobukazu Takemura (竹村延和 Takemura Nobukazu; born August 28, 1968, in Hirakata, Osaka) is a Japanese musician and artist. He became interested in music at a young age by listening to the radio, and began to make music at home with a tape recorder and keyboard. During high school, after a record store job that exposed him to jazz and hip-hop, he had regular gigs in the clubs of Osaka and Kyoto as a battle DJ before launching his music career. Takemura's music career has seen him cover a wide range of genres and styles within short periods of time. Beginning his career in hip-hop and jazz, Takemura later entered into a prolific period as an electronic musician, exploring genres such as glitch, drum and bass and minimalism. Takemura's most recent work has included chamber music and performance art.

Career
In 1990, Takemura founded the instrumental hip hop group Audio Sports with Yamatsuka Eye (of The Boredoms) and Aki Onda. Their first album, Era of Glittering Gas, was released in 1992 (after which Onda subsequently took control of the project).

In 1992, Takemura formed the nu-jazz collective Spiritual Vibes, which released several albums and a few singles throughout the early to mid-1990s. During this period Takemura would occasionally toy with (and eventually pursue full-time in the late 1990s) his own solo releases, typically under the names of DJ Takemura or Kool Jazz Productions. He has released music under the pseudonyms of DJ Takemura, Child's View and Assembler, and his music has covered a wide variety of genres in a short amount of time, ranging from hip-hop instrumentals, to jazz, to chamber music and electronic minimalism, breakbeat, noise pop, glitch and jungle music. The vast majority of Takemura's music has been recorded in his home-made "Moonlit Studio", in his Kyoto apartment. He founded the Lollop and Childisc labels in the 1990s after meeting musicians who were unable to release their music due to not having a record label. His voluminous releases, remixes, and collaborations make a comprehensive discography difficult, and his music often defies any easy categorization. Takemura's first U.S. release was Funfair on the Bubble Core label in 1998, a slightly altered release of the Yoru No Yuenchi album released previously in Japan. This was followed by Scope on the Thrill Jockey label in 1999, an album that was released solely in the U.S. He has frequently collaborated with fellow Childisc vocalist/composer Aki Tsuyuko, with her vocals having been sampled on many of his albums.

His unique and complex approach to melody and instrumentation has generated a catalog of collaborations with critically acclaimed artists including Issey Miyake, Zu, Steve Reich, DJ Spooky, Yo La Tengo, Tortoise, and Tujiko Noriko. Takemura performed live extensively in the early 2000s, having toured the U.S. opening for Tortoise and Plaid, as well as touring the U.K. with a full live band playing his music on a sponsorship from the British Arts Council. Takemura was also responsible for the sound design of Sony's robotic dog AIBO.

Takemura moved from his long-term home of Kyoto to Berlin, Germany in 2008. In February 2014, Takemura released Zeitraum, a compilation of music, sounds and images he had created from 2004 – 2013 for various projects, commissions and collaborations. Zeitraum is Takemura's first solo album release in 11 years.

Discography
''Note: This discography only includes solo and collaboration releases under the names of "Nobukazu Takemura", "Child's View", "Assembler" or "DJ Takemura". None of Takemura's group releases, such as with Audio Sports or Spiritual Vibes, are included.''

title: Nobukazu Takemura


text:
Talk:Seinfeld

Home Media
It might be more helpful if the streaming section headings are listed by country rather than by streaming service? — Preceding unsigned comment added by Aswiseman (talk • contribs) 21:54, 25 May 2021 (UTC)

Cross-overs?
The article makes no mention of the show being part of NBC's "Must-See TV" line-up, or of the fairly significant crossovers with other, unrelated series, such as the revelation that Paul Reiser's character in Mad About You previously rented the apartment that Kramer later moves into after him, right across the hall from Jerry Seinfeld's apartment. rowley (talk) 00:51, 20 April 2022 (UTC)

Germanophobe
"The in-show character is a mild germophobe" Isn't that spelled germanophobe?? 46.188.167.218 (talk) 13:22, 29 September 2022 (UTC)

 * No? If you're afraid of germs then you're a germophobe. ― Blaze WolfTalkBlaze Wolf#6545 13:23, 29 September 2022 (UTC)

"'feld" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=%27feld&redirect=no 'feld] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. estar8806 (talk) ★ 22:53, 16 July 2023 (UTC)

title: Talk:Seinfeld


text:
Talk:Integration by parts

(Untitled section)

 * An alternative notation has the advantage that the factors of the original expression are identified as f and g

