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Wool

Wool is the textile fiber obtained from sheep and other mammals, especially goats, rabbits, and camelids. The term may also refer to inorganic materials, such as mineral wool and glass wool, that have some properties similar to animal wool.

As an animal fiber, wool consists of protein together with a small percentage of lipids. This makes it chemically quite distinct from cotton and other plant fibers, which are mainly cellulose.

Characteristics
Wool is produced by follicles which are small cells located in the skin. These follicles are located in the upper layer of the skin called the epidermis and push down into the second skin layer called the dermis as the wool fibers grow. Follicles can be classed as either primary or secondary follicles. Primary follicles produce three types of fiber: kemp, medullated fibers, and true wool fibers. Secondary follicles only produce true wool fibers. Medullated fibers share nearly identical characteristics to hair and are long but lack crimp and elasticity. Kemp fibers are very coarse and shed out. Wool's crimp refers to the strong natural wave present in each wool fiber as it is presented on the animal. Wool's crimp, and to a lesser degree scales, make it easier to spin the fleece by helping the individual fibers attach, so they stay together. Because of the crimp, wool fabrics have greater bulk than other textiles, and they hold air, which causes the fabric to retain heat. Wool has a high specific thermal resistance, so it impedes heat transfer in general. This effect has benefited desert peoples, as Bedouins and Tuaregs use wool clothes for insulation.

The felting of wool occurs upon hammering or other mechanical agitation as the microscopic barbs on the surface of wool fibers hook together. Felting generally comes under two main areas, dry felting and wet felting. Wet felting occurs when water and a lubricant (especially an alkali such as soap) are applied to the wool which is then agitated until the fibers mix and bond together. Temperature shock while damp or wet accentuates the felting process. Some natural felting can occur on the animal's back.

Wool has several qualities that distinguish it from hair or fur: it is crimped and elastic.

The amount of crimp corresponds to the fineness of the wool fibers. A fine wool like Merino may have up to 40 crimps per centimetre (100 crimps per inch), while coarser wool like karakul may have less than one (one or two crimps per inch). In contrast, hair has little if any scale and no crimp, and little ability to bind into yarn. On sheep, the hair part of the fleece is called kemp. The relative amounts of kemp to wool vary from breed to breed and make some fleeces more desirable for spinning, felting, or carding into batts for quilts or other insulating products, including the famous tweed cloth of Scotland.

Wool fibers readily absorb moisture, but are not hollow. Wool can absorb almost one-third of its own weight in water. Wool absorbs sound like many other fabrics. It is generally a creamy white color, although some breeds of sheep produce natural colors, such as black, brown, silver, and random mixes.

Wool ignites at a higher temperature than cotton and some synthetic fibers. It has a lower rate of flame spread, a lower rate of heat release, a lower heat of combustion, and does not melt or drip; it forms a char that is insulating and self-extinguishing, and it contributes less to toxic gases and smoke than other flooring products when used in carpets. Wool carpets are specified for high safety environments, such as trains and aircraft. Wool is usually specified for garments for firefighters, soldiers, and others in occupations where they are exposed to the likelihood of fire.

Wool causes an allergic reaction in some people.

Shearing

Sheep shearing is the process in which a worker (a shearer) cuts off the woollen fleece of a sheep. After shearing, wool-classers separate the wool into four main categories:

 * fleece (which makes up the vast bulk)
 * broken
 * bellies
 * locks

The quality of fleeces is determined by a technique known as wool classing, whereby a qualified person, called a wool classer, groups wools of similar grading together to maximize the return for the farmer or sheep owner. In Australia, before being auctioned, all Merino fleece wool is objectively measured for average diameter (micron), yield (including the amount of vegetable matter), staple length, staple strength, and sometimes color and comfort factor.

Scouring

Wool straight off a sheep is known as "raw wool", "greasy wool" or "wool in the grease". This wool contains a high level of valuable lanolin, as well as the sheep's dead skin and sweat residue, and generally also contains pesticides and vegetable matter from the animal's environment. Before the wool can be used for commercial purposes, it must be scoured, a process of cleaning the greasy wool. Scouring may be as simple as a bath in warm water or as complicated as an industrial process using detergent and alkali in specialized equipment. In north west England, special potash pits were constructed to produce potash used in the manufacture of a soft soap for scouring locally produced white wool.

Vegetable matter in commercial wool is often removed by chemical carbonization. In less-processed wools, vegetable matter may be removed by hand and some of the lanolin left intact through the use of gentler detergents. This semigrease wool can be worked into yarn and knitted into particularly water-resistant mittens or sweaters, such as those of the Aran Island fishermen. Lanolin removed from wool is widely used in cosmetic products such as hand creams.

Fineness and yield
Raw wool has many impurities; vegetable matter, sand, dirt and yolk which is a mixture of suint (sweat), grease, urine stains and dung locks. The sheep's body yields many types of wool with differing strengths, thicknesses, length of staple and impurities. The raw wool (greasy) is processed into 'top'. 'Worsted top' requires strong straight and parallel fibres.

The quality of wool is determined by its fiber diameter, crimp, yield, color, and staple strength. Fiber diameter is the single most important wool characteristic determining quality and price.

Merino wool is typically 90 - 115 mm in length and is very fine (between 12 and 24 microns). The finest and most valuable wool comes from Merino hoggets. Wool taken from sheep produced for meat is typically coarser, and has fibers 1.5 - 6 in in length. Damage or breaks in the wool can occur if the sheep is stressed while it is growing its fleece, resulting in a thin spot where the fleece is likely to break.

Wool is also separated into grades based on the measurement of the wool's diameter in microns and also its style. These grades may vary depending on the breed or purpose of the wool. For example:

Any wool finer than 25 microns can be used for garments, while coarser grades are used for outerwear or rugs. The finer the wool, the softer it is, while coarser grades are more durable and less prone to pilling.

The finest Australian and New Zealand Merino wools are known as 1PP, which is the industry benchmark of excellence for Merino wool 16.9 microns and finer. This style represents the top level of fineness, character, color, and style as determined on the basis of a series of parameters in accordance with the original dictates of British wool as applied by the Australian Wool Exchange (AWEX) Council. Only a few dozen of the millions of bales auctioned every year can be classified and marked 1PP.

In the United States, three classifications of wool are named in the Wool Products Labeling Act of 1939. Wool is "the fiber from the fleece of the sheep or lamb or hair of the Angora or Cashmere goat (and may include the so-called specialty fibers from the hair of the camel, alpaca, llama, and vicuna) which has never been reclaimed from any woven or felted wool product". "Virgin wool" and "new wool" are also used to refer to such never used wool. There are two categories of recycled wool (also called reclaimed or shoddy wool). "Reprocessed wool" identifies "wool which has been woven or felted into a wool product and subsequently reduced to a fibrous state without having been used by the ultimate consumer". "Reused wool" refers to such wool that has been used by the ultimate consumer.

History
Wild sheep were more hairy than woolly. Although sheep were domesticated some 9,000 to 11,000 years ago, archaeological evidence from statuary found at sites in Iran suggests selection for woolly sheep may have begun around 6000 BC, with the earliest woven wool garments having only been dated to two to three thousand years later. Woolly sheep were introduced into Europe from the Near East in the early part of the 4th millennium BC. The oldest known European wool textile, c. 1500 BC, was preserved in a Danish bog. Prior to invention of shears—probably in the Iron Age—the wool was plucked out by hand or by bronze combs. In Roman times, wool, linen, and leather clothed the European population; cotton from India was a curiosity of which only naturalists had heard, and silks, imported along the Silk Road from China, were extravagant luxury goods. Pliny the Elder records in his Natural History that the reputation for producing the finest wool was enjoyed by Tarentum, where selective breeding had produced sheep with superior fleeces, but which required special care.

In medieval times, as trade connections expanded, the Champagne fairs revolved around the production of wool cloth in small centers such as Provins. The network developed by the annual fairs meant the woolens of Provins might find their way to Naples, Sicily, Cyprus, Majorca, Spain, and even Constantinople. The wool trade developed into serious business, a generator of capital. In the 13th century, the wool trade became the economic engine of the Low Countries and central Italy. By the end of the 14th century, Italy predominated. The Florentine wool guild, Arte della Lana, sent the imported English wool to the San Martino convent for processing. Italian wool from Abruzzo and Spanish merino wools were processed at Garbo workshops. Abruzzo wool had once been the most accessible for the Florentine guild, until improved relations with merchants in Iberia made merino wool more available. By the 16th century Italian wool exports to the Levant had declined, eventually replaced by silk production.

The value of exports of English raw wool were rivaled only by the 15th-century sheepwalks of Castile and were a significant source of income to the English crown, which in 1275 had imposed an export tax on wool called the "Great Custom". The importance of wool to the English economy can be seen in the fact that since the 14th century, the presiding officer of the House of Lords has sat on the "Woolsack", a chair stuffed with wool.

Economies of scale were instituted in the Cistercian houses, which had accumulated great tracts of land during the 12th and early 13th centuries, when land prices were low and labor still scarce. Raw wool was baled and shipped from North Sea ports to the textile cities of Flanders, notably Ypres and Ghent, where it was dyed and worked up as cloth. At the time of the Black Death, English textile industries consumed about 10% of English wool production. The English textile trade grew during the 15th century, to the point where export of wool was discouraged. Over the centuries, various British laws controlled the wool trade or required the use of wool even in burials. The smuggling of wool out of the country, known as owling, was at one time punishable by the cutting off of a hand. After the Restoration, fine English woolens began to compete with silks in the international market, partly aided by the Navigation Acts; in 1699, the English crown forbade its American colonies to trade wool with anyone but England herself.

A great deal of the value of woollen textiles was in the dyeing and finishing of the woven product. In each of the centers of the textile trade, the manufacturing process came to be subdivided into a collection of trades, overseen by an entrepreneur in a system called by the English the "putting-out" system, or "cottage industry", and the Verlagssystem by the Germans. In this system of producing wool cloth, once perpetuated in the production of Harris tweeds, the entrepreneur provides the raw materials and an advance, the remainder being paid upon delivery of the product. Written contracts bound the artisans to specified terms. Fernand Braudel traces the appearance of the system in the 13th-century economic boom, quoting a document of 1275. The system effectively bypassed the guilds' restrictions.

Before the flowering of the Renaissance, the Medici and other great banking houses of Florence had built their wealth and banking system on their textile industry based on wool, overseen by the Arte della Lana, the wool guild: wool textile interests guided Florentine policies. Francesco Datini, the "merchant of Prato", established in 1383 an Arte della Lana for that small Tuscan city. The sheepwalks of Castile were controlled by the Mesta union of sheep owners. They shaped the landscape and the fortunes of the meseta that lies in the heart of the Iberian peninsula; in the 16th century, a unified Spain allowed export of Merino lambs only with royal permission. The German wool market – based on sheep of Spanish origin – did not overtake British wool until comparatively late. Later, the Industrial Revolution introduced mass production technology into wool and wool cloth manufacturing. Australia's colonial economy was based on sheep raising, and the Australian wool trade eventually overtook that of the Germans by 1845, furnishing wool for Bradford, which developed as the heart of industrialized woolens production.

