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Triality

In mathematics, triality is a relationship among three vector spaces, analogous to the duality relation between dual vector spaces. Most commonly, it describes those special features of the Dynkin diagram D4 and the associated Lie group Spin(8), the double cover of 8-dimensional rotation group SO(8), arising because the group has an outer automorphism of order three. There is a geometrical version of triality, analogous to duality in projective geometry.

Of all simple Lie groups, Spin(8) has the most symmetrical Dynkin diagram, D4. The diagram has four nodes with one node located at the center, and the other three attached symmetrically. The symmetry group of the diagram is the symmetric group S3 which acts by permuting the three legs. This gives rise to an S3 group of outer automorphisms of Spin(8). This automorphism group permutes the three 8-dimensional irreducible representations of Spin(8); these being the vector representation and two chiral spin representations. These automorphisms do not project to automorphisms of SO(8). The vector representation—the natural action of SO(8) (hence Spin(8)) on $F^{8}$—consists over the real numbers of Euclidean 8-vectors and is generally known as the "defining module", while the chiral spin representations are also known as "half-spin representations", and all three of these are fundamental representations.

No other connected Dynkin diagram has an automorphism group of order greater than 2; for other Dn (corresponding to other even Spin groups, Spin(2n)), there is still the automorphism corresponding to switching the two half-spin representations, but these are not isomorphic to the vector representation.

Roughly speaking, symmetries of the Dynkin diagram lead to automorphisms of the Tits building associated with the group. For special linear groups, one obtains projective duality. For Spin(8), one finds a curious phenomenon involving 1-, 2-, and 4-dimensional subspaces of 8-dimensional space, historically known as "geometric triality".

The exceptional 3-fold symmetry of the D4 diagram also gives rise to the Steinberg group 3D4.

General formulation
A duality between two vector spaces over a field $F$ is a non-degenerate bilinear form
 * $$ V_1\times V_2\to F,$$

i.e., for each non-zero vector $v$ in one of the two vector spaces, the pairing with $v$ is a non-zero linear functional on the other.

Similarly, a triality between three vector spaces over a field $F$ is a non-degenerate trilinear form
 * $$ V_1\times V_2\times V_3\to F,$$

i.e., each non-zero vector in one of the three vector spaces induces a duality between the other two.

By choosing vectors $e_{i}$ in each $V_{i}$ on which the trilinear form evaluates to 1, we find that the three vector spaces are all isomorphic to each other, and to their duals. Denoting this common vector space by $V$, the triality may be re-expressed as a bilinear multiplication
 * $$ V \times V \to V$$

where each $e_{i}$ corresponds to the identity element in $V$. The non-degeneracy condition now implies that $V$ is a composition algebra. It follows that $V$ has dimension 1, 2, 4 or 8. If further $F = R$ and the form used to identify $V$ with its dual is positively definite, then $V$ is a Euclidean Hurwitz algebra, and is therefore isomorphic to R, C, H or O.

Conversely, composition algebras immediately give rise to trialities by taking each $V_{i}$ equal to the algebra, and contracting the multiplication with the inner product on the algebra to make a trilinear form.

An alternative construction of trialities uses spinors in dimensions 1, 2, 4 and 8. The eight-dimensional case corresponds to the triality property of Spin(8).

title: Triality


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Morinda citrifolia

Morinda citrifolia is a fruit-bearing tree in the coffee family, Rubiaceae, native to Southeast Asia and Australasia, which was spread across the Pacific by Polynesian sailors. The species is now cultivated throughout the tropics and widely naturalised. There are over 100 names for this fruit across different regions, including great morinda, Indian mulberry, noni, beach mulberry, vomit fruit, awl tree, and rotten cheese fruit.

The pungent odour of the fresh fruit has made it a famine food in most regions, but it remains a staple food among some cultures and is used in traditional medicine. In the consumer market, dietary supplements are sold in various formats, such as capsules and juices.

Common names

 * Chinese: Hai ba ji, Wu ning (Singapore), Luo ling (Singapore, Taiwan)
 * Cook Islands, Niue, Samoa, Tonga: Nonu, noni, nenu, nano, nonu atoni, gogu atoni
 * English, Tahiti: Canary wood (Australia), Indian mulberry, Large-leaved Morinda, Noni (Hawaii), Noni fruit, Noni plant, Pain killer tree (Caribbean), Pain Bush, Pain Killer Bush
 * Fiji: Kura
 * Flores island: keloré (in Lamalera)
 * French: Nono (Tahiti)
 * Federated States of Micronesia: Nen (lagoon Chuukese), Weipwul (Pohnpei), Ii (Kosrae), Mangalweg (Yap), Nopur (Chuuk)
 * Guam, Northern Marianas: Lada, Ladda
 * Kiribati: Non
 * Marshall Islands: Nen, nin
 * Malay: Bengkudu, Bengkudu daun besar, Bengkudu laki-laki, Mengkudu (Indonesia), Pacel (Indonesia), Mengkoedoe, Mengkudi, Mengkudi Besar, Mengkudu besar, menkudu
 * Palau: Kesengel, lel, ngel
 * Rotuma: Ura
 * Spanish: Mora de la India, Noni (Puerto Rico)
 * Tamil: Munja pavattay
 * Telugu: Maddi chettu, Molagha

 * Some other names

 * awl tree
 * Ba Ji Tian
 * Ach
 * Baga
 * Bangkoro
 * Bilimbi
 * Boi Doieur
 * brimstone tree
 * Bumbo
 * Bungbo
 * Bunuela
 * Canoe Plant
 * Cheese fruit, Cheesefruit
 * Coca
 * Doleur
 * Feuille Douleur
 * Dye Tree
 * Feuille Froide
 * Forbidden Fruit
 * Fromagier
 * Gardenia Hediona
 * Grand morinda
 * Great morinda
 * Headache Tree
 * Hog Apple
 * Huevo de Reuma
 * inda
 * Leichhardt´s Tree
 * Limburger Tree
 * Mirier de Java
 * Mona
 * Monii
 * Nhàu
 * Nhàu Lớn
 * Nhàu Núi
 * Nho
 * Nhor Preyu
 * Nhor Thom
 * Nigua
 * Nino
 * Nona
 * Nuna
 * Nony
 * Och
 * Pina de Puerco
 * Pinuela
 * Pomme Macaque
 * Rubarbe Caraibe
 * Ruibarbo Caribe
 * Togari Wood
 * Urati
 * Wild Pine
 * Yor Ban

Description
Morinda citrifolia is a shrub or small tree up to 6 m tall, with grey-brown bark. The twigs are more or less square in cross-section and often fleshy. Stipules are present, very broad and obtuse at the apex, measuring up to 2 cm wide and long. The large leaves are arranged in opposite pairs on the twigs, reaching up to 25 cm long by 13 cm wide. They are elliptic to ovate in shape and have 6–9 pairs of lateral veins. Domatia are usually present as dense tufts of hairs in the junctions of the lateral veins with the midrib.

The inflorescences are dense heads of flowers produced at the apex of the branch. They are leaf-opposed, replacing one leaf in the pair. There may be up to 90–100 flowers in the head, but only a few open at a time. The flowers are white and tubular with five lobes, measuring about 15 cm long and across.

The fruit is a multiple fruit consisting of fused drupes, each containing four seeds. They are initially green, transitioning through pale yellow to white or grey, and when ripe they emit a pungent odour similar to blue cheese. They are irregularly ellipsoid or ovoid, and may reach up to 9x6 cm.

Phenology
The plants flower and fruit throughout the year. It is common to see flowers and fruit in varying stages of development on a plant at any given time.

Growing habitats
Morinda citrifolia grows in shady forests and on open rocky or sandy shores. It takes 18 months for the plant to mature, and yields 4 and 8 kg of fruit per month throughout the year. It is tolerant of saline soils, drought conditions, and secondary soils. It can be found in various environments including volcanic terrains and clearings or limestone outcrops, as well as in coral atolls. It can grow up to 9 m tall and has large, simple, dark green, shiny, and deeply veined leaves.

Ecology
Morinda citrifolia is attractive to weaver ants, which make their nests by using the leaves of this tree. These ants protect the plant from some plant-parasitic insects. The smell of the fruit also attracts fruit bats, which aid in dispersing the seeds. Drosophila sechellia, a type of fruit fly endemic to the Seychelles, feeds exclusively on these fruits.

Uses
A variety of beverages (juice drinks), powders (from dried ripe or unripe fruits), cosmetic products (lotions, soaps), oil (from seeds), and leaf powders (for encapsulation or pills) have been introduced into the consumer market.

Culinary
Indigenous peoples used the fruit as emergency food during famines. Therefore, it is also called "starvation fruit". Despite its strong smell and bitter taste, the fruit was nevertheless eaten as a famine food, and, in some Pacific Islands, even as a staple food, either raw or cooked. Southeast Asians and Aboriginal Australians consume fresh fruit with salt or cook it with curry. The seeds are edible when roasted. In Thai cuisine, the leaves known as bai-yo are used as a leaf vegetable and are the main ingredient of Kaeng bai-yo, cooked with coconut milk. The fruit luk-yo is added as a salad ingredient to some versions of green papaya salad.

In Cambodia, the leaves are an essential part of the national dish fish amok.

Traditional medicine
Green fruit, leaves, and root or rhizomes might have been used in Polynesian cultures as a general tonic, in addition to its traditional place in Polynesian culture as a famine food. Although Morinda is considered to have biological properties in traditional medicine, there is no confirmed evidence of clinical efficacy for any intended use. In 2018, a Hawaiian manufacturer of food and skincare products based on this fruit was issued an FDA warning letter for marketing unapproved drugs and making false health claims in violation of the US Food, Drug, and Cosmetic Act.

Dyes
The fruit has traditionally been used by Austronesian peoples mainly for producing dyes. It was carried into the Pacific Islands as canoe plants by Austronesian voyagers. Morinda bark produces a brownish-purplish dye that may be used for making batik. In Hawaii, yellowish dye is extracted from its roots to dye cloth. Yolngu artists at Bula'Bula Arts in Ramingining, in central Arnhem Land in the Northern Territory, Australia, use the roots and bark of djundom, as it is known to them, to dye the fibres of pandanus to create a wide variety of artifacts.