Why is that an advantage? It seems arbitrary to say it's better to call them f and g than to call them u and v. Michael Hardy 00:27, 15 Nov 2003 (UTC)

 * That's not what I meant. The "classic" notation tells you what to do when you are integrating "f(x)g'(x)". The "alternative" integrates "f(x)g(x)". See? -- Tarquin 18:58, 15 Nov 2003 (UTC)

Please revise the "recursive formulation" section
I suggest the author of section 4 “recursive formulation” http://en.wikipedia.org/w/index.php?title=Integration_by_parts&action=edit&section=4 of the article Integration_by_parts to revise the recursive formula that is suspected to be mistaken or notation needs to be further clarified. It seems to differ from the corresponding formula in Mathworld: http://mathworld.wolfram.com/IntegrationbyParts.html. Consider inclusion of another term on RHS, integral of product of some functions.

Q: Recursive formulation
In the section Recursive formulation, what are the $$v_i\,$$? Are they distinct?

Thanks!

Naming of tabular form
I am in strong doubt about most of the given names for the tabular form of repeated integration by parts. Especially, I have a hard time to assume that this film title is really given in the cited reference. Purgy (talk) 17:18, 29 July 2018 (UTC)

 * For now I consider this as settled. Purgy (talk) 07:05, 30 July 2018 (UTC)

Weird formatting glitch on the desktop version
There's a strange math formatting glitch occurring on this page, though only on the desktop version, with a wide page. The formatting for "dv = v'(x)dx" in the third paragraph mysteriously has the second v rotated 90 degrees counter-clockwise, as well as mirrored (I think). Worth noting is that this doesn't show up on the mobile version, neither in the app or on en.m.wikipedia.org, and it disappears when the window is made narrower. I would attempt to fix it, but I'm personally entirely clueless on why this occurs

On further inspection, there are lots of occurrences of this glitch on this page, seemingly at random. There's more twisted vs, but I've also spotted at least one x, and even a prime.

TerraDOOM (talk) 06:21, 7 October 2021 (UTC)

title: Talk:Integration by parts


text:
Talk:Fundamental theorem of calculus

y is a function of t, not x...
Thanks to the original author(s) of this page. There is one detail that confused me when I was learning the topic. Only later did I realize the subtlety which I consider an error.

In the "Geometric Meaning" section, it starts with "For a continuous function y = f(x) whose graph is plotted as a curve, each value of x has a corresponding area function A(x), representing the area beneath the curve between 0 and x."

This is not quite correct. The area function, A, is indeed a function of x. (x being the upper value of the integral, aka area under the curve.) However, the continuous function y, is NOT a function of x. The independent axis in the graph should be something other than x, traditionally t. The way it is presented, x is a value on the independent axis, and creates a point of the graph at [x, f(x)].

If we wanted to use x for the independent axis, then we would need to assign points on that axis to be something like x1 and x2. You can't say the independent axis is x and then say there is a value x at a certain point on it.

I know this is a subtelty, but it is worth understanding. It confused me for a long time until the light bulb went on! 149.32.192.38 (talk) 22:19, 6 March 2023 (UTC)

 * The function is $f$, and $y$ is the value of $f$ at $x$. See Function (mathematics) for the definition of this standard notation. D.Lazard (talk) 10:48, 7 March 2023 (UTC)
 * I agree with you 100%, but you do not refute my point. This is why I consider this a subtlety.
 * The point here is that f cannot be a function of x, when you pick a point on the axis and call it "x." You can call the point on the axis x1, x2, x3 or anything other than x. But it cannot be x.
 * I challenge you to find any other proof of the FTC that starts with "For a continuous function y as a function of x...." The area function, A, is indeed a function of x. However, the original function f (i.e. the curve that bounds the area) must be a function of a variable other than x. Again, traditionally t in other proofs of the FTC.
 * It may seem like I'm being pedantic, but I was hung up on this for a long time while trying to develop a deeper understanding of the FTC. 149.32.192.38 (talk) 14:46, 7 March 2023 (UTC)
 * This may help explain my point:
 * https://ximera.osu.edu/mooculus/calculus1/firstFundamentalTheoremOfCalculus/digInFirstFundamentalTheoremOfCalculus
 * Specifically notice the comments about the accumulation function. 149.32.192.38 (talk) 15:04, 7 March 2023 (UTC)
 * One last note.
 * In the "Proof of the first part" section of this article, it properly states:
 * "For a given f(t)..."
 * This is correct, and directly contradicts the first sentence in the "Geometric Meaning" section:
 * "For a continuous function y = f(x)..."
 * I know this seems pedantic, but it is important to know there is a differnce betweem f(t) and f(x) while proving the FTC. 149.32.192.38 (talk) 15:13, 7 March 2023 (UTC)
 * I have changed "For a given f(t)...” into "For a given function f ...” because the former formulation in incorrect, since this is not the value f(x) of the function at some point that is given, but the function in its entirety. I have also fixed similarly the beginning of the paragraph . You must be aware that in “the function $$y=f(x)$$" and "$$x\mapsto A(x)$$", the symbols $x$ and $y$ are placeholders that have no value. They could be replaced with, say, $$\cdot$$ and $$*$$ without changing the function. So, there is no harm of using $x$ and $y$ for specific values. D.Lazard (talk) 16:31, 7 March 2023 (UTC)