Due to decreasing demand with increased use of synthetic fibers, wool production is much less than what it was in the past. The collapse in the price of wool began in late 1966 with a 40% drop; with occasional interruptions, the price has tended down. The result has been sharply reduced production and movement of resources into production of other commodities, in the case of sheep growers, to production of meat.

Superwash wool (or washable wool) technology first appeared in the early 1970s to produce wool that has been specially treated so it is machine washable and may be tumble-dried. This wool is produced using an acid bath that removes the "scales" from the fiber, or by coating the fiber with a polymer that prevents the scales from attaching to each other and causing shrinkage. This process results in a fiber that holds longevity and durability over synthetic materials, while retaining its shape.

In December 2004, a bale of the then world's finest wool, averaging 11.8 microns, sold for AU$3,000 per kilogram at auction in Melbourne. This fleece wool tested with an average yield of 74.5%, 68 mm long, and had 40 newtons per kilotex strength. The result was A$279,000 for the bale. The finest bale of wool ever auctioned was sold for a seasonal record of AU$2690 per kilo during June 2008. This bale was produced by the Hillcreston Pinehill Partnership and measured 11.6 microns, 72.1% yield, and had a 43 newtons per kilotex strength measurement. The bale realized $247,480 and was exported to India.

In 2007, a new wool suit was developed and sold in Japan that can be washed in the shower, and which dries off ready to wear within hours with no ironing required. The suit was developed using Australian Merino wool, and it enables woven products made from wool, such as suits, trousers, and skirts, to be cleaned using a domestic shower at home.

In December 2006, the General Assembly of the United Nations proclaimed 2009 to be the International Year of Natural Fibres, so as to raise the profile of wool and other natural fibers.

Production
Global wool production is about 2 e6t per year, of which 60% goes into apparel. Wool comprises ca 3% of the global textile market, but its value is higher owing to dyeing and other modifications of the material. Australia is a leading producer of wool which is mostly from Merino sheep but has been eclipsed by China in terms of total weight. New Zealand (2016) is the third-largest producer of wool, and the largest producer of crossbred wool. Breeds such as Lincoln, Romney, Drysdale, and Elliotdale produce coarser fibers, and wool from these sheep is usually used for making carpets.

In the United States, Texas, New Mexico, and Colorado have large commercial sheep flocks and their mainstay is the Rambouillet (or French Merino). Also, a thriving home-flock contingent of small-scale farmers raise small hobby flocks of specialty sheep for the hand-spinning market. These small-scale farmers offer a wide selection of fleece. Global woolclip (total amount of wool shorn) 2020
 * 1) China: 19% of global wool-clip (334 e6kg greasy, 2020)
 * 2) Australia: 16%
 * 3) New Zealand: 8%
 * 4) Turkey: 4%
 * 5) United Kingdom: 4%
 * 6) Morocco: 3%
 * 7) Iran: 3%
 * 8) Russia: 3%
 * 9) South Africa: 3%
 * 10) India: 3%

Organic wool has gained in popularity. This wool is limited in supply and much of it comes from New Zealand and Australia. Organic wool has become easier to find in clothing and other products, but these products often carry a higher price.

Wool is environmentally preferable (as compared to petroleum-based nylon or polypropylene) as a material for carpets, as well, in particular when combined with a natural binding and the use of formaldehyde-free glues.

Animal rights groups have noted issues with the production of wool, such as mulesing.

Australia
About 85% of wool sold in Australia is sold by open cry auction.

Other countries
The British Wool Marketing Board operates a central marketing system for UK fleece wool with the aim of achieving the best possible net returns for farmers.

Less than half of New Zealand's wool is sold at auction, while around 45% of farmers sell wool directly to private buyers and end-users.

United States sheep producers market wool with private or cooperative wool warehouses, but wool pools are common in many states. In some cases, wool is pooled in a local market area, but sold through a wool warehouse. Wool offered with objective measurement test results is preferred. Imported apparel wool and carpet wool goes directly to central markets, where it is handled by the large merchants and manufacturers.

Yarn

Shoddy or recycled wool is made by cutting or tearing apart existing wool fabric and respinning the resulting fibers. As this process makes the wool fibers shorter, the remanufactured fabric is inferior to the original. The recycled wool may be mixed with raw wool, wool noil, or another fiber such as cotton to increase the average fiber length. Such yarns are typically used as weft yarns with a cotton warp. This process was invented in the Heavy Woollen District of West Yorkshire and created a microeconomy in this area for many years.

Worsted is a strong, long-staple, combed wool yarn with a hard surface.

Woolen is a soft, short-staple, carded wool yarn typically used for knitting. In traditional weaving, woolen weft yarn (for softness and warmth) is frequently combined with a worsted warp yarn for strength on the loom.

Uses
In addition to clothing, wool has been used for blankets, horse rugs, saddle cloths, carpeting, insulation and upholstery. Dyed wool can be used to create other forms of art such as wet and needle felting. Wool felt covers piano hammers, and it is used to absorb odors and noise in heavy machinery and stereo speakers. Ancient Greeks lined their helmets with felt, and Roman legionnaires used breastplates made of wool felt.

Wool as well as cotton has also been traditionally used for cloth diapers. Wool fiber exteriors are hydrophobic (repel water) and the interior of the wool fiber is hygroscopic (attracts water); this makes a wool garment suitable cover for a wet diaper by inhibiting wicking, so outer garments remain dry. Wool felted and treated with lanolin is water resistant, air permeable, and slightly antibacterial, so it resists the buildup of odor. Some modern cloth diapers use felted wool fabric for covers, and there are several modern commercial knitting patterns for wool diaper covers.

Initial studies of woollen underwear have found it prevented heat and sweat rashes because it more readily absorbs the moisture than other fibers.

As an animal protein, wool can be used as a soil fertilizer, being a slow-release source of nitrogen.

Researchers at the Royal Melbourne Institute of Technology school of fashion and textiles have discovered a blend of wool and Kevlar, the synthetic fiber widely used in body armor, was lighter, cheaper and worked better in damp conditions than Kevlar alone. Kevlar, when used alone, loses about 20% of its effectiveness when wet, so required an expensive waterproofing process. Wool increased friction in a vest with 28–30 layers of fabric, to provide the same level of bullet resistance as 36 layers of Kevlar alone.

Events
A buyer of Merino wool, Ermenegildo Zegna, has offered awards for Australian wool producers. In 1963, the first Ermenegildo Zegna Perpetual Trophy was presented in Tasmania for growers of "Superfine skirted Merino fleece". In 1980, a national award, the Ermenegildo Zegna Trophy for Extrafine Wool Production, was launched. In 2004, this award became known as the Ermenegildo Zegna Unprotected Wool Trophy. In 1998, an Ermenegildo Zegna Protected Wool Trophy was launched for fleece from sheep coated for around nine months of the year.

In 2002, the Ermenegildo Zegna Vellus Aureum Trophy was launched for wool that is 13.9 microns or finer. Wool from Australia, New Zealand, Argentina, and South Africa may enter, and a winner is named from each country. In April 2008, New Zealand won the Ermenegildo Zegna Vellus Aureum Trophy for the first time with a fleece that measured 10.8 microns. This contest awards the winning fleece weight with the same weight in gold as a prize, hence the name.

In 2010, an ultrafine, 10-micron fleece, from Windradeen, near Pyramul, New South Wales, won the Ermenegildo Zegna Vellus Aureum International Trophy.

Since 2000, Loro Piana has awarded a cup for the world's finest bale of wool that produces just enough fabric for 50 tailor-made suits. The prize is awarded to an Australian or New Zealand wool grower who produces the year's finest bale.

The New England Merino Field days which display local studs, wool, and sheep are held during January, in even numbered years around the Walcha, New South Wales district. The Annual Wool Fashion Awards, which showcase the use of Merino wool by fashion designers, are hosted by the city of Armidale, New South Wales, in March each year. This event encourages young and established fashion designers to display their talents. During each May, Armidale hosts the annual New England Wool Expo to display wool fashions, handicrafts, demonstrations, shearing competitions, yard dog trials, and more.

In July, the annual Australian Sheep and Wool Show is held in Bendigo, Victoria. This is the largest sheep and wool show in the world, with goats and alpacas, as well as woolcraft competitions and displays, fleece competitions, sheepdog trials, shearing, and wool handling. The largest competition in the world for objectively measured fleeces is the Australian Fleece Competition, which is held annually at Bendigo. In 2008, 475 entries came from all states of Australia, with first and second prizes going to the Northern Tablelands fleeces.

Production

 * Glossary of sheep husbandry
 * Lambswool
 * Sheep husbandry
 * Sheep shearing
 * Wool bale

Processing

 * Canvas work
 * Carding
 * Combing
 * Dyeing
 * Fulling
 * Knitting
 * Spinning
 * Textile manufacturing
 * Weaving

Refined products

 * Felt
 * Fiber art
 * Tweed
 * Worsted
 * Yarn
 * Wool crepe
 * Wool satin
 * Wool coating
 * Wool melton

Organizations

 * British Wool Marketing Board
 * IWTO
 * Worshipful Company of Woolmen

Miscellaneous wool

 * Alpaca wool
 * Angora wool
 * Cashmere wool
 * Chiengora wool
 * Glass wool
 * Llama wool
 * Lopi
 * Mineral wool
 * Mohair
 * Pashmina
 * Shahtoosh
 * Tibetan fur

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

title: Wool


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1103

Year 1103 (MCIII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar.

Levant

 * Spring – Bohemond I, Norman prince of Antioch, is released from Seljuk imprisonment at Niksar, after a ransom is paid of 100,000 gold pieces. During his absence, Tancred (Bohemond's nephew) attacks the Byzantines, and re-captures the cities of Tarsus, Adana and Mamistra in Cilicia. Tancred is deprived of his lordship by Bohemond's return, and is rewarded with a small fief within the Principality of Antioch.
 * The Crusaders under Raymond IV invade the Beqaa Valley and capture Tortosa to isolate Tripoli. Raymond expands towards the Orontes River, and begins to build a castle on the Mons Peregrinus which helps in the Siege of Tripoli (see 1102). Emperor Alexios I supports the Crusaders by sending a Byzantine fleet (ten ships) to blockade the port of Tripoli.
 * Summer – The Crusaders led by Bohemond I and Joscelin of Courtenay raid the territory of Aleppo to gain supplies. They capture the town of Muslimiyah, and extract a large tribute. Sultan Fakhr al-Mulk Radwan, the Seljuk ruler of Aleppo, agrees to pay 7,000 gold pieces and ten horses to the Crusaders while Bohemond agrees to release all Seljuk prisoners captured at Muslimiyah.

Europe

 * August 24 – King Magnus III is killed in battle with the Ulaid in Ulster. Sigurd Jorsalfare, Øystein Magnusson and Olaf Magnusson succeed him as joint kings of Norway.

Britain

 * April 27 – Anselm, archbishop of Canterbury, again goes into exile after a dispute with King Henry I over the appointment of bishops and abbots to important Church positions.
 * August 5 – Queen Matilda of Scotland, wife of Henry I, gives birth to their first son William Adelin at Winchester. They already have a daughter, Princess Matilda.

China

 * Li Jie, Chinese government minister, publishes his Yingzao Fashi technical treatise on Chinese architecture, during the reign of Emperor Hui Zong of the Song Dynasty.