Applying a mordant to the fabric before dyeing is necessary when using extracts of this plant as a dye. This process can be labor-intensive if the goal is to achieve shades and hues with the morinda dye.

Nutrients and phytochemicals
Morinda citrifolia fruit powder contains carbohydrates and dietary fibre in moderate amounts. These macronutrients reside in the fruit pulp, as M. citrifolia juice has sparse nutrient content. The main micronutrients of M. citrifolia pulp powder include vitamin C, vitamin B3), iron, and potassium. Vitamin A, calcium, and sodium are present in moderate amounts. Compared to powdered pulp, only vitamin C is retained in the analysis of M. citrifolia juice. The juice contains 34 mg of vitamin C per 100 g, which is 64% of the amount found in a raw navel orange (53 mg per 100 g of orange, or 89% of the Daily Value). Sodium levels in M. citrifolia juice (about 3% of Dietary Reference Intake, DRI) are high compared to an orange, while potassium content is moderate.

Morinda citrifolia fruit contains several phytochemicals, including lignans, oligo- and polysaccharides, flavonoids, iridoids such as deacetylasperulosidic acid, fatty acids, scopoletin, catechin, beta-sitosterol, damnacanthal, and alkaloids.

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

title: Morinda citrifolia


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Hvítá (Árnessýsla)

Hvítá (Icelandic, "white river") is a river in Iceland that begins at Hvítárvatn glacier lake on Langjökull glacier in the highlands of Iceland at 64.61667°N, -19.83333°W. The river flows for 40 km before dropping down into a narrow gorge at Gullfoss waterfall.

Thereafter, the river flows between Biskupstungur and Hrunamannahreppur districts. Here, Hvítá combines with three other rivers: Tungufljót, Brúará, and Stóra-Laxá , doubling the volume of the river. It proceeds to run through the flatlands near Grímsnes and behind Ingólfsfjall mountain. Just north of Selfoss town, it meets Sog River where it becomes Ölfusá as it flows into the Atlantic Ocean.

Because of danger of flooding, especially during winter, Hvítá has a reputation of being the most dangerous river in Iceland.

Organised rafting excursions take place on parts of the river. The river is bridged at 4 locations, thrice at the lowland and once near the source in the highland where it is only open over the summer.

title: Hvítá (Árnessýsla)


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Midget car racing

Midget cars, also speedcars in Australia, is a class of racing cars. The cars are very small with a very high power-to-weight ratio and typically use four cylinder engines. They originated in the United States in the 1930s and are raced on most continents. There is a worldwide tour and national midget tours in the United States, Australia, Argentina and New Zealand.

Cars
Typically, these four-cylinder-engine cars have 300 hp to 400 hp and weigh 900 lb. The high power and small size of the cars combine to make midget racing quite dangerous; for this reason, modern midget cars are fully equipped with roll cages and other safety features. Some early major midget car manufacturers include Kurtis Kraft (1930s to 1950s) and Solar (1944–46). Midgets are intended to be driven for races of relatively short distances, usually 2.5 to 25 miles (4 to 40 km). Some events are staged inside arenas, like the Chili Bowl held in early January at the Tulsa Expo Center in Tulsa, Oklahoma. There are midget races in dirt track racing and in asphalt (paved tracks).

There are three-quarter (TQ) midgets which developed from "midget midget" cars of the late 1940s. Quarter midgets are one-quarter the size of a full midget car.

History
The first organized Midget car race happened on June 4, 1933. The sports' first regular weekly program began on August 10, 1933 at the Loyola High School Stadium in Los Angeles under the control of the first official governing body, the Midget Auto Racing Association (MARA). After spreading across the country, the sport traveled around the world; first to Australia in 1934 at Melbourne's Olympic Park on December 15, and to New Zealand in 1937. Early midget races were held on board tracks previously used for bicycle racing. When the purpose-built speedway at Gilmore Stadium was completed, racing ended at the school stadium, and hundreds of tracks began to spring up across the United States. Angell Park Speedway in Sun Prairie, Wisconsin (near Madison) is another major track in the United States operating since the first half of the twentieth century.

The AAA Contest Board soon started sanctioning midget races across the country, facing opposition from independent drivers and racetracks. After the AAA withdrew from sanctioning races in 1955, the United States Auto Club took over as the major sanctioning body of midget car racing in the United States. NASCAR had a midget division from 1952 to 1968.

Soon after in Australia, speedcar racing became popular with the first Australian Speedcar Championship being contested in Melbourne in 1935, its popularity running through the country's "golden era" of the 1950s and 1960s. Australian promoters such as Adelaide's Kym Bonython who ran the Rowley Park Speedway, and Empire Speedways who ran the Brisbane Exhibition Ground and the famous Sydney Showground Speedway, often imported drivers from the US, such as the popular Jimmy Davies. Promoters in Australia during this period often staged races billed as either a "world speedcar championship" or "world speedcar derby". During this time speedcars were arguably the most popular category in Australian speedway with crowds of up to 30,000 attending meetings at the Sydney Showground and over 10,000 in Adelaide and Brisbane.

Speedcars continue to race in Australia, with the major events being the Australian Championship, and the Australian Speedcar Grand Prix (first run in 1938). Along with various state championships, there is also the Speedcar Super Series which travels throughout Australia. Speedcar crowds of 10,000 people are common in Australia for these major events.

In December 2013, POWRi Midget Racing began a 16-event Lucas Oil POWRi Midget World Championship that ran until June 2014. Drivers competed in New Zealand and Australia at the beginning of the 2013–14 season and ended in the United States.

Midget car racing also grew in popularity in the Northeast of the United States, in part due to racers like Bill Schindler and events at tracks like that at Hinchcliffe Stadium.

Stepping stone to high profile divisions

Many IndyCar and NASCAR drivers use midget car racing as an intermediate stepping stone on their way to more high-profile divisions, including Tony Stewart, Sarah Fisher, Rodger Ward, A. J. Foyt, Mario Andretti, Johnnie Parsons, Ryan Newman, Kyle Larson, Jeff Gordon, Christopher Bell, Bill Vukovich, and others. Events are sometimes held on weeknights so that popular and famous drivers from other, higher-profiled types of motor racing (who race in those higher-profiled types of racing on the weekends) will be available to compete, and so that it does not conflict with drivers' home tracks.

Notable midget car races
In 1959, Lime Rock Park held a famous Formula Libre race, where Rodger Ward shocked the expensive and exotic sports cars by beating them on the road course in an Offenhauser powered midget car, usually used on oval tracks. Ward used an advantageous power-to-weight ratio and dirt-track cornering abilities to steal the win.

Notable annual midget car racing events

 * Chili Bowl – Tulsa Expo Center, Tulsa, Oklahoma
 * Fireman Nationals – Angell Park Speedway, Sun Prairie, Wisconsin
 * Four Crown Nationals – Eldora Speedway, Allen Township, Darke County, Ohio
 * Hut Hundred – Terre Haute Action Track, Terre Haute, Indiana
 * Bryan Clauson Classic - Indianapolis Motor Speedway, Speedway, Indiana
 * Night before the 500 – O'Reilly Raceway Park, Indianapolis, Indiana
 * The Rumble in Fort Wayne – Allen County War Memorial Coliseum Expo Center, Fort Wayne, Indiana
 * Turkey Night Grand Prix – Ventura Raceway, Irwindale Speedway
 * World 50-lap Classic – Western Springs Stadium, Auckland, New Zealand
 * New Zealand Midget Championship – Rotates on various tracks throughout New Zealand
 * Australian Speedcar Championship – Rotates on various tracks throughout Australia
 * Australian Speedcar Grand Prix – Rotates between tracks throughout eastern Australia
 * Magic Man 34 – Perth Motorplex Speedway, Kwinana Beach, Western Australia
 * Tim Crouch Memorial – Murray Bridge Speedway, Murray Bridge, South Australia
 * Boston Louie Memorial – Seekonk Speedway, Seekonk, Massachusetts
 * Ryan Stone Memorial - Ruapuna Speedway, Christchurch, New Zealand

Australia

 * SpeedcarsAustralia.com – Official website of Australia's Speedcar governing body, Speedcars Australia Inc
 * QSRA – Queensland Speedcar Racing Assos. official website
 * SAspeedcars.com – South Australian Speedcar Association (covers South Australia & the Northern Territory)
 * V.S.D.A – Victorian Speedcar Drivers Association Inc
 * wasda.com.au – Western Australian Speedcar Drivers Association (Perth Club)
 * Speedcar Association of NSW (Sydney Club)
 * 50 Lap Speedcar Classic, Valvoline Raceway/Sydney Speedway, New South Wales, Australia

New Zealand

 * Speedway New Zealand
 * New Zealand Speedway Directory Links to New Zealand Speedway Websites
 * Macgors NZ Speedway

United Kingdom

 * Grand Prix Midget Club

United States

 * National
 * USAC – USAC National Midget Series
 * POWRi – POWRi Midget Series

 * Regional
 * BMARA – Badger Midget Auto Racing Association (the oldest sanctioning body)
 * POWRi West Lucas Oil Midget Series
 * AMRA – Arizona Midget Racing Association
 * ARDC – American Racing Drivers Club
 * BCRA – Bay Cities Racing Association (co-sanction with POWRi since 2019)
 * NEMA – Northeastern Midget Association
 * American Three Quarter Midget Racing Association
 * STARS– Short Track Auto Racing Series
 * RMMRA – Rocky Mountain Midget Racing Association
 * SMRS – Southern Midget Racing Series
 * IRS – Illini Racing Series
 * USSA – United States Speed Association
 * WMRA – Washington Midget Racing Association
 * SMMS Southern States Midget Series
 * Northwest Focus Midget Series

title: Midget car racing


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Vysočina Region

The Vysočina Region (Kraj Vysočina) is an administrative unit (kraj) of the Czech Republic. Its capital is Jihlava.