"The first part of the theorem" in the introduction
(I apologize if this is wrong - if so, please delete this)

The second paragraph on the introduction contains the statement:
 * The first part of the theorem, the first fundamental theorem of calculus, states that for a function $f$, an antiderivative or indefinite integral $F$ may be obtained as the integral of $f$ over an interval with a variable upper bound.

Shouldn't this be how $F$ is defined, not the theorem itself? I.e. shouldn't it be something like:

 * The first part of the theorem, the first fundamental theorem of calculus, states that for a function $f$, if an antiderivative or indefinite integral $F$ is defined as as the integral of $f$ over an interval with a variable upper bound $x$, then

 * $$F'(x) = f(x).$$

BouleyBay (talk) 13:08, 31 May 2023 (UTC)

 * I don't understand your proposed alternative. The first part of the theorem says that, given f, if we define a new function (usually denoted F) as a certain integral of f with a variable upper bound, then F is an antiderivative of f (equiv: then F' = f).  That's what the original sentence says.  Your version is either circular or redundant; if the words "an antiderivative or indefinite integral" were replaced by "another function" then it would be fine (and equivalent to what is already written).  I am not deeply wedded to the current wording, quite possibly it could be clearer.  --JBL (talk) 17:34, 31 May 2023 (UTC)
 * I think it should be:
 * $$F(x) - F(a) = \int_a^x{f(x) \, dx} \rightarrow F(x) = \int_a^x{f(x) \, dx} + F(a)$$
 * Later on, in the corollary, the lower boundary is included.
 * Alternatively, one should specify that there is a constant of integration C that is yet to be defined. 2A02:2454:C00A:6400:89E5:3344:B32E:8F10 (talk) 10:43, 4 June 2024 (UTC)
 * The original question is about the introduction; there are no equations in the introduction. This makes the meaning of your comment rather obscure.  --JBL (talk) 20:30, 4 June 2024 (UTC)

Order of theorems
I'm wondering whether the article has the order of the Fundamental Theorems of Calculus reversed... several sources (https://math.stackexchange.com/questions/3635636/confused-about-the-fundamental-theorem-of-calculus, or Calculus, 11th edition by Larson and Edwards, to name a few) state that the First Fundamental Theorem of Calculus gives int:a-->b (f(x))=F(b)-F(a), while the Second Fundamental Theorem of Calculus states that d/dx (int:a-->x (f(t))dt) = f(x). This seems to go against the naming used in this article. Apologies for the lack of proper mathematical notation in this post. PeterRet (talk) 06:57, 13 February 2024 (UTC)

 * I agree, I didn't look too hard for an authoritative source, but the AOPS Calculus text I had next to me agrees that the first "part" or First Fundamental Theorem states that:
 * $$\int\limits_a^b f (x) dx =F(b) - F(a) $$
 * and that the second is:
 * $$ g(x) = \int\limits_{x_0}^x f(t) dt $$
 * Wyrdwritere (talk) 18:52, 9 July 2024 (UTC)

Further Explanation Required
In the section "Proof of the first part", there is a line saying "the latter equality resulting from the basic properties of integrals and the additivity of areas.". I am not aware of any Wikipedia page which lists basic properties of integrals. Also, the properties which are being used should be mentioned. 183.83.216.129 (talk) 11:53, 26 April 2024 (UTC)

Possible very minor typo for current Reference 11
A very minor issue, but it would seem that Reference 11, as of the time of writing, refers to theorem 7.21 instead of 8.21 of Rudin's RCA, which should be the correct number, having checked a copy of the book. But since it could be a chapter numbering difference between different versions of the book, I've opted to just open a topic here. Sorry for the bother. 2001:660:6402:408:1867:ABEE:384A:B949 (talk) 12:24, 11 July 2024 (UTC)

title: Talk:Fundamental theorem of calculus