Religion

 * The Scandinavian city of Lund in the Swedish province of Scania becomes a see of the Catholic Church, namely the Archdiocese of Lund (approximate date).

Births

 * February 24 – Toba, emperor of Japan (d. 1156)
 * March 24 – Yue Fei, Chinese general and poet (d. 1142)
 * August 5 – William Adelin, duke of Normandy (d. 1120)
 * Adeliza of Louvain, queen of England (d. 1151)
 * Aénor de Châtellerault, duchess of Aquitaine (d. 1130)
 * Alfonso I, count of Tripoli and Toulouse (d. 1148)
 * Heilika of Lengenfeld, German countess (d. 1170)
 * Henry II, margrave of the Saxon Ostmark (d. 1123)
 * Rögnvald Kali Kolsson, Norwegian earl (d. 1158)
 * Vsevolod of Pskov, Kievan prince (approximate date)
 * Wivina, French Benedictine abbess (d. 1168)

Deaths

 * January 17 – Frutolf of Michelsberg, German monk
 * March 18 – Sybilla of Conversano, Norman duchess
 * July 10 – Eric I, king of Denmark
 * August 24 – Magnus III, king of Norway (b. 1073)
 * October 19 – Humbert II, count of Savoy (b. 1065)
 * Al-Hakim al-Munajjim, Persian Nizari missionary
 * Boedil Thurgotsdatter, Danish queen
 * Ebles II, French nobleman (House of Montdidier)
 * Henry I, German nobleman (House of Wettin)
 * Isaac Alfasi, Algerian Talmudist and posek (b. 1013)
 * Manegold of Lautenbach, German priest (b. 1030)
 * Osbern FitzOsbern, bishop of Exeter (b. 1032)
 * Sibylla of Burgundy, duchess of Burgundy (b. 1065)
 * William Firmatus, Norman hermit and pilgrim (b. 1026)

title: 1103


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Emperor Toba

Emperor Toba (鳥羽天皇) was the 74th Emperor of Japan, according to the traditional order of succession.

Toba's reign spanned the years from 1107 through 1123.

Genealogy
Before his ascension to the Chrysanthemum Throne, his personal name (his imina) was Munehito-shinnō (宗仁親王).

He was the son of Emperor Horikawa. His mother was Empress Dowager Fujiwara no Ishi (藤原苡子)

Toba had three Empresses, some consort ladies and 14 imperial sons and daughters.

 * chūgū : Fujiwara no Tamako (藤原璋子) later Taikenmon’in (待賢門院), Fujiwara no Kinzane‘s daughter
 * First Son: Imperial Prince Akihito (顕仁親王) later Emperor Sutoku
 * First Daughter: Imperial Princess Yoshiko/Kishi (禧子内親王; 1122–1133) – Saiin at Kamo Shrine
 * Second Son: Imperial Prince Michihito (通仁親王; 1124–1129)
 * Third Son: Imperial Prince Kimihito (君仁親王; 1125–1143)
 * Second Daughter: Imperial Princess Muneko (統子内親王) later Jōsaimon-in (上西門院), – Saiin at Kamo Shrine.
 * Fourth Son: Imperial Prince Masahito (雅仁親王) later Emperor Go-Shirakawa
 * Fifth Son: Imperial Prince Motohito? (本仁親王; 1129–1169) later Imperial Prince priest Kakushō (覚性法親王)

 * kōgō: Fujiwara no Yasuko/Taishi (藤原泰子) later Kōyō-in (高陽院), Fujiwara no Tadazane’s daughter

 * kōgō: Fujiwara no Nariko (藤原得子) later Bifukumon’in (美福門院), Fujiwara no Nagazane’s daughter.
 * Daughter: Imperial Princess Toshiko/Eishi (叡子内親王; 1135–1148)
 * Daughter: Imperial Princess Akiko (暲子内親王; 1137–1211) later Hachijo’in (八条院)
 * Ninth Son: Imperial Prince Narihito (体仁親王), later Emperor Konoe
 * Daughter: Imperial Imperial Princess Yoshiko/Shushi (姝子内親王) later Takamatsu’in (高松院), chūgū (Empress) to Emperor Nijō)

 * Court Lady Ki Ieko (紀家子), Mino-no-Tsubone (美濃局), Ki no Mitsukiyo’s daughter
 * Sixth Son: Imperial Prince Priest Dōkei (道恵法親王; 1132–1168)
 * Seventh Son: Imperial Prince Priest Kakukai (覚快法親王; 1134–1181)
 * Daughter: Aya Gozen (阿夜御前; d.1195)

 * Sanjō-no-Tsubone (三条局; d.1138), Fujiwara no Iemasa’s daughter
 * Daughter: Imperial Princess Kenshi (妍子内親王; d.1161) Yoshida saigū (Imperial Princess serving at Ise Shrine)

 * Kasuga-no-Tsubone (春日局), Tokudaiji Saneyosi‘s daughter
 * Seventh Daughter: Imperial Princess Shōshi/Nobuko (頌子内親王; 1145–1208)

 * Fujitsubo-Nyogo (藤壺女御), Tachibana Toshitsuna‘s daughter
 * Shin-yo? (真誉) – Buddhist nun

 * Tosa-no-Tsubone (土佐局), Minamoto no Mitsuyasu‘s daughter

 * Fujiwara no Sanehira‘s Daughter
 * Daughter: Princess Takamatsu (高松宮) (apparently no connection with Arisugawa-no-miya, which was originally named Takamatsu-no-miya)

 * Unknown
 * Imperial Prince Priest Saichū (最忠法親王)
 * Imperial Prince Dōka? (道果親王)

Events of Toba's life
When his mother died, his grandfather, former-Emperor Shirakawa, took him under his care and raised him.

 * August 9, 1107 (Kajō 2, 19th day of the 7th month): In the 21st year of Emperor Horikawa's reign (堀河天皇21年), the emperor ("tennō") died at the age of 29; and the succession (‘‘senso’’) was received by his only son. Shortly thereafter, Emperor Toba is said to have acceded to the throne (‘‘sokui’’).

During the initial years of Toba's reign, the actual power was held by his grandfather, the "retired" Emperor Shirakawa, in a process known as cloistered rule.

 * 1110 (Ten'ei 3, 6th month): The Miidera-ji burned down. This was the second time the temple was destroyed by fire, the first time being in 1081.
 * February 25, 1123 (Hōan 4, 28th day of the 1st month): In the 17th year of Emperor Toba's reign (鳥羽天皇17年), Toba was forced to abdicate by his grandfather, retired-Emperor Shirakawa. Toba gave up the throne in favor of his son Akihito, who would become Emperor Sutoku.  Toba was only 20 years old when he renounced his title; and he had already reigned for 16 years:  two in the nengō Tennin, three in Ten'ei, five in the nengō Eikyū, two in Gen'ei, and four in the nengō Hōan.  At this time, Toba took the title Daijō-tennō.  The succession (senso) was received by his son.
 * 1123 (Hōan 4, 2nd month): Emperor Sutoku is said to have acceded to the throne (sokui).
 * 1129 (Daiji 4): "retired" Emperor Shirakawa died; and Toba himself began to rule as cloistered emperor. Toba continued to hold power through the reigns of three emperors, Emperor Sutoku, Emperor Konoe, and Emperor Go-Shirakawa.
 * 1134 (Chōshō 3): The former-Emperor Toba made a pilgrimage to the Kumano Shrines. He was accompanied by sadaijin  Hanazono no Arahito and udaijin Naka-no-in Munetada.  The excursion was enjoyed by all, and great quantities of sake were consumed.

Kugyō
Kugyō (公卿) is a collective term for the very few most powerful men attached to the court of the Emperor of Japan in pre-Meiji eras. Even during those years in which the court's actual influence outside the palace walls was minimal, the hierarchic organization persisted.

In general, this elite group included only three to four men at a time. These were hereditary courtiers whose experience and background would have brought them to the pinnacle of a life's career. During Toba's reign, this apex of the Daijō-kan included:
 * Sesshō, Fujiwara Tadazane, 1078–1162.
 * Kampaku, Fujiwara Tadazane.
 * Kampaku, Fujiwara Tadamichi, 1097–1164.
 * Daijō-daijin, Fujiwara Tadazane.
 * Sadaijin, Fujiwara Tadamichi.
 * Sadaijin, Hanazono no Arahito.
 * Udaijin, Naka-no-in Munetada.
 * Naidaijin
 * Dainagon

Eras of Toba's reign
The years of Toba's reign are more specifically identified by more than one era name or nengō.
 * Kajō           (1106–1108)
 * Tennin (1108–1110)
 * Ten-ei              (1110–1113)
 * Eikyū         (1113–1118)
 * Gen'ei              (1118–1120)
 * Hōan           (1120–1124)

title: Emperor Toba


text:
Emperor Sutoku

Emperor Sutoku (崇徳天皇) was the 75th emperor of Japan, according to the traditional order of succession.

Sutoku's reign spanned the years from 1123 through 1142.

Genealogy
Before his ascension to the Chrysanthemum Throne, his personal name (his imina) was Akihito (顕仁). Sutoku was the eldest son of Emperor Toba. Some old texts say he was instead the son of Toba's grandfather, Emperor Shirakawa.

 * Chūgū: Fujiwara no Kiyoko (藤原 聖子) later Kōkamon'in (皇嘉門院), Fujiwara no Tadamichi's daughter
 * Hyounosuke-no-Tsubone (兵衛佐局), Minamoto no Masamune's adopted daughter
 * First son: Imperial Prince Shigehito (重仁親王) (1140–1162).
 * Mikawa-dono (三河), Minamoto no Morotsune's daughter
 * Fifth Son: Kakue (覚恵; 1151–1184)
 * Karasuma-no-Tsubone (烏丸局)

Events of Sutoku's life

 * February 25, 1123 (Hōan 4, 28th day of the 1st month): In the 16th year of Emperor Toba's reign (鳥羽天皇二十五年), he abdicated; and the succession (‘‘senso’’) was received by his son, aged 3.
 * Hōan 4, in the 2nd month (1123): Emperor Sutoku is said to have acceded to the throne (‘‘sokui’’).
 * 1124 (Tenji 1, 2nd month): Former-Emperor Shirakawa and former-Emperor Toba went in carriages to outside the city where they could all together enjoy contemplating the flowers. Taiken-mon'in (? – August 26, 1145) (formerly Fujiwara no Shōshi), who was Toba's empress and Sutoku's mother, joined the procession along with many other women of the court. Their cortege was brilliant and colorful.  A great many men of the court in hunting clothes followed the ladies in this parade.  Fujiwara no Tadamichi then followed in a carriage, accompanied by bands of musicians and women who were to sing for the emperors.
 * 1124 (Tenji 1, 10th month): Shirakawa visited Mount Kōya.
 * 1125 (Tenji 2, 10th month): The emperor visited Iwashimizu Shrine and the Kamo Shrines; and afterwards, he also visited the shrines Hirano, Ōharano, Mutsunoo, Kitano, Gion and several others.
 * 1128 (Daiji 3, 3rd month): Taiken-mon'in ordered the construction of Enshō-ji in fulfillment of a sacred vow. This was one in a series of "sacred vow temples" (gogan-ji) built by imperial command following a precedent established by Emperor Shirakawa's Hosshō-ji.
 * 1128 (Daiji 3, 6th month): Fujiwara no Tadamichi is relieved of his responsibilities and duties as sesshō (regent); and simultaneously, Tadamichi is named kampaku.
 * August 17, 1135 (Hōen 1, 7th day of the 7th month): Former-Emperor Shirakawa died at the age of 77.
 * 1141 (Eiji 1, 3rd month): The former emperor Toba accepted the tonsure in becoming a monk at the age of 39.