The region is located in the central part of the country. It is one of just three in the country (the others being Prague and the Central Bohemian Region) which does not have a border with a foreign country.

The Vysočina Region is home to three UNESCO World Heritage Sites, the most in any region in the Czech Republic.

Administrative divisions
The Vysočina Region is divided into 5 districts:

On a lower level, the region has 704 municipalities, second-most in the country behind the Central Bohemian Region.

Geography
The region is located in the central part of the Czech Republic, partly in the southeast of the historical region of Bohemia and partly in the southwest of the historical region of Moravia. The entire Vysočina Region is located in the nature region of Bohemian-Moravian Highlands, from whose colloquial name vysočina (meaning "the highlands") the region got its name. Within the country, the region has a relatively high altitude and is the source of many rivers. The most important rivers are the Sázava, Jihlava, Svratka and Oslava.

Population
As of 1 January 2024 the population of the Vysočina Region was 517,960, which was the third lowest out of regions in the Czech Republic. 49.7% of population were men, which was the highest share in the Czech Republic. The density of Vysočina Region is the second lowest in the Czech Republic (75 inhabitants per km2).

The table shows cities and towns in the region with the largest population (as of 1 January 2024):

Culture

With three UNESCO World Heritage Sites, the region is home to more of these than any other region of the Czech Republic. These are the historical centre of Telč, the Pilgrimage Church of Saint John of Nepomuk in Žďár nad Sázavou and the Jewish Quarter and St Procopius' Basilica in Třebíč.

Transport
The Vysočina Region is intersected by the D1 motorway, which passes through Jihlava on the way between Prague and Brno. A total of 93 km of motorway is present in the region. The length of operated railway lines in the region is 622 km. In 2014 a plan was announced by which a high-speed train, capable of reaching speeds of 350 km/h would run through the region, involving a total of four stops within the territory. Construction is projected to begin in 2025.

Education
In the Vysočina Region there are two organisations providing further education, namely College of Polytechnics Jihlava

title: Vysočina Region


text:
SO(8)

In mathematics, SO(8) is the special orthogonal group acting on eight-dimensional Euclidean space. It could be either a real or complex simple Lie group of rank 4 and dimension 28.

Spin(8)
Like all special orthogonal groups of $$n > 2$$, SO(8) is not simply connected, having a fundamental group isomorphic to Z2. The universal cover of SO(8) is the spin group Spin(8).

Center
The center of SO(8) is Z2, the diagonal matrices {±I} (as for all SO(2n) with 2n ≥ 4), while the center of Spin(8) is Z2×Z2 (as for all Spin(4n), 4n ≥ 4).

Triality
SO(8) is unique among the simple Lie groups in that its Dynkin diagram, (D4 under the Dynkin classification), possesses a three-fold symmetry. This gives rise to peculiar feature of Spin(8) known as triality. Related to this is the fact that the two spinor representations, as well as the fundamental vector representation, of Spin(8) are all eight-dimensional (for all other spin groups the spinor representation is either smaller or larger than the vector representation). The triality automorphism of Spin(8) lives in the outer automorphism group of Spin(8) which is isomorphic to the symmetric group S3 that permutes these three representations. The automorphism group acts on the center Z2 x Z2 (which also has automorphism group isomorphic to S3 which may also be considered as the general linear group over the finite field with two elements, S3 ≅GL(2,2)). When one quotients Spin(8) by one central Z2, breaking this symmetry and obtaining SO(8), the remaining outer automorphism group is only Z2. The triality symmetry acts again on the further quotient SO(8)/Z2.

Sometimes Spin(8) appears naturally in an "enlarged" form, as the automorphism group of Spin(8), which breaks up as a semidirect product: Aut(Spin(8)) ≅ PSO (8) ⋊ S3.

Unit octonions
Elements of SO(8) can be described with unit octonions, analogously to how elements of SO(2) can be described with unit complex numbers and elements of SO(4) can be described with unit quaternions. However the relationship is more complicated, partly due to the non-associativity of the octonions. A general element in SO(8) can be described as the product of 7 left-multiplications, 7 right-multiplications and also 7 bimultiplications by unit octonions (a bimultiplication being the composition of a left-multiplication and a right-multiplication by the same octonion and is unambiguously defined due to octonions obeying the Moufang identities).

It can be shown that an element of SO(8) can be constructed with bimultiplications, by first showing that pairs of reflections through the origin in 8-dimensional space correspond to pairs of bimultiplications by unit octonions. The triality automorphism of Spin(8) described below provides similar constructions with left multiplications and right multiplications.

Octonions and triality
If $$x,y,z\in\mathbb{O}$$ and $$(xy)z=1$$, it can be shown that this is equivalent to $$x(yz)=1$$, meaning that $$xyz=1$$ without ambiguity. A triple of maps $$(\alpha,\beta,\gamma)$$ that preserve this identity, so that $$x^\alpha y^\beta z^\gamma=1$$ is called an isotopy. If the three maps of an isotopy are in $$\operatorname{SO(8)}$$, the isotopy is called an orthogonal isotopy. If $$\gamma\in \operatorname{SO(8)}$$, then following the above $$\gamma$$ can be described as the product of bimultiplications of unit octonions, say $$\gamma=B_{u_1}...B_{u_n}$$. Let $$\alpha,\beta \in \operatorname{SO(8)}$$ be the corresponding products of left and right multiplications by the conjugates (i.e., the multiplicative inverses) of the same unit octonions, so $$\alpha=L_{\overline{u_1}}...L_{\overline{u_n}}$$, $$\beta=R_{\overline{u_1}}...R_{\overline{u_n}}$$. A simple calculation shows that $$(\alpha,\beta,\gamma)$$ is an isotopy. As a result of the non-associativity of the octonions, the only other orthogonal isotopy for $$\gamma$$ is $$(-\alpha,-\beta,\gamma)$$. As the set of orthogonal isotopies produce a 2-to-1 cover of $$\operatorname{SO}(8)$$, they must in fact be $$\operatorname{Spin}(8)$$.

Multiplicative inverses of octonions are two-sided, which means that $$xyz=1$$ is equivalent to $$yzx=1$$. This means that a given isotopy $$(\alpha,\beta,\gamma)$$ can be permuted cyclically to give two further isotopies $$(\beta,\gamma,\alpha)$$ and $$(\gamma,\alpha,\beta)$$. This produces an order 3 outer automorphism of $$\operatorname{Spin}(8)$$. This "triality" automorphism is exceptional among spin groups. There is no triality automorphism of $$\operatorname{SO}(8)$$, as for a given $$\gamma$$ the corresponding maps $$\alpha,\beta$$ are only uniquely determined up to sign.

Root system

 * $$(\pm 1,\pm 1,0,0)$$
 * $$(\pm 1,0,\pm 1,0)$$
 * $$(\pm 1,0,0,\pm 1)$$
 * $$(0,\pm 1,\pm 1,0)$$
 * $$(0,\pm 1,0,\pm 1)$$
 * $$(0,0,\pm 1,\pm 1)$$

Weyl group
Its Weyl/Coxeter group has 4! × 8 = 192 elements.

Cartan matrix

\begin{pmatrix} 2 & -1 & -1 & -1\\ -1 &  2 &  0 &  0\\ -1 &  0 &  2 &  0\\ -1 &  0 &  0 &  2 \end{pmatrix} $$

title: SO(8)


text:
Bambi

Bambi is a 1942 American animated drama film produced by Walt Disney Productions and released by RKO Radio Pictures. Loosely based on Felix Salten's 1923 novel Bambi, a Life in the Woods, the production was supervised by David D. Hand, and was directed by a team of sequence directors, including James Algar, Bill Roberts, Norman Wright, Sam Armstrong, Paul Satterfield, and Graham Heid.

The main characters are Bambi, a white-tailed deer; his parents (the Great Prince of the forest and his unnamed mother); his friends Thumper (a pink-nosed rabbit); and Flower (a skunk); and his childhood friend and future mate, Faline. In the original book, Bambi was a roe deer, a species native to Europe; but Disney decided to base the character on a mule deer from Arrowhead, California. Illustrator Maurice "Jake" Day convinced Disney that the mule deer had large "mule-like" ears and were more common to western North America; but that the white-tail deer was more recognized throughout America.

The film received three Academy Award nominations: Best Sound (Sam Slyfield), Best Song (for "Love Is a Song" sung by Donald Novis) and Original Music Score.

In June 2008, the American Film Institute presented a list of its "10 Top 10"—the best ten films in each of ten classic American film genres—after polling over 1,500 people from the creative community. Bambi placed third in animation. In December 2011, the film was added to the National Film Registry of the Library of Congress as being "culturally, historically and aesthetically significant".

In January 2020, it was announced that a photorealistic computer-animated remake was in development.

Plot
In a Maine forest, a doe gives birth to a male fawn named Bambi, who will one day take over the position of Great Prince of the Forest, who guards the woodland creatures. Bambi grows up very attached to his mother, with whom he spends most of his time. The fawn is befriended by an eager, energetic male rabbit named Thumper, who helps to teach him to walk and speak, a young male skunk he mistakenly calls "Flower" (who is so flattered, he keeps the name) and a female fawn named Faline. Curious and inquisitive, Bambi frequently asks about the world around him and is cautioned about the dangers of life as a forest creature by his loving mother. One day out in a meadow, Bambi briefly sees the Great Prince but does not realize that he is his father. As the Great Prince wanders uphill, he discovers the human hunter, named "Man" by all the animals, is coming and rushes down to the meadow to get everyone to safety. Bambi is briefly separated from his mother during that time but is escorted to her by the Great Prince as the three of them make it back in the forest just as Man fires his gun.