In 1151, Sutoku ordered Waka imperial anthology Shika Wakashū.

In 1156, after being defeated by forces loyal to Emperor Go-Shirakawa in the Hōgen Rebellion, he was exiled to Sanuki Province (modern-day Kagawa prefecture on the island of Shikoku). Emperor Sutoku's reign lasted for 19 years: 2 years in the nengō Tenji, 5 years in Daiji, 1 year in 'Tenshō, 3 years in Chōshō, 6 years in Hōen, and 1 year in Eiji.

The site of Sutoku's grave is settled. This emperor is traditionally venerated at a memorial Shinto shrine (misasagi) in Sakaide, Kagawa. He was also enshrined (or sealed away ... ) in Shiramine Shrine in Kyoto and Kotohira-gū in Kagawa Prefecture. The former is also associated with the god of football, worshipped by Kuge clan Asukai in times of yore, while the latter enshrined Ō-mono-nushi-no-mikoto, a god known to have restored harmony in Yamato (or blackmailed Emperor Sujin ... ) in exchange for worship and nepotism.

The Imperial Household Agency designates this location as Sutoku's mausoleum. It is formally named Shiramine no misasagi.

Kugyō
Kugyō (公卿) is a collective term for the very few most powerful men attached to the court of the Emperor of Japan in pre-Meiji eras. In general, this elite group included only three to four men at a time. These were hereditary courtiers whose experience and background would have brought them to the pinnacle of a life's career. During Sutoku's reign, this apex of the Daijō-kan included:
 * Sesshō, Fujiwara no Tadamichi, 1097–1164.
 * Daijō-daijin, Fujiwara no Tadamichi.
 * Sadaijin
 * Udaijin
 * Nadaijin, Fujiwara no Yorinaga, 1120–1156.
 * Dainagon

Eras of Sutoku's reign
The years of Sutoku's reign are more specifically identified by more than one era name or nengō.
 * Hōan (1120–1124)
 * Tenji (1124–1126)
 * Daiji (1126–1131)
 * Tenshō (1131–1132)
 * Chōshō (1132–1135)
 * Hōen (1135–1141)
 * Eiji (1141–1142)

Legends
After Sutoku's abdication and exile, he devoted himself to monastic life. He copied numerous scriptures and offered them to the court. Fearing that the scriptures were cursed, the court refused to accept them. Snubbed, Sutoku was said to have resented the court and, upon his death, became an vengeful spirit (怨霊). Everything from the subsequent fall in fortune of the Imperial court, the rise of the samurai powers, droughts and internal unrests were blamed on his haunting.

Along with Sugawara no Michizane and Taira no Masakado, he is often called one of the “Three Great Onryō of Japan.”.

Literary works from the Edo period such as and Chinsetsu Yumiharizuki (椿説弓張月) and ukiyo-e paintings by Utagawa Yoshitsuya depict Emperor Sutoku as an.

In 2023, the heavy metal band Onmyo-Za produced the song Shiramine (白峯), about Emperor Sutoku as a.

title: Emperor Sutoku


text:
1164

Year 1164 (MCLXIV) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar.

Scotland

 * Battle of Renfrew: A Norse-Gaelic army led by Lord Somerled, ruler of the Isles, invades Scotland and is routed by the Scottish forces under the command of Walter fitz Alan and Herbert of Selkirk, bishop of Glasgow.

England

 * January 30 – King Henry II tries to delimit spiritual and royal jurisdictions in the Constitutions of Clarendon, written in large part by his councilor Richard de Luci.
 * November 2 – Thomas Becket, having contended with Henry II over the power of secular courts, is found guilty of contempt of court, and exiled to France.

Levant

 * Spring – Saladin accompanies his uncle, General Shirkuh, with an army sent to the Fatimid Caliphate (modern Egypt) by Nur al-Din, ruler (atabeg) of Syria.
 * August 12 – Battle of Harim: Zangid forces under Nur al-Din defeat and capture Bohemond III of Antioch, Raymond of Tripoli, and Hugh of Lusignan.

Africa

 * A commercial treaty grants access to Almohad-dominated ports to merchants from several European powers, including Marseille and Savona.

Asia

 * September 14 – Emperor Sutoku of Japan dies in Sanuki Province (on the island of Shikoku), having lived in exile from the capital at Kyoto since 1156.

Markets

 * Venice secures its loans against fiscal revenues, to obtain lower interest rates. In the first operation of this kind, the Republic obtains 1150 silver marci, for 12 years of the taxes levied on the Rialto market.

Religion

 * April 20 – Antipope Victor IV dies at Rome and is succeeded by Paschal III, who has gained election through the influence of Archchancellor Rainald of Dassel.
 * August 5 – Uppsala is recognized as the seat of the Swedish metropolitan, with the coronation of its first archbishop Stefan, by Pope Alexander III.
 * King Olaf II of Norway is canonized as Saint Olaf by Alexander III, making him a universally recognised saint of the Catholic Church.
 * Rainald of Dassel brings relics of the Three Magi from Milan to Cologne as a gift for Holy Roman Emperor Frederick Barbarossa.

Births

 * July 16 – Frederick V, son of Frederick Barbarossa
 * December 28 – Rokujō, emperor of Japan (d. 1176)
 * Fulk of Pavia, Italian prelate and bishop (d. 1229)
 * Hatakeyama Shigetada, Japanese samurai (d. 1205)
 * Ibn Tumlus, Moorish scholar and physician (d. 1223)
 * Isabel de Bolebec, English noblewoman (d. 1245)
 * Shi Miyuan, Chinese official and politician (d. 1233)

Deaths

 * January 30 – William of Anjou, viscount of Dieppe (b. 1136)
 * March 13 – Fujiwara no Tadamichi, Japanese regent (b. 1097)
 * April 20 – Victor IV, antipope of Rome (b. 1095)
 * May 16 – Héloïse, French scholar and abbess
 * May 19 – Bashnouna, Egyptian monk and martyr
 * June 18 – Elisabeth of Schönau, German abbess
 * September 4 – Henry II, prince-bishop of Liège
 * September 14 – Sutoku, emperor of Japan (b. 1119)
 * November 11 – Hugh of Amiens, French archbishop
 * December 23 – Hartmann of Brixen, German bishop (b. 1090)
 * December 31 – Ottokar III, margrave of Styria (b. 1124)
 * Herbert of Selkirk, Scottish bishop and chancellor
 * Hodierna of Jerusalem, countess of Tripoli (b. 1110)
 * Ortlieb of Zwiefalten, German Benedictine abbot
 * Zhang Jun, Chinese grand chancellor (b. 1097)

title: 1164


text:
Half-reaction

In chemistry, a half reaction (or half-cell reaction) is either the oxidation or reduction reaction component of a redox reaction. A half reaction is obtained by considering the change in oxidation states of individual substances involved in the redox reaction. Often, the concept of half reactions is used to describe what occurs in an electrochemical cell, such as a Galvanic cell battery. Half reactions can be written to describe both the metal undergoing oxidation (known as the anode) and the metal undergoing reduction (known as the cathode).

Half reactions are often used as a method of balancing redox reactions. For oxidation-reduction reactions in acidic conditions, after balancing the atoms and oxidation numbers, one will need to add H+ ions to balance the hydrogen ions in the half reaction. For oxidation-reduction reactions in basic conditions, after balancing the atoms and oxidation numbers, first treat it as an acidic solution and then add OH- ions to balance the H+ ions in the half reactions (which would give H2O).

Example: Zn and Cu Galvanic cell

Consider the Galvanic cell shown in the adjacent image: it is constructed with a piece of zinc (Zn) submerged in a solution of zinc sulfate (ZnSO4) and a piece of copper (Cu) submerged in a solution of copper(II) sulfate (CuSO4). The overall reaction is:

At the Zn anode, oxidation takes place (the metal loses electrons). This is represented in the following oxidation half reaction (note that the electrons are on the products side):

At the Cu cathode, reduction takes place (electrons are accepted). This is represented in the following reduction half reaction (note that the electrons are on the reactants side):

Example: oxidation of magnesium
Consider the example burning of magnesium ribbon (Mg). When magnesium burns, it combines with oxygen (O2) from the air to form magnesium oxide (MgO) according to the following equation:

Magnesium oxide is an ionic compound containing Mg(2+) and O(2-) ions whereas Mg_{(s)} and O_{2(g)} are elements with no charges. The Mg_{(s)} with zero charge gains a +2 charge going from the reactant side to product side, and the O_{2(g)} with zero charge gains a –2 charge. This is because when Mg_{(s)} becomes Mg(2+), it loses 2 electrons. Since there are 2 Mg on left side, a total of 4 electrons are lost according to the following oxidation half reaction:

On the other hand, O2 was reduced: its oxidation state goes from 0 to -2. Thus, a reduction half reaction can be written for the O2 as it gains 4 electrons:

The overall reaction is the sum of both half reactions:

When chemical reaction, especially, redox reaction takes place, we do not see the electrons as they appear and disappear during the course of the reaction. What we see is the reactants (starting material) and end products. Due to this, electrons appearing on both sides of the equation are canceled. After canceling, the equation is re-written as

Two ions, positive (Mg(2+)) and negative (O(2-)) exist on product side and they combine immediately to form a compound magnesium oxide (MgO) due to their opposite charges (electrostatic attraction). In any given oxidation-reduction reaction, there are two half reactions—oxidation half reaction and reduction half reaction. The sum of these two half reactions is the oxidation–reduction reaction.

Half-reaction balancing method
Consider the reaction below:

The two elements involved, iron and chlorine, each change oxidation state; iron from +2 to +3, chlorine from 0 to −1. There are then effectively two half reactions occurring. These changes can be represented in formulas by inserting appropriate electrons into each half reaction:

Given two half reactions it is possible, with knowledge of appropriate electrode potentials, to arrive at the complete (original) reaction the same way. The decomposition of a reaction into half reactions is key to understanding a variety of chemical processes. For example, in the above reaction, it can be shown that this is a redox reaction in which Fe is oxidised, and Cl is reduced. Note the transfer of electrons from Fe to Cl. Decomposition is also a way to simplify the balancing of a chemical equation. A chemist can atom balance and charge balance one piece of an equation at a time.

For example:
 * Fe(2+) -> Fe(3+) + e- becomes 2Fe(2+) -> 2Fe(3+) + 2e-
 * is added to Cl2 + 2e- -> 2Cl-
 * and finally becomes Cl2 + 2Fe(2+) -> 2Cl- + 2Fe(3+)

It is also possible and sometimes necessary to consider a half reaction in either basic or acidic conditions, as there may be an acidic or basic electrolyte in the redox reaction. Due to this electrolyte it may be more difficult to satisfy the balance of both the atoms and charges. This is done by adding H2O, OH-, e-, and/or H+ to either side of the reaction until both atoms and charges are balanced.