During Bambi's first winter, he and Thumper play in the snow while Flower hibernates. One day his mother takes him to find food when Man shows up again. As they run off, his mother is shot and killed by the hunter, leaving the little fawn mournful and alone. Taking pity on his abandoned son, the Great Prince leads Bambi home as he reveals to him that he is his father. Next year, Bambi has matured into a young stag, and his childhood friends have also entered young adulthood. They are warned about becoming "twitterpated" by Friend Owl and that they will eventually fall in love, but the trio views the concept of romance with scorn. Thumper and Flower soon encounter their beautiful romantic counterparts and abandon their former thoughts on love. Bambi himself encounters Faline as a beautiful doe. Their courtship is quickly interrupted by a belligerent older stag named Ronno, who attempts to force Faline away from Bambi. Bambi successfully manages to defeat Ronno in battle and earn the rights to the doe's affections.

Bambi is awakened afterward by the smell of smoke; he follows it and discovers it leads to a hunter camp. His father warns Bambi that Man has returned with more hunters. Bambi is separated from Faline in the turmoil, but finds her cornered by Man's vicious hunting dogs, which he manages to ward off. Bambi escapes them and is shot by Man, but survives. Meanwhile, at the "Man's" camp, their campfire suddenly spreads into the forest, resulting in a wildfire from which the forest residents flee in fear. Bambi, his father, Faline, and the forest animals manage to reach shelter on a riverbank. The following spring, Faline gives birth to twins under Bambi's watchful eye as the new Great Prince of the Forest.

Voice cast
The voice cast was all uncredited, as was the practice at the time for many animated films.

 * Donnie Dunagan as Bambi, the film's title character and protagonist
 * Bobby Stewart as Baby Bambi
 * Hardie Albright as Adolescent Bambi
 * John Sutherland as Adult Bambi
 * Peter Behn as Thumper, a rabbit friend of Bambi's
 * Tim Davis as Adolescent Thumper
 * Sam Edwards as Young Adult Thumper
 * Paula Winslowe as Bambi's Mother and the Pheasant
 * Stan Alexander as Flower, a striped skunk and another friend of Bambi's
 * Tim Davis as Adolescent Flower
 * Sterling Holloway as Young Adult Flower
 * Will Wright as Friend Owl
 * Cammie King as Faline, a female deer whom Bambi eventually falls in love with
 * Ann Gillis as Adult Faline
 * Fred Shields as the Great Prince of the Forest
 * Margaret Lee as Mrs. Rabbit
 * Mary Lansing as Aunt Ena and Mrs. Possum
 * Perce Pearce as Mr. Mole
 * Thelma Boardman as Girl Bunny, Quail Mother, Female Pheasant

Development
In 1933, Sidney Franklin purchased the rights to Felix Salten's novel Bambi, a Life in the Woods (1923) to produce a live-action film for Metro-Goldwyn-Mayer, but soon realized that it would be too difficult to achieve. Joseph M. Schenck of United Artists suggested him to make an animated version in alliance with Walt Disney, who was contemplating the idea of his first full-length feature at the time, with Bambi as one of the possible choices. Later that year, Franklin approached him with the idea, but Disney eventually refused, feeling that his animation studio was unprepared for the technical difficulties that Bambi would have presented. Franklin sold the film rights to Walt Disney in April 1937. Disney began work on crafting an animated adaptation immediately, intending it to be the company's second feature-length animated film and their first to be based on a specific, recent work. However, the original novel was written for an adult audience, and was considered too "grim" and "somber" for a regular light-hearted Disney film. The artists also discovered that it would be challenging to animate deer realistically. These difficulties resulted in Disney putting production on hold while the studio worked on several other projects, and eventually Pinocchio became the studio's second film. In 1938, Disney assigned Perce Pearce and Carl Fallberg to work on the film's storyboards, but attention was soon drawn away as the studio began working on Fantasia. Finally, on August 17, 1939, production on Bambi began in earnest, but progressed slowly owing to changes in the studio personnel, location, and methodology of handling animation at the time.

Writing
There were many interpretations of the story. As writer and animator Mel Shaw recalled: The story of Bambi had a so many possibilities, you could go off on a million tangents. I remember one situation when Walt became involved with himself. He said 'Suppose we have Bambi step on an ant hill and we cut inside and see all the damage he's done to the ant civilization'. We spent weeks and weeks developing the ants, and then all of a sudden we decided, you know, we're way off the story, this has got nothing to do with the story of Bambi. We also had a family of grasshoppers, and they get into a family squabble of this or that, and Bambi is watching all of this, and here's the big head of Bambi in the grasshoppers. And what's that got to do with the story, and this would go on many times.

Originally the film was intended to have six individual bunny characters, similar to the dwarfs in Snow White. However Perce Pearce suggested that they could instead have five generic rabbits and one rabbit with a different color than the rest, with one tooth, would have a very distinct personality. This character later became known as Thumper.

There originally was a brief shot in the scene where Bambi's mother dies after jumping over a log and getting shot by a man. Larry Morey, however, felt the scene was too dramatic, and that it was emotional enough to justify having her death occur off screen. Walt Disney was also eager to show the man burned to death by his fire that he inadvertently started, but this was discarded when it was decided not to show the man at all. There was also a scene involving two autumn leaves conversing like an old married couple before parting ways and falling to the ground, but Disney found that talking flora did not work in the context of the film, and instead a visual metaphor of two realistic leaves falling to the ground was used instead. Disney and his story team also developed the characters consisting of a squirrel and a chipmunk that were to be a comic duo reminiscent of Laurel and Hardy. However, after years of experimentation, Walt felt that the story should focus on the three principal characters: Bambi, Thumper and Flower. The squirrel and chipmunk make only brief appearances in the final film.

The writing was completed in July 1940, by which time the film's budget had increased to $858,000.

Animation
Although the animators had animated deer in Snow White, they were animated, in the words of Eric Larson, "like big flour sacks". Disney wanted the animals in Bambi to be more realistic and expressive than those in Snow White. He had Rico LeBrun, a painter of animals, come and lecture to the animators on the structure and movement of animals. The animators visited the Los Angeles Zoo and Disney set up a small zoo at the studio with animals such as rabbits, ducks, owls, and skunks, and a pair of fawns named Bambi and Faline so that the artists could see first-hand the movement of these animals. LeBrun's sketches depicted realistic animals, but as characters they lacked personality. Marc Davis created the final design of Bambi by incorporating LeBrun's realistic study of deer anatomy but exaggerating the character's face by making his proportions baby-like (short snout, big eyes, etc.). Although there were no humans in Bambi, live-action footage of humans was used for one scene: actress Jane Randolph and Ice Capades star Donna Atwood acted as live-action references for the scene where Bambi and Thumper are on the icy pond. The animators learned a lot about animals during the film's production, giving them a broader spectrum of animation styles to use in future projects.

The backgrounds for the film were inspired by the Eastern American woodlands. One of the earliest and best-known artists for the Disney studio, Maurice "Jake" Day, spent several weeks in the Vermont and Maine forests, sketching and photographing deer, fawns, and the surrounding wilderness areas. However his first sketches were too "busy" as the eye did not know where to focus. Tyrus Wong, a Chinese animator, showed Day some of his impressionistic paintings of a forest. Day liked the paintings and appointed him art director of the film. Wong's backgrounds were revolutionary since they had more detail around the center and less around the edges, thus leading a viewer's eye to the characters.

Due to World War II, which began in Europe in 1939, Pinocchio and Fantasia failed at the box office. Facing financial difficulty, Disney was forced to cut 12 minutes from the film before final animation to save production costs.

Original theatrical run
Bambi premiered in London on August 8, 1942, as the first Disney film to premiere abroad. It was released in theaters in United States five days later, on August 13. The film was released during World War II and did not perform as well as hoped. Roy O. Disney sent a telegram to his brother Walt after the New York opening of the film that read: "Fell short of our holdover figure by $4,000. Just came from Music Hall. Unable to make any deal to stay third week ... Night business is our problem." The film earned RKO theatrical rentals of $1,270,000 in the United States and Canada in its initial release.

Disney lacked access to much of the European market during the war, however, the film earned rentals of $1,685,000 internationally for an initial worldwide total of $2,955,000, Disney's third highest, behind Snow White and the Seven Dwarfs (1937) with $7.8 million and Pinocchio (1940) with $3.2 million.

Re-releases
The film was re-released to theatres in the United States in 1947, 1957, 1966, 1975, 1982 and 1988. In its first reissue in the United States in 1947, the film earned additional domestic rentals of $900,000 but did much better 10 years later, more than doubling the domestic rental total with a further $2.5 million taking its total domestic rental earnings to $4.7 million.

The film earned $14 million in domestic rentals from its reissues in 1966 and 1975 giving it a total domestic rental of $18,735,000, which equates to a gross of around $40 million. In 1982, it grossed another $23 million in the United States and Canada and in 1988, a further $39 million, taking its total in the United States and Canada to $102 million, making it (at the time) the second highest-grossing animated movie of all-time after Snow White and the Seven Dwarfs. With grosses from international reissues, the film has a worldwide gross of $267 million.

Home media
Prior to Bambi's initial release on home video on September 28, 1989, initial orders placed in the United States and Canada up to the end of August totaled 9.8 million units, the second largest number of orders for a video at the time, behind E.T. the Extra-Terrestrial, with a wholesale value of $167 million. Even in home video, it has seen multiple releases, including three VHS releases — in 1989 (Classics Version), 1997 (Masterpiece Collection Version), and 2005 (Platinum Edition version), one Betamax release in 1989 (Classics version), two Laserdisc releases in 1989 (Classics version) and 1997 (Masterpiece Collection version). In 2005, a digitally remastered and restored Platinum Edition DVD was released; it went on moratorium on January 31, 2007.

Bambi was released as a Diamond Edition on March 1, 2011, consisting of a Blu-ray and DVD combo pack. This release included multiple bonus features not previously included in Bambi home releases: a documentary entitled Inside Walt's Story Meetings – Enhanced Edition, two deleted scenes, a deleted song, an image gallery, and a game entitled Disney's Big Book of Knowledge: Bambi Edition. This release also marked the first use of "Disney Second Screen", a feature which is accessed via a computer or iPad app download that syncs with the Blu-ray disc, allowing the viewer to follow along by interacting with animated flip-books, galleries and trivia while watching the movie. A UK version of Diamond Edition was released on February 7, 2011.

In honor of the film's 75th anniversary, Bambi was released as part of the Walt Disney Signature Collection on May 23, 2017 (digital) and June 6, 2017 (Blu-ray/DVD/digital combo pack).

On August 18, 2023, Bambi was re-released in cinemas across the UK only for one week as part of Disney's 100th anniversary.

Localization
On the initiative of Stephen Greymoming, professor of Native American studies and anthropology at the University of Montana, an Arapaho-language dubbing of the movie was produced in 1994, in collaboration with the Northern Plains Educational Foundation. The final product was, however, only a partial dubbing, as the spoken parts were dubbed in Arapaho, but all the songs were left in English. The dubbed version of the movie premiered on November 3 the same year, and Disney later provided the Arapaho Nation with 2000 VHS tapes of the movie. The dubbing was never issued again in any other forms, until it was uploaded on the streaming platform Disney+ in October 2022. Bambi was the first of three Disney movies to receive a dubbing in a Native American language. The next such instance had to wait until 2016, when Pixar's Finding Nemo received a dubbing in Navajo, and then Disney's Moana in Hawaiian two years later. While the first was also made available on Disney+, the latter was only distributed for free in schools in Hawaii, and never received any home media release form.

Critical response
At the time of the film's release, Bambi received mixed reviews from the critics, mainly because of the lack of fantasy elements in the film and objection towards a dramatic story of animals and their struggle to survive in the woods and avoid the threat of humans. The New York Times claimed that "In the search for perfection, Mr. Disney has come perilously close to tossing away his whole world of cartoon fantasy." Manny Farber of The New Republic wrote that "Bambi is interesting because it's the first one that's been entirely unpleasant…Mickey wouldn't be caught dead in this."

Farber added that "In an attempt to ape the trumped-up realism of flesh and blood movies, he has given up fantasy, which was pretty much the magic element." Even Disney's daughter Diane complained, saying that Bambi's mother did not need to die. When Walt claimed that he was only following the book, Diane protested, saying that he had taken other liberties before and that Walt Disney could do whatever he wanted.

Today, however, Bambi is viewed much more favorably. On the review aggregator website Rotten Tomatoes, the film has an approval rating of 91% based on 53 reviews with an average rating of. The website consensus reads: "Elegantly animated and deeply touching, Bambi is an enduring, endearing, and moving Disney classic." Critics Mick Martin and Marsha Porter call the film "the crowning achievement of Walt Disney's animation studio". English film historian Leslie Halliwell wrote that Bambi was "one of Disney's most memorable and brilliant achievements with a great comic character in Thumper and a climactic forest fire sequence that is genuinely thrilling." He concluded that it was "a triumph of the animator's arts".

Accolades
In June 2008, the American Film Institute revealed its "10 Top 10" – the best ten films in ten classic American film genres – after polling over 1,500 people from the creative community. Bambi was acknowledged as the third best film in the animation genre. It is also listed in the Top 25 Horror Movies of All Time by Time magazine. Bambi, Time states, "has a primal shock that still haunts oldsters who saw it 40, 50, 65 years ago."

American Film Institute
 * AFI's 100 Years... 100 Movies – Nominated
 * AFI's 100 Years... 100 Heroes and Villains:
 * Man – No. 20 Villain
 * AFI's 100 Years of Film Scores – Nominated
 * AFI's 100 Years... 100 Movies (10th Anniversary Edition) – Nominated
 * AFI's 10 Top 10 – No. 3 Animated film

Legacy
The off-screen villain "Man" has been placed No. 20 on AFI's List of Heroes and Villains.

Some critics have cited parallels between Frank Churchill's theme music for "Man" (which consisted of three simple notes) and John Williams's theme music in Jaws (which consists of two notes).

Paul McCartney has credited the shooting death of Bambi's mother for his initial interest in animal rights.

Soon after the film's release, Walt Disney allowed his characters to appear in fire prevention public service campaigns. However, Bambi was only loaned to the government for a year, so a new symbol was needed, leading to the creation of Smokey Bear. Bambi and his mother also make a cameo appearance in the satirical 1955 Donald Duck short No Hunting: drinking from a forest stream, the deer are startled by a sudden trickle of beer cans and other debris, and Bambi's mother tells him, "Man is in the forest. Let's dig out."

In 2006, the Ad Council, in partnership with the United States Forest Service, started a series of Public Service Announcements that feature footage from Bambi and Bambi II for wildfire prevention. During the ads, as the Bambi footage is shown, the screen will momentarily fade into black with the text "Don't let our forests...become once upon a time", and usually (but not always) ending the ads with Bambi's line "Mother, what we gonna do today?" followed by Smokey Bear saying "Only you can prevent wildfires" as the Smokey logo is shown on the screen. Bambi had previously been the Forest Service's advertising icon beginning in 1942, but was only allowed by Disney to use the character for a year.

In December 2011, Bambi was among the films selected for preservation in the Library of Congress' National Film Registry. In its induction, the Registry said that the film was one of Walt Disney's favorites and that it has been "recognized for its eloquent message of nature conservation."

Characters of the film appear in several other Disney media, such as guest appearances in the animated television series House of Mouse, Bambi being a character to summon in the video game Kingdom Hearts and its sequel Kingdom Hearts: Chain of Memories, and Bambi, Thumper, Flower, Faline and Great Prince of the Forest being playable characters in Disney Magic Kingdoms.

On December 17, 2018, a prison sentence passed against a man, in what is considered the biggest deer poaching case in Missouri history, contained the stipulation that the prisoner must view the film at least once each month during his one-year prison sentence.

Comic adaptation
The Silly Symphony Sunday comic strip ran a three-month-long adaptation of Bambi from July 19 to October 4, 1942.

Sequel
Set in the middle of Bambi, Bambi II shows the Great Prince of the Forest struggling to raise the motherless Bambi, and Bambi's doubts about his father's love. The film was released direct-to-video on February 7, 2006. While the film was a direct-to-video release in the United States and other countries, including Canada, China, Hong Kong, Japan and Taiwan, it was a theatrical release in some countries, including Australia, Austria, Brazil, Dominican Republic, France, Mexico, the United Kingdom and some other European countries.

CGI remake
On January 28, 2020, it was announced that a photorealistic CGI feature-length remake is in development with a script co-written by Geneva Robertson-Dworet and Lindsey Beer. Paul Weitz, Chris Weitz, and Andrew Miano will produce the film; a joint-venture production between Walt Disney Pictures, Depth of Field Studios, and Known Universe Productions. Disney described the film as a "companion piece" to The Jungle Book (2016) and The Lion King (2019), as the three films feature wildlife that requires extensive CGI and special effects. On June 13, 2023, it was revealed that Sarah Polley is in talks to direct the film, which is said to be a musical that will feature music from six-time Grammy-winning country star Kacey Musgraves. Micah Fitzerman-Blue and Noah Harpster wrote the most recent draft of the script. As of March 2024, Polley was reportedly no longer attached as director.

Copyright
The copyrights for Bambi, a Life in the Woods were inherited by Anna Wyler, Salten's daughter, who renewed them in 1954. After her death, Wyler's husband sold the rights to Twin Books, a publishing company which subsequently filed a lawsuit against Disney, claiming Disney owed it money for the continued licensing for the use of the book. Disney countered by claiming that Salten had published the story in 1923 without a copyright notice, thus it immediately entered into the public domain. Disney also argued that if the claimed 1923 publication date was accurate, then the copyright renewal filed in 1954 had been registered after the deadline and was thus invalid. The courts initially upheld Disney's view; however, in 1996, the Ninth Circuit Court reversed the decision on appeal in Twin Books Corp. v. Walt Disney Co., 83 F.3d 1162 (1996).

The American copyright of the novel expired on January 1, 2022.

title: Bambi


text:
Talk:Complementary colors

HELP!!!
There are some fundamental problems with this article. Primary colors do not allow us to form the full range of human perceivable colors. Take a look at gamut and also Google it and you should be able to find that the gamut of a trichromatic TV or computer screen is far from the entire range of possible colors. The discussion of primary colors as a means of forming a color gamut doesn't belong in an article on complimentary color in the first place. Primary colors are only relevant to complementary colors from a historical standpoint where, for example, certain primaries/secondaries were picked for painting, etc. But from a color science standpoint, any color has a complementary such that when the two are added they will form gray (or the color of the illuminant in a subtractive system). It's irrelevant which colors are primaries.

If you want to understand primaries, the true authority is the CIE. Again, you will have to go outside of Wikipedia to get a thorough understanding of this topic. The short answer is that the only way to get the full gamut of human perceivable colors with three primaries is to make your primaries imaginary colors (or allow subtraction of colors in an otherwise additive system).

If this makes your brain hurt, you're not alone. I don't really feel completely authoritative on all this either. I will try to complete a complementary wavelength article to go with the dominant wavelength article when I have time (not for a while I'm afraid). This should cover complementary color except for the historical stuff, which we can keep here.