Consider the half reaction below:

OH-, H2O, and e- can be used to balance the charges and atoms in basic conditions, as long as it is assumed that the reaction is in water.

Again consider the half reaction below:

H+, H2O, and e- can be used to balance the charges and atoms in acidic conditions, as long as it is assumed that the reaction is in water.

Notice that both sides are both charge balanced and atom balanced.

Often there will be both H+ and OH- present in acidic and basic conditions but that the resulting reaction of the two ions will yield water, H2O (shown below):

title: Half-reaction


text:
Talk:Chordate

Pigment & Differential Biology
There are some soft constraints that separate Chordata from other biological lineages, but have not yet been made part of the formal definition.
 * Pigmentation : Chordata are not capable of blue pigmentation, that is to say blue skin pigmentation. Blue skin pigmentation is not to be confused with the biological alteration of (for example) feathers in birds -- that appear blue via an evolved prism mechanism in the feather structure.

There still is a lot of differential (DNA sequence based) comparison research going on that is trying to separate out the simplest forms of chordata. As around 90% of the species on Earth don't have a backbone like chordata. Some of these species may have lost their chordata like structures over time and this complication continues to complicate the complete definition of Chordata. Eyreland (talk) 03:04, 10 September 2016 (UTC)

What about blue skinned frogs, blue skinned monkeys like mandrills, blue skinned wattles on turkeys and cassowaries and blue fish? Are none of those pigmented? — Preceding unsigned comment added by 51.6.66.130 (talk) 09:14, 6 February 2017 (UTC)

 * Good point, I have removed it as unsourced, and contradicted by many creatures. --Jules  (Mrjulesd) 02:20, 13 March 2017 (UTC)

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Cladogram
The cladogram under phylogeny is so full of problems that it should be edited or removed: Condrychthyes is missing! Sarcopterygii appears to be a synonym of Tetrapods! — Preceding unsigned comment added by Gabe Lemag (talk • contribs) 17:33, 5 March 2018 (UTC)
 * I agree that is could be improved, but I oppose removal. The Chondrichthyes could be included; the Sarcopterygii gave rise to the tetrapods (plus a few odd fish such as the coelacanths and lung-fish) and this is consistent with the cladogram. --Jules  (Mrjulesd) 17:46, 5 March 2018 (UTC)

Rank of Tetrapoda and Sarcopterygii
This sentence doesn't make sense:
 * Benton included the Superclass Tetrapoda in the Subclass Sarcopterygii

You can't have a superclass within a subclass - should it be the other way round? 31.50.203.97 (talk) 11:48, 15 September 2019 (UTC)
 * Some of Benton's rank usage is rather ideoscncratic. He can use the same rank several times in a taxonomic heirarchy and he does use higher ranks for groups like Tetrapoda and Aves. If you look at the Appendix in the 4th edition of his Vertebrate Palaeontology, you can see on p436 that he does list Superclass Tetrapoda under Subclass Sarcopterygii. The online classification for the third edition has the same, but I can't find it online now. Below is the listing:
 * Subclass Sarcopterygii
 * Order Dipnoi
 * Infraclass Crossopterygii
 * †Order Porolepiformes
 * Superorder unnamed
 * †Order Onychodontida
 * Order Actinistia
 * Infraclass Tetrapodomorpha
 * †Order Rhizodontida
 * Superorder Osteolepidida
 * †Order Osteolepiformes
 * †Family Tristichopteridae
 * †Order Panderichthyida
 * Superclass Tetrapoda
 * I know it is confusing, but that is correctly quoting the source. It might be better to omit his ranks and just state that Tetrapoda are placed within Sarcopterygii.
 * An example of repeating the same rank occurs within Reptilia. He uses Division Archosauriformes under Infraclass Archosauromorpha and later uses Division Mesoeucrocodylia under Order Crocodylia and Division Coelurosauria under Infraorder Tetanurae. Division is used at three different levels within the same taxonomic hierarchy.  Jts1882 | talk 15:01, 15 September 2019 (UTC)

Cephalochordata: (Acrania) or (Acraniata) or nix the lot?
In the classification section, Cephalochordata is listed with Acraniata in brackets behind it. Haeckel's 1866 Acrania is considered synonymous with Cephalochordata according to its page (though it is also shown on a specific internal branch of the tree of that page, which is a problem all of its own), but I am not sure of the taxonomic history of Acraniata. The Acraniata page is a redirect to Invertebrate, whereas Acrania page is for the developmental defect by the same name (not linked here to spare the reader some pretty graphic imagery). There seems to be some chaos here that needs to be straightened out. Can we remove the piece in brackets, as Cephalochordata is simply the most accepted name right now? Or does it have some greater historical significance of which I am unaware? Dr Mark D. Scherz 08:31, 9 April 2021 (UTC)
 * My understanding is that Acraniata is a historic group of organisms without a distinct cranium. As such it would include Cephalochordata, Hemichordata and Urochordata, which makes it paraphyletic with respect to Craniata. I don't think it should be used as a synonym of Cephalochordata. —  Jts1882 | talk 09:02, 9 April 2021 (UTC)
 * However, Benton's Vertebrate Palaeontology does list "Cephalochordata (Acraniata)" (p433) and is the source cited for the listing. Nelson's Fishes of the World has a section "Subphylum Cephalochordata (Acrania, in part)" (p16). —  Jts1882 | talk 09:31, 9 April 2021 (UTC)

title: Talk:Chordate


text:
Type XXI submarine

Type XXI submarines were a class of German diesel–electric Elektroboot (German: "electric boat") submarines designed during the Second World War. One hundred and eighteen were completed, with four being combat-ready. During the war only two were put into active service and went on patrols, but these were not used in combat.

They were the first submarines designed to operate primarily submerged, rather than spending most of their time as surface ships that could submerge for brief periods as a means of escaping detection. They incorporated many batteries to increase the time they could spend submerged, to as much as several days, and they only needed to surface to periscope depth for recharging via a snorkel. The design included many general improvements as well: much greater underwater speed by an improved hull design, greatly improved diving times, power-assisted torpedo reloading and greatly improved crew accommodations. However, the design was also flawed in many ways, with the submarines being mechanically unreliable and, according to post-war analysis, vulnerable to combat damage. The Type XXI submarines were also rushed into production before design work was complete, and the inexperienced facilities which constructed the boats were unable to meet necessary quality standards.

After the war, several navies obtained Type XXIs and operated them for decades in various roles, while large navies introduced new submarine designs based on them. These include the Soviet Whiskey-class submarine, American Tang-class submarine, British Porpoise, and Swedish Hajen III-class submarine classes, all based on the Type XXI design to some extent.

Description
The main features of the Type XXI were the hydrodynamically streamlined hull and conning tower and the large number of battery cells, roughly triple that of the German Type VII submarine. This gave these boats great underwater range and dramatically reduced the time spent on or near the surface. They could travel submerged at about 5 kn for about 75 hours before recharging batteries, which took less than five hours using the snorkel due to the new super-charged diesel engines. Being designed primarily for submerged use, the Type XXI's maximum surface speed (15.6 knots) was slightly lower than that of the Type IX (18.2 knots) but its submerged speed was more than twice that of the Type IX (17.2 knots versus 7.7 knots) because they were equipped with much more powerful electric drive motors and had less drag.

The Type XXI was also much quieter than the VIIC, making it more difficult to detect when submerged, and the design eliminated protruding components that had created drag in earlier models. The new, streamlined hull design allowed submerged speed of 17.2 kn, versus  7.6 kn for the Type VIIC. The ability to outrun many surface ships while submerged, combined with improved dive times (also a product of the new hull form), made the Type XXI much more difficult to pursue and destroy. It also provided a 'sprint ability' when positioning itself for an attack. Older boats had to surface to sprint into position. This often revealed a boat's location, especially after aircraft became available for convoy escort. The Type XXI was also equipped with an additional pair of electric creep motors for occasions when silent running was necessary.

The Type XXI was equipped with six bow torpedo tubes (instead of the more common four in German submarines) and carried 23 torpedoes. It featured an electric torpedo-reloading system that allowed all six bow torpedo tubes to be reloaded faster than a Type VIIC could reload one tube. The Type XXI could fire 18 torpedoes in less than 20 minutes. The class also featured a very sensitive passive sonar for the time, housed in the "chin" of the hull.

The Type XXIs also had better facilities than previous U-boat classes, with much roomier crew berths, and a freezer to prevent food spoilage. The increased capacity allowed for a crew of 57.

A post-war assessment of the Type XXI by the United States Navy concluded that while the design had some admirable features, it was seriously flawed. The submarines' engines were underpowered, which limited the surface speed and increased the time required to charge the batteries. The hydraulic system was unduly complex, and its main elements were located outside the pressure hull. This made the system highly vulnerable to corrosion and damage. The snorkel was also badly designed, and difficult to use in practice.

Construction
This was the first U-boat to be constructed of modular components to allow for the manufacture of the various components in different factories and subsequent assembly at the shipyard.

Between 1943 and 1945, 118 boats were assembled by Blohm & Voss of Hamburg, AG Weser of Bremen and Schichau-Werke of Danzig. Each hull was constructed from nine prefabricated sections with final assembly at the shipyards. This new method allowed for a hypothetical construction time of less than six months per vessel, but in practice all the assembled U-boats were plagued with severe quality problems that required extensive post-production work and time to rectify. One of the reasons for these shortcomings was that sections were made by companies having little experience with shipbuilding, after a decision by Albert Speer. As a result, of 118 Type XXIs constructed, only four were fit for combat before the Second World War ended in Europe. Of these, only two conducted combat patrols and neither sank any Allied ships. Post-war assessments by the US Navy and British Royal Navy also found that the completed submarines had poor structural integrity due to the manufacturing problems. This rendered the submarines highly vulnerable to depth charges, and gave them a lesser maximum diving depth than earlier U-boat designs.

It was planned that final assembly of Type XXI boats would eventually be carried out in the Valentin submarine pens, a massive, bomb–hardened concrete bunker built at the small port of Farge, near Bremen. The pens were constructed between 1943 and 1945, using about 10,000 concentration camp prisoners and prisoners of war as forced labour. The facility was 90% completed when, during March 1945, it was heavily damaged by Allied bombing with Grand Slam "earthquake" bombs and abandoned. A few weeks later the area was captured by the British Army.

Due to the combination of design and construction problems, historian Clay Blair judged that "the XXI could not have made a big difference in the Battle of the Atlantic.

Radar detector
The FuMB Ant 3 Bali radar detector and antenna was located on top of the snorkel head.

Radar transmitter
The Type XXI boats were fitted with the FuMO 65 Hohentwiel U1 with the Type F432 D2 radar transmitter.

Germany

GS U-2511 and GS U-3008 were the only Type XXIs used for war patrols, and neither sank any ships. The commander of U-2511 claimed the U-boat had a British cruiser in her sights on 4 May when news of the German cease-fire was received. He further claimed she made a practice attack before leaving the scene undetected.

During 1957, GS U-2540, which had been scuttled at the end of the war, was raised and refitted as research vessel Wilhelm Bauer of the Bundesmarine. It was operated by both military and civilian crews for research purposes until 1982. During 1984, it was made available for display to the public by the Deutsches Schiffahrtsmuseum (German Maritime Museum) in Bremerhaven, Germany.