I'm really sorry to just complain and not help fix things, but I just don't have the time right now and thought I'd better at least point out the problems as I saw them. --Chinasaur 08:43, 4 Oct 2004 (UTC)

 * I agree with you on the inappropriateness of referring to the primary and secondary colours in this article, so I did your dirty work for you and deleted the references. I am looking forward to your article on complementary wavelengths. :-) --Heron 11:50, 4 Oct 2004 (UTC)

 * It should be recognised that here is a theoretical and a practical approach. The practical approach is based on the three types of colour receptors - cones - in the human eye: red, green and blue. This is the origin of primary colours. Thus it makes perfect sense to use them.
 * TV screens are three-chromatic for the above reason. As to the imperfect colour reproduction, it is not a limitation of the three-chromatic approach but was a technical problem. Engineers couldn't make a better phosphorus, later LEDs. The quality was limited by the technology. Yes, the still current sRGB is poor with it's 16 million colours. However, current digital movie cameras have 16 bit/channel colour resolution IE:2.814749767×10¹⁴ - 281 trillion - colours. This is important during the editing but not for the end product. A DLP cinema projector is offering 35.2 trillion colours. More than enough to exceed the limitation of the human eye - about ten times.
 * Now the author of the article needs to decide how to combine/separate/discuss theory vs practicality. Naturally, neither are right or wrong. Just different. — Preceding unsigned comment added by 115.70.29.185 (talk) 03:25, 4 May 2021 (UTC)

Americanize
I tried to make the orthography of the article consistent. There were mostly "colour"s but some "color"s. But the article is named "color" so I changed it that way. If a great majority of people working on this article are British and have trouble remembering the American spelling, we might want to consider a move to Complementary colour, but otherwise I think this is the easiest solution. --Chinasaur 18:15, 4 Oct 2004 (UTC)

Colour is the spelling recognized around the world, color is the spelling in just one nation. I support formally changing the spelling of this word everywhere it appears. 66.46.152.30 18:36, 11 August 2006 (UTC)

I reverted your changes. Wikipedia practice is to keep whatever spelling was used first in the article; in this case, "color". See the Color talk page for the most recent of numerous lengthy debates on this topic. -- Laura S  |  talk to me  19:17, 11 August 2006 (UTC) Put also spelt Colour on the opening sentence. —Preceding unsigned comment added by 88.105.51.100 (talk) 12:50, 23 October 2010 (UTC)

Complementarity and Negativity.
This is ridiculous! This article says that yellow is the complement of purple, but at yellow it says that yellow is the complement of blue. 66.245.26.248 18:32, 27 May 2004 (UTC)

 * Good point. I have tried to fix the article. -- Heron 16:03, 7 Aug 2004 (UTC)

 * I will look over this article with an eye to both psychology, where red is the complement of green and to photography, where red is the negative of cyan. Artistically, both cyan and green make adequate complements, but to the photoreceptors in the eye, green is better. Photographically, red is the negative of cyan, not green. It's worth noting that the receptors for blue in the eye are very well suited to receiving violet. IOW, more difference is between the peaks for blue and green than the peaks for red and green. My main reference is a textbook that I no longer possess: Physiological psychology (I might even need to look at the University of Alberta calendar to remember the author). BTW, violet is a better word than purple for the complement of yellow, because purple can be confused with dark majenta or a 2:1 mix of majenta and cyan. Know what? Your monitor doesn't do violet. —Preceding unsigned comment added by Brewhaha@edmc.net (talk • contribs)

 * It would be better to start a new section than to respond to an old item from 2004. As for your concept of "negative colors", please provide a verifiable source.  You seem to be taking this article into a direction that is unfamiliar to me, and I'm quite familiar with color science and its application in photography.  I'm going to revert your edit for now, since I think this "negative colors" approach is rather non-standard.  I recommend you start over with a new section below, and certainly back up any major changes with sources. Dicklyon 15:32, 30 March 2007 (UTC)

 * Neil R. Carlson calls it the 'opponent-color system', and it's based on action potentials in ganglia. I've been a wikipedian for quite a while, and I don't think I've ever reverted an article in entirety. The question that gets me is how the brain confuses violet with a mixture of blue and red, and I'm looking at graphs of light absorbance in pigment to put it in words. Brewhaha@edmc.net 11:35, 24 June 2007 (UTC)

Now, can anyone answer the question "Why are the 2 sets of colors different"?? Please read this very slowly and carefully:

In the summer of 2003, I stumbled across a site at http://www.gamecheetz.com/Rant.html that appears to explain very logically. It has a color section. When I stumbled across it, I thought it was logical in every way except one: it has not been widely adopted as standard. In February 2004, I edited various color edits to see how difficult the information could ever get widely adopted. Now, go to Talk:Color. The 7-section supgroup titled "What are the primary colors??" that is being discussed about the edits that I made sounded strange, but now I will reveal the truth: all I was trying to do is make the information mentioned in the above external link widely adopted, and it turned out that it can't. Three months later, I contacted the owner of the web site, convincing the owner that their information cannot be widely adopted, and the reason turned out to be that it was only the webmaster's opinion as of when the information was presented, and the opinion was changed. "The black-white scale and blue-yellow scales each have gray in the center, but the red-green scale has yellow. Thus, yellow is both a primary and a secondary color! No other color is both primary and secondary." (In contrast to the webmaster's previous belief as of when I stumbled across the page, which was all 3 scales contained gray.) Even later, I asked the webmaster how the red-green scale looks to someone who is red-green color blind and the answer was that the webmaster (contrary to what I thought when I stumbled across their site) is not an expert on colors.

 * There are two kinds of red-green color blindness. One is called protanopia and represents when the red cones are filled with green pigment. Deuteranopia represents the transverse. Tritanopia is about a complete absence of blue pigment. It's very rare. In protanopia, the subject would see darkness towards the green end. Someone with the second kind of anopia would see darkness toward the red end. Brewhaha@edmc.net 11:35, 24 June 2007 (UTC)

Now, are any of you registered Wikipedians able to answer the question with your best knowledge: "Why are the 2 sets of primary colors in paint and light different??" 66.32.241.40 02:18, 8 Aug 2004 (UTC)

As for that rant, the guy is seems to have mulled over the issue, but came to the wrong conclusions because he just doesn't know how the brain perceives different colors. The most comprehensive site on color I have found is http://www.handprint.com/HP/WCL/wcolor.html, and if you are interested I suggest you check it out. The reason all this information isn't discussed is because I think it's out of the realm of wikipeida (as you can see there there is a TON of info... too much to include in one encyclopedia article).

FYI the reason there are 2 sets of primary colors is because paint absorbs light, and colored lights emit it (that's why the primary colors of light are called "additive primary colors" and the primary colors of pigment are called "subtractive primary colors". Ctachme 05:04, 8 Aug 2004 (UTC)

 * No. That's not the question. The question is whether green or cyan makes a better complement for red. A paint artist will tell you green. A neurobiologist will tell you green. Another question is whether violet makes a better complement for yellow than blue. It's a shame that someone simply reverted my edits. What am I supposed to do? I would resolve the controversy by distinguishing complementarity from negativity. Brewhaha@edmc.net 11:35, 24 June 2007 (UTC)

 * Yes, Ctachme, that's true, but painters use a third set of primary colours: red, blue and yellow. I think these were chosen because they were once the only colours that could be manufactured in a stable form suitable for paint pigments, and modern painters still refer to these as the "primary colours".  Traditionally, yellow was made from orpiment (an arsenic compound), blue from lapis lazuli (a gemstone), and red from Chinese cinnabar or vermilion (a mercury ore).  The complements of these pigments are red/green, blue/orange and yellow/purple. -- Heron 16:18, 8 Aug 2004 (UTC)

 * But shouldn't the stance be that the so called "painter's primary colors" are only worthy of historical note because as you just said, it was based only on available pigments, not on the actual colors that the eye considers primary? I see no reason to pretend this historical note is still fact. The three subtractive primary colors are yellow, cyan and magenta with compliments of blue, red and green, and the additive primary colors are just the opposite (blue/yellow, red/cyan and green/magenta). Ctachme 02:38, 9 Aug 2004 (UTC)

 * The controversy rayjez even today between technicians and artists. I've been led to distinguish negative colors from complementary colors. Maybe I'm trailblazing. Nothing is new in that. It's worth noting that cyan is next to green and violet is next to blue on the spectrum. The neurobiology serves as the initial stage of what allows some people to find a number between about one and sixteen for a hue. Brewhaha@edmc.net 11:35, 24 June 2007 (UTC)

 * OK, I concede that there is no value in promoting the RYB 'primaries'. My point is that there are still many books out there that cling to the old theory, and that people should be able to find that theory somewhere on Wikipedia, even if it is only in an historical note.  Would you accept, for example, a note under blue saying "Blue is an additive primary colour.  It was once considered a subtractive primary colour, the complement of orange, but this theory has now been superseded by the more accurate cyan/magenta/yellow system of subtractive primary colours"? -- Heron 08:36, 9 Aug 2004 (UTC)

 * Sure, that would seem fine to me, as long as all of the colors were updated to reflect this. Ctachme 11:53, 9 Aug 2004 (UTC)

Cleaning, explaining, clarifying...
Changelog:
 * I explained the function of additive complementary pairs.
 * Gray is (literally) a shade of white; changed "shade of gray" to "shade of white".
 * RGB section ended up being adupe of additive section; I removed it and will copy the formula from it to the additive section at a later date, with a better example than black and white.
 * Looking at a chart is not a good way of remembering... Some might consider this cheating.

I'm still not pleased with the complementary subtractive section. I don't think purple and yellow or red and green pigments will combine to produce the illuminant color. But it's 2:25am and I get up in 6 hours for work so, another time. Ayeroxor 06:27, Jun 23, 2005 (UTC)

 * Yes, sorry, I think the "color of the illuminant" was something of a red herring for this discussion. Sorry because I think I put that in at some point.  I think the current article is now at least roughly accurate, but not very readable.  Hopefully more color science people and artists will help correct technical errors while lay people can make it things more readable in WP's iterative process from here.  --Chinasaur 22:20, 28 December 2005 (UTC)

 * I'm taking those color pairs back out. Could you justify including them?  They don't make much sense to me and I doubt they have much formal validity in color science.  They are more relevant to CMKY printing than anything else I can think of.  --Chinasaur 09:21, 18 January 2006 (UTC)

 * They make a lot of sense to most people :o) There is very strong empirical evidence that the three primaries and the three secondaries form the main concepts by which colour perception in general is ordered; certainly RGB sensors are the main components of the sensory apparatus. It is thus useful to order them in complementary pairs and mention them explicitly, the more so because it is very common to do so and we as an encyclopedia must reflect this social practice. It is not our place to endorse or condemn. However we might add that the value of this ordering in colour science is very limited. Of its "formal validity" I know little; but a material validity is present ;o)--MWAK 12:31, 25 January 2006 (UTC)

Grey
If you think about it, there should be a shade of grey that when inverted, will produce the same colour (ie; it is exactly halfway between black and white). Does anyone know what its hex is equal to, and if so, could you add it to the article as a piece of trivia?Tuck99 04:21, 25 February 2007 (UTC)
 * The closest you can come, in a typical 8-bit space, is 127 or 128, which are inverse of each other. It's too trivial to be worth a mention. Dicklyon 05:06, 25 February 2007 (UTC)

 * I'd say it depends on what you mean by "inverted", and on factors like amount of ambient light, etc. “Complementary” usually just refers to hues, in my experience, not even really to particular colors. --jacobolus (t) 22:19, 10 August 2007 (UTC)

Simply wrong
The article currently claims: "In the RGB color model (and derived models such as HSV), primary colors and secondary colors are paired in this way: Red and green, yellow and purple, blue and orange." With all the people obviously knowing the differences between the various color wheels and theories, how can something as commonly known as the RGB color model and it's complementary colors still be wrongly described? In the RGB color model, red is the opposite of cyan, green is opposite of purple and blue is opposite of yellow. The first image in this article even confirms this. Unless anyone can justify why the piece of text I just quoted is correct, I'll edit the above text. JoaCHIP (talk) 18:39, 1 March 2009 (UTC)

You are right. I think this is obvious enough that I have finally edited the text. The opposite of red (255, 0, 0)is obviously (0, 255, 255), which is cyan, so you are obviously right. You can use any RGB color scale to prove this. Same with blue with yellow [(0, 0, 255) with (255, 255, 0)] and green with MAGENTA (not purple) [(0, 255, 0), (255, 0, 255)]. (255 can be substituted by any number, really, but you get the idea). I think this justifies editing that piece of text, and so I did. T.c.w7468 (talk) 23:25, 5 May 2009 (UTC)

Oh yeah and by the way... http://en.wikipedia.org/wiki/File:RBG_color_wheel.svg. There's some proof. T.c.w7468 (talk) 23:30, 5 May 2009 (UTC)

This was also labeled incorrectly in the afterimage section. The afterimage opposite of red is also cyan, so I've edited "green" to say "cyan" as it was clearly wrong, and any image if an inverted American flag will use cyan, and not green, as its red opposite. MXVN (talk) 05:52, 6 December 2011 (UTC)

Complimentary colors used by various professional sports teams.
I noticed that a few professional sports teams, such as the Mets, Knicks and Islanders (blue & orange), along with the Lakers (purple & gold), use complimentary colors as their primary colors. Is that relevant information? Mr. Brain (talk) 04:09, 4 May 2009 (UTC)

what is transparent, translucent,and opaquein science?
transparent is something that lets light right through

translucent is something that makes light scatter

opaque is something that does no let light through

Recent Edits
Some editors are removing large swaths of this article and replacing material with unsourced information and conjecture. Perhaps before making further dramatic changes, the issue should be discussed here. Taroaldo (talk) 19:23, 18 July 2010 (UTC)

Afterimages
I just removed a clarification needed tag from afterimages, as i think it was pretty clear how the afterimage is formed. I added a bit more clarification just to make it more clear.Larryisgood (talk) 16:41, 26 January 2011 (UTC)

The term "colored shadow"
Colored shadow redirects to this article, but the term is not explained, here. Shouldn`t that be changed?! --Hans Dunkelberg (talk) 08:45, 3 July 2011 (UTC)

red and green
It is a grave heresy, unless we essentially redefine "red" with a deviation towards magenta and "green" with a deviation towards cyan. Which sources speak about this and what exactly they say? Incnis Mrsi (talk) 10:48, 19 January 2013 (UTC)

Russian Wikipedia refers to books of Bride M. Whelan. Does anybody read his books? Incnis Mrsi (talk) 11:03, 19 January 2013 (UTC)

 * Well, we should look at it this way: under the Wikipedia NPOV rule we must try to give an exposition of both systems: the traditional one and the scientific one. We give them due weight by indeed saying that the one is scientific and the other traditional and mention the latter last. Of course reality is a bit more complicated as is shown by works as those of Mr Whelan who take a sort of "in between" position: they take a traditional colour wheel and then squeeze in cyan and (not very saturated) magenta somewhere. That makes such "systems" severely incoherent but that doesn't matter much as they are not even popular science books: they are just popular. They aim at giving the reader a happy colour experience and perhaps help him a bit in decorating his house (should the poor man try to actually mix paint according to the precepts he is in for a very unhappy surprise, obviously). Such books cannot be used as serious references.--MWAK (talk) 09:28, 21 January 2013 (UTC)

I don't understand the problem with red–green complementarity in the RYB system. I'll add a book source. Dicklyon (talk) 03:26, 8 June 2013 (UTC)
 * Do you want to say that a painter’s red and green can be mixed (in appropriate proportion) to produce something perceived nearly as a neutral grey? Incnis Mrsi (talk) 04:57, 8 June 2013 (UTC)
 * I probably wouldn't go that far; they'd probably make a muddy brownish color, like this guy shows. But they're still considered complementary in that system, and if you used a red slightly on the magenta side and a green toward the cyan side a little, as you note, they might make a neutral mix.  If you mix appropriate amounts of the three primaries red, yellow, and blue, you should be able to make a neutral; the relative amounts of blue and yellow in that mix will be a green of sorts, no?  Of course, it does depend on what the absorption spectra of those primaries look like.  Here's a page where red and green paints mix to make a fairly neutral blackish color.  Dicklyon (talk) 05:15, 8 June 2013 (UTC)
 * I agree that a non-spectral (i.e. without a dominant wavelength) “red” and a non-standard wave-shortened “green” (something like emerald) can be perceptually complementary. So named (ironically) Natural Color System really makes namely this choice. But it has no sense (except for making linguistic constructions) to draw a triangle (or hexagon, or rhombus) diagrams and to label vertices and midpoints with some words like “red”, “yellow”, “green”, and “blue”, without specifying their meaning. Is RYB color model presented in a more intelligent way by B.M.Whelan s and most Wikipedians? One can draw an arbitrary color triangle (such as yellow–blue–black), make custom “secondary color” definitions (such as white=yellow+blue, brown=yellow+black), and then say that blue and brown are complementary in the YBK color model. Incnis Mrsi (talk) 06:04, 8 June 2013 (UTC)

P.S. I concluded that the source of confusion is conflicting definitions of “red”. I tried to explain something of it at Color Theory/Misconceptions – feel free to correct if needed. Incnis Mrsi (talk) 13:36, 15 June 2013 (UTC)

Johann Wolfgang von Goethe and his theory
I spent 4 days without Internet, and today surprisingly see all references to them disappeared from the article. It is not good. Incnis Mrsi (talk) 13:10, 3 June 2013 (UTC)

Plese don't worry, the historical section isn't finished. Goethe will return shortly, along with Maxwell and Young. I just need to line up the correct references. SiefkinDR (talk) 14:40, 3 June 2013 (UTC)

 * Why were they removed? I think you need to work more slowly and carefully.  Dicklyon (talk) 05:17, 8 June 2013 (UTC)

 * Incnis, you, too. I now see that in this edit  you added an unsourced assertion that the widespread concepts of complementarity in the RYB system are just wrong.  You don't get to decide that.  I always revert unsourced assertions of errors and confusions when I see them, and I'm sorry I missed this.  It is not WP:NPOV.  We need to respect and fairly represent even those color systems that predate the more colorimetrically accurate concepts.  Dicklyon (talk) 05:26, 8 June 2013 (UTC)
 * When I edited the article, the only reference was Theory of Colours (van Gogh’s perverse Café was absent at the time), and Goethe did not write a Whelanian crap, he actually examined and researched the perception. Theory of Colours does not describe the complementary of green as “red”. Maybe van Gogh did, but Goethe did not. Incnis Mrsi (talk) 06:15, 8 June 2013 (UTC)

additive colors and subtractive colors… operate by different rules, and [have] different primary and complementary colors
Theoretically it is true, as rules for mixing differ, but actually (not terminologically) this difference is tiny. The citation intended to suggest (although it does not explicated) that van Gogh was right with his red–green “complementarity” but in his (pigment) system. No, he was not, and this pair was likely a misconception appeared somewhere in 19th-century.

There is almost no difference between RGB’s and pigments’ complementaries in actual colors (not names). The case with orange: actually, the same color, but referred to as “blue” (except in heraldry) historically and as “azure” since 20th century. These words were nearly synonymous and diverged with establishment of modern color terminology in mid-20th century. Just look at the “blue” of van Gogh’s paints.

The complementary of yellow, nowadays called the (color wheel) blue, was historically known as indigo: read the latter article to find a citation. It has no big difference with violet, which Goethe named as yellow’s complementary. BTW, Goethe’s “violet” is hardly different from (modern) “indigo”. Goethe did not make a noticeable error with these two pairs.