France
GS U-2518 became FRENCH SUBMARINE Roland Morillot. It was used for active service during the Suez Crisis in 1956, and remained in commission until 1967. It was scrapped in 1969.

Soviet Union
Four Type XXI boats were assigned to the USSR by the Potsdam Agreement; these were GS U-2529, GS U-3035, GS U-3041, and GS U-3515, which were commissioned into the Soviet Navy as SOVIET SUBMARINE B-27, SOVIET SUBMARINE B-28, B-29, and SOVIET SUBMARINE B-30 (later B-100) respectively. However, Western intelligence believed the Soviets had acquired several more Type XXI boats; a review by the U.S. Joint Intelligence Committee for the Joint Chiefs of Staff during January 1948 estimated the Soviet Navy then had 15 Type XXIs operational, could complete construction of 6 more within 2 months, and could build another 39 within a year and a half from prefabricated sections, since several factories producing Type XXI components and the assembly yard at Danzig had been captured by the Soviets at the end of World War II. U-3538 — U-3557 (respectively TS-5 – TS-19 and TS-32 – TS-38) remained incomplete at Danzig and were scrapped or sunk during 1947. The four boats assigned by Potsdam were used in trials and tests until 1955, then scuttled or used for weapon testing between 1958 and 1973. The Type XXI design formed the basis for several Soviet design projects, Projects 611, 613, 614, 633, and 644. These became the submarine classes known by their NATO codes as Zulu-class submarine, Whiskey-class submarine and Romeo-class submarine submarine classes.

United Kingdom

GS U-3017 was commissioned into the Royal Navy as HMS N41. It was used for tests until being scrapped during November 1949.

United States
The United States Navy acquired GS U-2513 and GS U-3008, operating them both in the Atlantic Ocean. During November 1946 President Harry S. Truman visited U-2513; the submarine dived to 440 ft with the President aboard. U-2513 was sunk as a target on 7 October 1951; U-3008 was sold for scrap on 15 September 1955.

Survivor

The only boat to survive intact is GS Wilhelm Bauer (ex-U-2540), at the German Maritime Museum in Bremerhaven. Records indicate that this sub was scuttled by her crew in 1945, salvaged in 1957 and refurbished for use by the West German Bundesmarine until retirement in 1982. She was then modified to appear in wartime configuration for exhibition purposes.

Notable wrecks
The wrecks of several Type XXI boats are known to exist. During 1985, it was discovered that the partially scrapped remains of GS U-2505, GS U-3004, and GS U-3506 were still in the partially demolished "Elbe II" U-boat bunker in Hamburg. The bunker has since been filled in with gravel, although even that did not initially deter many souvenir hunters who measured the position of open hatches and dug down to them to allow the removal of artifacts. The wrecks now lie beneath a car park (parking lot), making them inaccessible.

GS U-2513 lies in 213 ft of water 70 nmi west of Key West, Florida. The boat has been visited by divers, but the depth makes this very difficult and the site is considered suitable for only advanced divers. Four other boats lie off the coast of Northern Ireland, where they were sunk during 1946 as part of Operation Deadlight. Both GS U-2511 and GS U-2506 were found by nautical archaeologist Innes McCartney during his Operation Deadlight expeditions between 2001 and 2003. Both were found to be in remarkably good condition. In April 2018 the wreck of GS U-3523 was found north of Skagen in Denmark.

Influences
The Type XXI design directly influenced advanced post-war submarines, the Greater Underwater Propulsion Power Program (GUPPY) improvements to the United States Gato-class submarine, Balao-class submarine, and Tench-class submarine-class submarines, and the Soviet submarine projects designated Whiskey-class submarine, Zulu-class submarine, and Romeo-class submarine by NATO. The Chinese-built Romeo-class submarines, and the subsequent Ming-class submarine, were based on Soviet blueprints.

title: Type XXI submarine


text:
User:Great throwdini

My Wikipedia ID was borrowed from one of the few decent television sitcoms in recent history, News Radio.

title: User:Great throwdini


text:
Albert I of Germany

Albert I of Habsburg (Albrecht I.) (July 1255 – 1 May 1308) was a Duke of Austria and Styria from 1282 and King of Germany from 1298 until his assassination. He was the eldest son of King Rudolf I of Germany and his first wife Gertrude of Hohenberg. Sometimes referred to as 'Albert the One-eyed' because of a battle injury that left him with a hollow eye socket and a permanent snarl.

Biography
From 1273 Albert ruled as a landgrave over his father's Swabian (Further Austrian) possessions in Alsace. In 1282 his father, the first German monarch from the House of Habsburg, invested him and his younger brother Rudolf II with the duchies of Austria and Styria, which he had seized from late King Ottokar II of Bohemia and defended in the 1278 Battle on the Marchfeld. By the 1283 Treaty of Rheinfelden his father entrusted Albert with their sole government, while Rudolf II ought to be compensated by the Further Austrian Habsburg home territories – which, however, never happened until his death in 1290. Albert and his Swabian ministeriales appear to have ruled the Austrian and Styrian duchies with conspicuous success, overcoming the resistance by local nobles.

King Rudolf I was unable to secure the succession to the German throne for his son, especially due to the objections raised by Ottokar's son King Wenceslaus II of Bohemia, and the plans to install Albert as successor of the assassinated King Ladislaus IV of Hungary in 1290 also failed. Upon Rudolf's death in 1291, the Prince-electors, fearing Albert's power and the implementation of a hereditary monarchy, chose Count Adolf of Nassau-Weilburg as King of the Romans. An uprising among his Styrian dependents compelled Albert to recognize the sovereignty of his rival and to confine himself for a time to the government of the Habsburg lands at Vienna.

He did not abandon his hopes of the throne, however, which were eventually realised: In 1298, he was chosen German king by some of the princes, who were bothered about Adolf's attempts to gain his own power bases in the lands of Thuringia and Meissen, again led by the Bohemian king Wenceslaus II. The armies of the rival kings met at the Battle of Göllheim near Worms, where Adolf was defeated and slain.

Submitting to a new election but securing the support of several influential princes by making extensive promises, he was chosen at the Imperial City of Frankfurt on 27 July 1298, and crowned at Aachen Cathedral on 24 August.

Although a hard, stern man, Albert had a keen sense of justice when his own interests were not involved, and few of the German kings possessed so practical an intelligence. He encouraged the cities, and not content with issuing proclamations against private war, formed alliances with the princes in order to enforce his decrees. The serfs, whose wrongs seldom attracted notice in an age indifferent to the claims of common humanity, found a friend in this severe monarch, and he protected even the despised and persecuted Jews. Stories of his cruelty and oppression in the Swiss cantons (cf. William Tell) did not appear until the 16th century, and are now regarded as legendary.

Albert sought to play an important part in European affairs. He seemed at first inclined to press a quarrel with the Kingdom of France over the Burgundian frontier, but the refusal of Pope Boniface VIII to recognize his election led him to change his policy, and, in 1299, he made a treaty with King Philip IV, by which his son Rudolph was to marry Blanche, the King's half-sister. He afterwards became estranged from Philip, but in 1303, Boniface recognized him as German king and future emperor; in return, Albert recognized the authority of the pope alone to bestow the Imperial crown, and promised that none of his sons should be elected German king without papal consent.

Albert had failed in his attempt to seize the counties of Holland and Zeeland, as vacant fiefs of the Holy Roman Empire, on the death of Count John I in 1299, but in 1306 he secured the crown of Bohemia for his son Rudolph III on the death of King Wenceslaus III. He also renewed the claim made by his predecessor, Adolf, on Thuringia, and interfered in a quarrel over the succession to the Hungarian throne. The Thuringian attack ended in Albert's defeat at the Battle of Lucka in 1307 and, in the same year, the death of his son Rudolph weakened his position in eastern Europe. His action in abolishing all tolls established on the Rhine since 1250 led the Rhenish prince-archbishops and the Elector of the Palatinate to form a league against him. Aided by the Imperial cities, however, he soon crushed the rising.

Death
Albert was on the way to suppress a revolt in Swabia when he was murdered on 1 May 1308, at Windisch on the Reuss, by his nephew Duke John, afterwards called "the Parricide" or "John Parricida".

Titles
His full name and titles were: Albert, by the grace of God, King of the Romans, Duke of Austria and Styria, Lord of Carniola, over the Wendish Mark and of Port Naon, Count of Habsburg and Kyburg, Landgrave of Alsace.

Marriage and children
In 1274, Albert had married Elizabeth, daughter of Count Meinhard II of Tyrol, who was a descendant of the Babenberg margraves of Austria who predated the Habsburgs' rule. The baptismal name Leopold, patron saint margrave of Austria, was given to one of their sons. Queen Elizabeth was in fact better connected to mighty German rulers than her husband: she was a descendant of earlier German kings, including Emperor Henry IV; she was also a niece of the Wittelsbach dukes of Bavaria, Austria's important neighbor.

Albert and Elizabeth had twelve children:
 * 1) Anna (1275, Vienna – 19 March 1327, Breslau), married:
 * 2) in Graz c. 1295 to Herman, Margrave of Brandenburg-Salzwedel;
 * 3) in Breslau 1310 to Henry VI the Good, Duke of Wrocław.
 * 4) Agnes (18 May 1281 – 10 June 1364, Königsfelden), married in Vienna 13 February 1296 King Andrew III of Hungary.
 * 5) Rudolph III (c. 1282 – 4 July 1307, Horažďovice) married but line extinct and predeceased his father.
 * 6) Elizabeth (1285 – 19 May 1353), married 1304 Frederick IV, Duke of Lorraine.
 * 7) Frederick I (1289 – 13 January 1330, Gutenstein) married to Isabella of Aragon, Queen of Germany but line extinct.
 * 8) Leopold I (4 August 1290 – 28 February 1326, Strassburg) married, had issue.
 * 9) Catherine (1295 – 18 January 1323, Naples), married Charles, Duke of Calabria in  1316.
 * 10) Albert II (12 December 1298, Vienna – 20 July 1358, Vienna).
 * 11) Henry the Gentle (1299 – 3 February 1327, Bruck an der Mur) married but line extinct.
 * 12) Meinhard (1300 – 1301), died in infancy.
 * 13) Otto (23 July 1301, Vienna – 26 February 1339, Vienna) married but line extinct.
 * Jutta (1302 – 5 March 1329), married Ludwig V, Count of Öttingen in Baden, 26 March 1319.

title: Albert I of Germany


text:
Albert II of Germany

Albert the Magnanimous, elected King of the Romans as Albert II (10 August 1397 – 27 October 1439), was emperor of the Holy Roman Empire and a member of the House of Habsburg. By inheritance he became Albert V, Duke of Austria. Through his wife (jure uxoris) he also became King of Hungary, Croatia, Bohemia, and inherited a claim to the Duchy of Luxembourg.

Biography
Albert was born in Vienna as the son of Albert IV, Duke of Austria, and Joanna Sophia of Bavaria.

He succeeded to the Duchy of Austria at the age of seven on his father's death in 1404. His uncle Duke William of Inner Austria, then head of the rivaling Leopoldinian line, served as regent for his nephew, followed by his brothers Leopold IV and Ernest the Iron in 1406. The quarrels between the brothers and their continued attempts to gain control over the Albertinian territories led to civil war-like conditions. Nevertheless, Albert, having received a good education, undertook the government of Austria proper on the occasion of Leopold's death in 1411 and succeeded, with the aid of his advisers, in ridding the duchy of the evils which had arisen during his minority.

In 1422 Albert married Elisabeth of Luxemburg, the daughter and heiress of the King Sigismund of Hungary (later also Holy Roman Emperor and King of Bohemia), and his second wife, the Slovenian noblewoman Barbara of Celje. Besides Hungary, Albert's marriage brought him claims to several Slavic kingdoms and principalities as well.

Albert assisted his father-in-law Sigismund in his campaigns against the Hussites, involving the Austrian duchy in the Hussite Wars. In return Sigismund designated him as his successor and granted him the title of a Margrave of Moravia in 1423. The Austrian lands were devastated several times and Albert also participated in the 1431 Battle of Domažlice where the Imperial troops suffered an embarrassing defeat. While his lands were harmed it was a showing of loyalty to the church as the church was trying to consolidate its influence and power.

When Sigismund died in 1437, Albert was crowned king of Hungary on 1 January 1438, and just as his predecessor did, he moved his court to the Hungarian Kingdom from where he later oversaw his other domains. Although crowned king of Bohemia six months after ascending to the Hungarian throne, he was unable to obtain possession of the country. He was engaged in warfare with the Bohemians and their Polish allies, when on 18 March 1438, he was chosen "King of the Romans" at Frankfurt, an honor which he does not appear to have sought. He was never crowned as Holy Roman Emperor.

Afterwards engaged in defending Hungary against the attacks of the Turks, he died on 27 October 1439 at Neszmély and was buried at Székesfehérvár. Albert was an energetic and warlike prince, whose short reign as a triple king gave great promise of usefulness for the Holy Roman Empire.

The Hussite Wars and Widespread Persecution
Beginning with the first crusade in the year 1095 persecution against those not within the Catholic faith were deemed as heretical and were to be destroyed, or converted. While the papal call for the end to heresy applied to Muslims traditionally, there was widespread violence that spread to other religious or social groups. Jews and lepers were the main targets along with Muslims in the crusade to destroy "devilry." The persecution of Jews came as no surprise in connection with the Hussite Wars. The call to arms against Heretics meant the call to arms against all who are not Christian, with the hopes of their destruction or conversion. However, the crusaders saw that as an opportunity to convert all who were not Christian, the Jews and lepers included not just the intended Muslims. If the heretics did not convert to Christianity they were massacred, usually burned. This would apply later in the Hussite Wars, which was a continuation of the crusades, as Albert II came to power as Duke of Austria, who was a willing participant in the fight against heresy. The Hussite Wars is a series of crusades against heresy in the Middle ages spanning from 1418-1437 and through his loyalty to the church and the persecutive works of his contemporaries, he would embark on his own persecutive journey against the Jews.

Jewish persecution
Beginning in the 11th century Jews started to define themselves as a people garnering a foothold as money lenders within their communities. Respectively, by the 13th century Jews in Europe and Austria had found themselves as a people with their own social identity. With this newfound identity persecution followed. Jewish people were subject to plundering and land stealing beginning in the 13th century as they were regarded as outsiders. However, the first major instance of Jewish persecution came with the First Crusade in the fall of 1095 and is thought of to be the beginning of a long line of Anti-Jewish persecution involving violence. Summoned by Pope Urban II with the hope of conquering the Holy Land, violence against the Jewish population came with inspiration from the rumor of a papal call to use violence against non-Christians, actually meaning Muslims. Pogroms were also organized to destroy Jewish communities which were highly effective. Overtime, historiographical works have tended to focus on the German-Austrian massacres due to how much evidence there is present. These German-Austrian massacres were arguably a great influence on Albert V and his Jewish persecutions and expulsions. The persecution of Jews would grow to encompass all of Europe for many centuries in which Albert V as Duke of Austria also took part in when he came to power.

Though the Jews in the Austrian duchy had been subject to local persecutions during the 13th and 14th century, their position remained relatively safe. Jewish communities prospered in several towns like Krems or the area around the Judenplatz at Vienna. During the confusion after the death of Duke Albert IV in 1404 their situation worsened sharply, culminating in the blaze of the Vienna synagogue on 5 November 1406, followed by riots and lootings.

With the ordering of campaign preparations against the Hussites by King Sigismund in the beginning of the 15th century taxes would be used to fund a crusade army. Albert V of Austria would follow suit keeping his good standing with the Catholic Church while he was in power. When Albert V came of age in 1411 and interfered in the Hussite Wars, he repeatedly established new taxes imposed on the Jewish community to finance his campaigns. Taxes would be established to destroy "devilry" and "imprudence". Like the Hussites, Jews were seen at this point as an enemy to Christendom. After the Hussites had devastated the duchy, the Austrian Jews were accused of collaboration and arms trade in favor of the enemies. The accusations of a host desecration at Enns in 1420 gave Albert pretext for the destruction of the Jewish community.

According to the 1463 Chronica Austriae by chronicler Thomas Ebendorfer, the duke on 23 May 1420, at the behest of the Church, ordered the imprisonment and forcible conversion of the Jews. Those that had not converted or escaped were sent off in boats down the Danube, while wealthy Jews remained under arrest, several of them tortured and stripped of their property. The forced baptism of Jewish children was stopped on intervention by Pope Martin V. On 12 March 1421 Albert sentenced the remaining Jews to death. Ninety-two men and 120 women were burned at the stake south of the Vienna city walls on 12 March 1421. The Jews were placed under an "eternal ban" and their synagogue was demolished. The persecutions in several Austrian towns are explicitly described in a 16th-century script called Vienna Gesera.

Full title
Full titulature Albert possessed went as follows: Albert, by the grace of God elected King of the Romans, always August, King of Hungary, Dalmatia, Croatia, Rama, Serbia, Galicia, Lodomeria, Cumania and Bulgaria, elected King of Bohemia, duke of Austria, Styria, Carinthia and Carniola, margrave of Moravia, Lord of the Wendish March and Port Naon, Count of Habsburg, Tyrol, Ferrete and Kyburg, etc. Margrave of Burgau and landgrave of Alsace.

In practise he often used a shorter version: Albert, by the grace of God elected King of the Romans, always August, King of Hungary, Dalmatia and Croatia, etc. elected King of Bohemia, duke of Austria, Styria, Carinthia and Carniola, Margrave of Moravia and Count of Tyrol, etc.

Family
His children with Elizabeth of Luxembourg were:
 * Anne of Austria (1432–1462), who married William III, Duke of Saxony. William became (1457–69) Duke of Luxembourg, in right of his wife
 * Elisabeth (c. 1436–1439 to 1505), who married Casimir IV of Poland, and whose son Vladislaus II of Bohemia later became king of Bohemia and Hungary
 * George (born and died at Vienna on 16 February 1435)
 * Ladislas V Posthumus of Bohemia, King of Hungary and Bohemia

title: Albert II of Germany


text:
Affine transformation

In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.

More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line.

If $X$ is the point set of an affine space, then every affine transformation on $X$ can be represented as the composition of a linear transformation on $X$ and a translation of $X$. Unlike a purely linear transformation, an affine transformation need not preserve the origin of the affine space. Thus, every linear transformation is affine, but not every affine transformation is linear.

Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, shear mapping, and compositions of them in any combination and sequence.

Viewing an affine space as the complement of a hyperplane at infinity of a projective space, the affine transformations are the projective transformations of that projective space that leave the hyperplane at infinity invariant, restricted to the complement of that hyperplane.

A generalization of an affine transformation is an affine map (or affine homomorphism or affine mapping) between two (potentially different) affine spaces over the same field $k$. Let $(X, V, k)$ and $(Z, W, k)$ be two affine spaces with $X$ and $Z$ the point sets and $V$ and $W$ the respective associated vector spaces over the field $k$. A map $f: X → Z$ is an affine map if there exists a linear map $m_{f} : V → W$ such that $m_{f} (x − y) = f (x) − f (y)$ for all $x, y$ in $X$.

Definition
Let $X$ be an affine space over a field $k$, and $V$ be its associated vector space. An affine transformation is a bijection $f$ from $X$ onto itself that is an affine map; this means that a linear map $g$ from $V$ to $V$ is well defined by the equation $$g(y-x) =f(y)-f(x);$$ here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that $$y-x= y'-x'$$ implies that $$f(y)-f(x)=f(y')-f(x').$$

If the dimension of $X$ is at least two, a semiaffine transformation $f$ of $X$ is a bijection from $X$ onto itself satisfying: These two conditions are satisfied by affine transformations, and express what is precisely meant by the expression that "$S$ preserves parallelism".
 * 1) For every $d$-dimensional affine subspace $X$ of $X$, then $f (S)$ is also a $d$-dimensional affine subspace of $S$.
 * 2) If $T$ and $X$ are parallel affine subspaces of $f$, then $f (S)$ and $f (T)$ are parallel.

These conditions are not independent as the second follows from the first. Furthermore, if the field $k$ has at least three elements, the first condition can be simplified to: $f$ is a collineation, that is, it maps lines to lines.

Structure
By the definition of an affine space, $V$ acts on $X$, so that, for every pair $$(x, \mathbf{v})$$ in $X × V$ there is associated a point $y$ in $X$. We can denote this action by $$\vec{v}(x) = y$$. Here we use the convention that $$\vec{v} = \textbf{v}$$ are two interchangeable notations for an element of $V$. By fixing a point $c$ in $X$ one can define a function $m_{c} : X → V$ by $m_{c}(x) = cx$. For any $c$, this function is one-to-one, and so, has an inverse function $m_{c}^{−1} : V → X$ given by $$m_c^{-1}(\textbf{v})=\vec{v}(c)$$. These functions can be used to turn $X$ into a vector space (with respect to the point $c$) by defining:
 * $$x + y = m_c^{-1}\left(m_c(x) + m_c(y)\right),\text{ for all } x,y \text{ in } X,$$ and
 * $$rx = m_c^{-1}\left(r m_c(x)\right), \text{ for all } r \text{ in } k \text{ and } x \text{ in } X.$$

This vector space has origin $c$ and formally needs to be distinguished from the affine space $X$, but common practice is to denote it by the same symbol and mention that it is a vector space after an origin has been specified. This identification permits points to be viewed as vectors and vice versa.

For any linear transformation $λ$ of $V$, we can define the function $L(c, λ) : X → X$ by
 * $$L(c, \lambda)(x) = m_c^{-1}\left(\lambda (m_c (x))\right) = c + \lambda (\vec{cx}).$$

Then $L(c, λ)$ is an affine transformation of $X$ which leaves the point $c$ fixed. It is a linear transformation of $X$, viewed as a vector space with origin $c$.

Let $σ$ be any affine transformation of $X$. Pick a point $c$ in $X$ and consider the translation of $X$ by the vector $$\bold{w} = \overrightarrow{c \sigma (c)}$$, denoted by $T_{w}$. Translations are affine transformations and the composition of affine transformations is an affine transformation. For this choice of $c$, there exists a unique linear transformation $λ$ of $V$ such that
 * $$\sigma (x) = T_{\bold{w}} \left( L(c, \lambda)(x) \right).$$

That is, an arbitrary affine transformation of $X$ is the composition of a linear transformation of $X$ (viewed as a vector space) and a translation of $X$.

This representation of affine transformations is often taken as the definition of an affine transformation (with the choice of origin being implicit).

Representation
As shown above, an affine map is the composition of two functions: a translation and a linear map. Ordinary vector algebra uses matrix multiplication to represent linear maps, and vector addition to represent translations. Formally, in the finite-dimensional case, if the linear map is represented as a multiplication by an invertible matrix $$A$$ and the translation as the addition of a vector $$\mathbf{b}$$, an affine map $$f$$ acting on a vector $$\mathbf{x}$$ can be represented as

 * $$ \mathbf{y} = f(\mathbf{x}) = A \mathbf{x} + \mathbf{b}. $$

Augmented matrix

Using an augmented matrix and an augmented vector, it is possible to represent both the translation and the linear map using a single matrix multiplication. The technique requires that all vectors be augmented with a "1" at the end, and all matrices be augmented with an extra row of zeros at the bottom, an extra column—the translation vector—to the right, and a "1" in the lower right corner. If $$A$$ is a matrix,

\begin{bmatrix} \mathbf{y} \\ 1 \end{bmatrix} = \left[ \begin{array}{ccc|c} & A & & \mathbf{b} \\ 0 & \cdots & 0 & 1 \end{array} \right] \begin{bmatrix} \mathbf{x} \\ 1 \end{bmatrix} $$

is equivalent to the following

 * $$ \mathbf{y} = A \mathbf{x} + \mathbf{b}. $$

The above-mentioned augmented matrix is called an affine transformation matrix. In the general case, when the last row vector is not restricted to be $$\left[ \begin{array}{ccc|c} 0 & \cdots & 0 & 1 \end{array} \right]$$, the matrix becomes a projective transformation matrix (as it can also be used to perform projective transformations).

This representation exhibits the set of all invertible affine transformations as the semidirect product of $$K^n$$ and $$\operatorname{GL}(n, K)$$. This is a group under the operation of composition of functions, called the affine group.

Ordinary matrix-vector multiplication always maps the origin to the origin, and could therefore never represent a translation, in which the origin must necessarily be mapped to some other point. By appending the additional coordinate "1" to every vector, one essentially considers the space to be mapped as a subset of a space with an additional dimension. In that space, the original space occupies the subset in which the additional coordinate is 1. Thus the origin of the original space can be found at $$(0,0, \dotsc, 0, 1)$$. A translation within the original space by means of a linear transformation of the higher-dimensional space is then possible (specifically, a shear transformation). The coordinates in the higher-dimensional space are an example of homogeneous coordinates. If the original space is Euclidean, the higher dimensional space is a real projective space.

The advantage of using homogeneous coordinates is that one can combine any number of affine transformations into one by multiplying the respective matrices. This property is used extensively in computer graphics, computer vision and robotics.

Example augmented matrix
Suppose you have three points that define a non-degenerate triangle in a plane, or four points that define a non-degenerate tetrahedron in 3-dimensional space, or generally $n + 1$ points $x1$, ..., $xn+1$ that define a non-degenerate simplex in $n$-dimensional space. Suppose you have corresponding destination points $y1$, ..., $yn+1$, where these new points can lie in a space with any number of dimensions. (Furthermore, the new points need not be distinct from each other and need not form a non-degenerate simplex.) The unique augmented matrix $M$ that achieves the affine transformation $$\begin{bmatrix}\mathbf{y}\\1\end{bmatrix} = M \begin{bmatrix}\mathbf{x}\\1\end{bmatrix}$$ is $$M = \begin{bmatrix}\mathbf{y}_1&\cdots&\mathbf{y}_{n+1}\\1&\cdots&1\end{bmatrix} \begin{bmatrix}\mathbf{x}_1&\cdots&\mathbf{x}_{n+1}\\1&\cdots&1\end{bmatrix}^{-1}.$$

Properties preserved
An affine transformation preserves:
 * 1) collinearity between points: three or more points which lie on the same line (called collinear points) continue to be collinear after the transformation.
 * 2) parallelism: two or more lines which are parallel, continue to be parallel after the transformation.
 * 3) convexity of sets: a convex set continues to be convex after the transformation. Moreover, the extreme points of the original set are mapped to the extreme points of the transformed set.
 * 4) ratios of lengths of parallel line segments: for distinct parallel segments defined by points $$p_1$$ and $$p_2$$, $$p_3$$ and $$p_4$$, the ratio of $$\overrightarrow{p_1p_2}$$ and $$\overrightarrow{p_3p_4}$$ is the same as that of $$\overrightarrow{f(p_1)f(p_2)}$$ and $$\overrightarrow{f(p_3)f(p_4)}$$.
 * 5) barycenters of weighted collections of points.

Groups
As an affine transformation is invertible, the square matrix $$A$$ appearing in its matrix representation is invertible. The matrix representation of the inverse transformation is thus

\left[ \begin{array}{ccc|c} & A^{-1} & & -A^{-1}\vec{b} \ \\ 0 & \ldots & 0 & 1 \end{array} \right]. $$

The invertible affine transformations (of an affine space onto itself) form the affine group, which has the general linear group of degree $$n$$ as subgroup and is itself a subgroup of the general linear group of degree $$n + 1$$.

The similarity transformations form the subgroup where $$A$$ is a scalar times an orthogonal matrix. For example, if the affine transformation acts on the plane and if the determinant of $$A$$ is 1 or −1 then the transformation is an equiareal mapping. Such transformations form a subgroup called the equi-affine group. A transformation that is both equi-affine and a similarity is an isometry of the plane taken with Euclidean distance.

Each of these groups has a subgroup of orientation-preserving or positive affine transformations: those where the determinant of $$A$$ is positive. In the last case this is in 3D the group of rigid transformations (proper rotations and pure translations).

If there is a fixed point, we can take that as the origin, and the affine transformation reduces to a linear transformation. This may make it easier to classify and understand the transformation. For example, describing a transformation as a rotation by a certain angle with respect to a certain axis may give a clearer idea of the overall behavior of the transformation than describing it as a combination of a translation and a rotation. However, this depends on application and context.

Affine maps
An affine map $$f\colon\mathcal{A} \to \mathcal{B}$$ between two affine spaces is a map on the points that acts linearly on the vectors (that is, the vectors between points of the space). In symbols, $$f$$ determines a linear transformation $$\varphi$$ such that, for any pair of points $$P, Q \in \mathcal{A}$$:

 * $$\overrightarrow{f(P)~f(Q)} = \varphi(\overrightarrow{PQ})$$

or
 * $$f(Q)-f(P) = \varphi(Q-P)$$.

We can interpret this definition in a few other ways, as follows.

If an origin $$O \in \mathcal{A}$$ is chosen, and $$B$$ denotes its image $$f(O) \in \mathcal{B}$$, then this means that for any vector $$\vec{x}$$:

 * $$f\colon (O+\vec{x}) \mapsto (B+\varphi(\vec{x}))$$.

If an origin $$O' \in \mathcal{B}$$ is also chosen, this can be decomposed as an affine transformation $$g\colon \mathcal{A} \to \mathcal{B}$$ that sends $$O \mapsto O'$$, namely

 * $$g\colon (O+\vec{x}) \mapsto (O'+\varphi(\vec{x}))$$,

followed by the translation by a vector $$\vec{b} = \overrightarrow{O'B}$$.

The conclusion is that, intuitively, $$f$$ consists of a translation and a linear map.

Alternative definition
Given two affine spaces $$\mathcal{A}$$ and $$\mathcal{B}$$, over the same field, a function $$f\colon \mathcal{A} \to \mathcal{B}$$ is an affine map if and only if for every family $$\{(a_i, \lambda_i)\}_{i\in I}$$ of weighted points in $$\mathcal{A}$$ such that
 * $$\sum_{i\in I}\lambda_i = 1$$,

we have

 * $$f\left(\sum_{i\in I}\lambda_i a_i\right)=\sum_{i\in I}\lambda_i f(a_i)$$.

In other words, $$f$$ preserves barycenters.

History
The word "affine" as a mathematical term is defined in connection with tangents to curves in Euler's 1748 Introductio in analysin infinitorum. Felix Klein attributes the term "affine transformation" to Möbius and Gauss.

Image transformation
In their applications to digital image processing, the affine transformations are analogous to printing on a sheet of rubber and stretching the sheet's edges parallel to the plane. This transform relocates pixels requiring intensity interpolation to approximate the value of moved pixels, bicubic interpolation is the standard for image transformations in image processing applications. Affine transformations scale, rotate, translate, mirror and shear images as shown in the following examples:

The affine transforms are applicable to the registration process where two or more images are aligned (registered). An example of image registration is the generation of panoramic images that are the product of multiple images stitched together.

Affine warping
The affine transform preserves parallel lines. However, the stretching and shearing transformations warp shapes, as the following example shows:

This is an example of image warping. However, the affine transformations do not facilitate projection onto a curved surface or radial distortions.

In the plane
Affine transformations in two real dimensions include:
 * pure translations,
 * scaling in a given direction, with respect to a line in another direction (not necessarily perpendicular), combined with translation that is not purely in the direction of scaling; taking "scaling" in a generalized sense it includes the cases that the scale factor is zero (projection) or negative; the latter includes reflection, and combined with translation it includes glide reflection,
 * rotation combined with a homothety and a translation,
 * shear mapping combined with a homothety and a translation, or
 * squeeze mapping combined with a homothety and a translation.

To visualise the general affine transformation of the Euclidean plane, take labelled parallelograms ABCD and A′B′C′D′. Whatever the choices of points, there is an affine transformation T of the plane taking A to A′, and each vertex similarly. Supposing we exclude the degenerate case where ABCD has zero area, there is a unique such affine transformation T. Drawing out a whole grid of parallelograms based on ABCD, the image T(P) of any point P is determined by noting that T(A) = A′, T applied to the line segment AB is A′B′, T applied to the line segment AC is A′C′, and T respects scalar multiples of vectors based at A. [If A, E, F are collinear then the ratio length(AF)/length(AE) is equal to length(A′F′)/length(A′E′).] Geometrically T transforms the grid based on ABCD to that based in A′B′C′D′.

Affine transformations do not respect lengths or angles; they multiply area by a constant factor

 * area of A′B′C′D′ / area of ABCD.

A given T may either be direct (respect orientation), or indirect (reverse orientation), and this may be determined by its effect on signed areas (as defined, for example, by the cross product of vectors).

Over the real numbers
The functions $$f\colon \R \to \R,\; f(x) = mx + c$$ with $$m$$ and $$c$$ in $$\R$$ and $$m\ne 0$$, are precisely the affine transformations of the real line.

In plane geometry
In $$\mathbb{R}^2$$, the transformation shown at left is accomplished using the map given by:

 * $$\begin{bmatrix} x \\ y\end{bmatrix} \mapsto \begin{bmatrix} 0&1\\ 2&1 \end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix} + \begin{bmatrix} -100 \\ -100\end{bmatrix}$$

Transforming the three corner points of the original triangle (in red) gives three new points which form the new triangle (in blue). This transformation skews and translates the original triangle.

In fact, all triangles are related to one another by affine transformations. This is also true for all parallelograms, but not for all quadrilaterals.

title: Affine transformation