Finally, subtractive complementary to red is known to be cyan, never green. So, “RYB complementaries” are a misconception having little to do with any (either physiological or pigment mixing) color process. But the article retouches this consideration down. Incnis Mrsi (talk) 20:24, 8 June 2013 (UTC)

 * The traditional role of red and green as complements in the RYB system that painters use is probably more related to a color opponent process than to the idea that complements mix to give a neutral. Either that or the colors that they call Red and Green are a bit off from what we call red and green in the RGB system.  But trying to explain the traditional RYB system in terms of modern colorimetry and the RGB system is a bit of a losing game in my opinion.  Let it stand on its  own and you'll be less bothered by it.  Dicklyon (talk) 01:34, 9 June 2013 (UTC)
 * A bit off, really? Get van Gogh and check whether he used a-bit-offed NCS so-named “red“ (actually crimson) and ”green” (actually emerald), or standard (both RGB and CMYK) ones. Incnis Mrsi (talk) 03:37, 9 June 2013 (UTC)
 * I wouldn't know how to get a hold of him. Dicklyon (talk) 04:51, 9 June 2013 (UTC)

It's true that Van Gogh said he was particularly crazy about using a crimson lake, which seems to have been alazarin crimson and thus close to magenta, and emerald green, closer to cyan, but for him those were red and green. SiefkinDR (talk) 06:07, 9 June 2013 (UTC)
 * BTW commons:Category:Le Café de nuit shows a great divergence in colors: one photo even shows an unambiguous cyan instead of ”green”. It’s not good. Incnis Mrsi (talk) 06:52, 9 June 2013 (UTC)

This book Blue and Yellow Don't Make Green has a good discussion of the different variants of red and green, and other pairs, that can be used as complements. Dicklyon (talk) 18:34, 19 June 2013 (UTC)

Needs a better lead image, please
Can we please come up with a better image for the top of this article? The picture of the pilot flying blind is confusing and adds no information at all about complementary colors. Most people who come to this article simply want to know what colors are complementary. I believe we need a color wheel or chart that shows people the complementary colors. Thank you! SiefkinDR (talk) 13:45, 9 June 2014 (UTC)

Creative arts
What are complementary colours 102.221.220.128 (talk) 16:44, 22 June 2022 (UTC)

title: Talk:Complementary colors


text:
Talk:Motion for more definite statement

Untitled
In response to notes below and this article, there seems to be a number of factual issues with this article. It may be advantageous for a licensed attorney to review. Among the potential issues: e 1. "...means of obtaining a more detailed motion from the opposing party..." - I am not clear if there are instances in which a motion for a more definitive statement ever pertains to another motion. I believe in most jurisdictions, an issue of lack of clarity with a motion would be handled via an objection to a motion. Generally, I think the motion for a more definitive statement pertains to a complaint -- i.e. a responsive item filed instead of and in advance of an answer to a complaint.

2. "The presiding judge will respond..." -- I am unclear why it is asserted a presiding judge would be the one to respond. My understanding is this would generally be handled by the judge assigned to a case.

In case the earlier talk comments pertain to the existing bulk of this article (and not earlier version), it appears this article pertains to the United States. The Federal Rules of Civil Procedure specifically refer to actions in federal courts. Most states, if not all, have their own rules of civil procedures for district courts of the state, that are based substantially on the federal rules of civil procedure. However, an action in a state court would not follow the federal rules; it would follow the specific rules for the district court. So, for example, an action in the Third Judicial District Court (state) for Utah (including Salt Lake County) would follow the Utah Rules for Civil Procedure.

Uberveritas (talk) 16:46, 11 June 2017 (UTC)

If anyone knows what jurisdiction, or even what country, this refers to please fill it in. DJ Clayworth 18:33, 27 May 2004 (UTC)
 * I assumed that in the US. The article mention Federal code of procedure. And what other editor would not bother to enter a country? Przepla 14:43, 19 Sep 2004 (UTC)

title: Talk:Motion for more definite statement


text:
Wikipedia:Articles for deletion/MrBits

This page is an archive of the discussion surrounding the proposed deletion of the page entitled Mr.Bits.

This page is kept as an historic record.

The result of the debate was to delete the article.

Orphan, dubious. Unvarifiable, vanity or prank? Top google hits for "Mr.Bits" don't seem relevant. Zero google hits for the terms Mr.Bits Chicago Comedian together, no hits for "The Bits & Clone Show", Bitskateers. -- Infrogmation 18:34, 27 May 2004 (UTC)
 * Delete. Looks like vanity or prank. Thue 19:06, 27 May 2004 (UTC)
 * Delete. As interesting as it was to read, I must concur. Acegikmo1 19:12, 27 May 2004 (UTC)
 * I'm not buying it. Delete. -- Cyrius|&#9998 19:27, May 27, 2004 (UTC)
 * Delete. Probable vanity, by anon. Andrewa 01:56, 28 May 2004 (UTC)

This page is now preserved as an archive of the debate and is no longer 'live'. Subsequent comments on the issue or the deletion should be placed on other relevant 'live' pages. Please do not edit this page.

title: Wikipedia:Articles for deletion/MrBits


text:
Iron Ring

The Iron Ring is a ring worn by many Canadian-trained engineers, as a symbol and reminder of the obligations and ethics associated with their profession. The ring is presented to engineering graduates in a private ceremony known as the Ritual of the Calling of an Engineer. The concept of the ritual and the rings originated from H. E. T. Haultain in 1922, with assistance from Rudyard Kipling, who crafted the ritual at Haultain's request.

Symbolism
The ring symbolizes the pride engineers have in their profession, while simultaneously reminding them of their humility. The ring serves as a reminder to the engineer and others of the engineer's obligation to live by a high standard of professional conduct. However, the ring is not a symbol of qualification as an engineer; engineering qualifications are determined by provincial and territorial licensing bodies.

History
The Iron Ring originated from H. E. T. Haultain, a mining engineering professor at the University of Toronto. On 25 January 1922, Haultain proposed that engineers take an ethical oath. From 1922 to 1925, the structure that would administer the oaths, or "callings," was organized. Known as the Corporation of the Seven Wardens, the organization was named in honour of the first seven presidents of the Canadian Society for Civil Engineers.

The text of the calling was written by English poet Rudyard Kipling, at the request of Haultain. Haultain asked Kipling to author the calling partly because of Kipling's poem The Sons of Martha, which paid tribute to an engineer. Kipling's calling sought to emphasize the responsibilities of an engineer, affirming their responsibility to "not henceforward suffer or pass, or be privy to the passing of, Bad Workmanship or Faulty Material." Kipling's calling also affirmed that an engineer must not compromise their work, in spite of external pressures; and was a call for professional unity between engineers.

On the 25 April 1925, Haultain administered the first Ritual of the Calling of an Engineer in the University Club in Montreal. A second ritual was administered in Toronto on 1 May 1925. Iron Rings are awarded to engineers during the ritual, in reference to "[their] Honour and Cold Iron," a phrase used in the calling. A myth persists that the initial batch of Iron Rings was made from the beams of the first Quebec Bridge, a bridge that collapsed during construction in 1907 due to poor planning and design by the overseeing engineers. However, the initial batch of Iron Rings were actually produced by World War I veterans at Christie Street Military Hospital in Toronto.

The Wardens originally considered expanding the ritual to the United States. However, they later ruled against expansion, fearing a loss of control over the ritual. Efforts to secure control of the ritual were made in 1935, when the obligation was copyrighted, and the Corporation of the Seven Wardens formally incorporated in 1938.

Design
The Iron Ring is made from either iron or stainless steel. It is intended to be worn on the little finger of the working (dominant) hand. There, the facets act as a sharp reminder of one's obligation while the engineer works, because it could drag on the writing surface while the engineer is drawing or writing. This is particularly true of recently obligated engineers, whose rings bear sharp, unworn, facets. Protocol dictates that the rings should be returned by retired engineers or by the families of deceased engineers. Some camps offer previously obligated or "experienced" rings, but they are now rare due to medical and practical complications.

The Iron Ring is small and understated, and was designed as a constant reminder, rather than a piece of jewelry. The Rings were originally hammered manually with a rough outer surface. The modern machined ring shares a similar design as a reminder of the manual process. Twelve half-circle facets are carved into the top and bottom of the outer surface, with the two sets of facets offset rotationally by fifteen degrees.

Presentation ceremony
The Ritual of the Calling of an Engineer is the ceremony where graduating engineers participate in the "calling," and receive their Iron Rings. The ritual is intended to invoke the moral, ethical and professional commitment of an engineer, with the ring provided as a reminder of this obligation. The ceremonies are private affairs with no publicity. Invitations to attend are extended to local engineering alumni and professional engineers by those who are scheduled to participate. Some universities extend an invitation to witness the ceremony to anyone in the engineering profession; however, engineers that have not undergone the ritual are not permitted to participate in it. Some graduating engineers choose to receive a ring passed on from a relative or mentor, giving the ceremony a personal touch.

The rings are given during the ceremony held at individual universities, each assigned one of 28 camps of the Corporation of the Seven Wardens. Because iron deteriorates turning the finger black and making the ring fit more loosely, all camps except Toronto have stopped conferring rings made of iron and have switched to stainless steel rings. At the Toronto camp, the individual ceremonies held at the University of Toronto, Toronto Metropolitan University, Ontario Tech University, and York University continue to provide recipients with a choice of rings made of iron or stainless steel.

Similar practices
Based upon the success of the Iron Ring in Canada, a similar program was created in the United States, where the Order of the Engineer was founded in 1970. The organization conducts similar ring ceremonies at a number of U.S. colleges, in which the recipient signs an "Obligation of the Engineer" and receives a stainless steel Engineer's Ring (which, unlike the Canadian Iron Ring, can be smooth and not faceted). The first such ceremony occurred on June 4, 1970, at the Cleveland State University under the supervision of Lloyd Chancy.

The NTH Ring is a ring awarded by the Norwegian University of Science and Technology, formerly Norwegian Institute of Technology (NTH), to graduates of their Masters of Science in architecture or engineering programs.

title: Iron Ring


text:
Wikipedia:Articles for deletion/Quantumphasetransition

Either this is a real term presented poorly or it's the greatest piece of quackery I've ever seen here. Is there a physicist in the house? - Lucky 6.9 18:38, 27 May 2004 (UTC)
 * From what (little) physics I know I can't find any inaccuracies. I think it would be more appropriate to list this at Pages_needing_attention. I have listed it there. Thue 18:56, 27 May 2004 (UTC)
 * Real term poorly presented. Move to Clean-up. I'll try if/when I can find my old textbooks. Rossami 20:59, 27 May 2004 (UTC)
 * "Quantum phase transition" gets over 7000 google hits. Clicking on a few google hits suggest that the page isn't blatent nonsense. I don't know enough of quantum physics to know how accurate the information is - but since I lack the knowledge to judge the accuracy, I won't vote for delete. Abigail 21:04, May 27, 2004 (UTC)
 * Keep. Real phenomenon. Not a good VfD listing IMO, we should be listing and voting on things we do know something about (as others have said more gently). There are other places for asking questions. As Wikipedia grows this becomes more and more important. Andrewa 21:09, 27 May 2004 (UTC)
 * In either case it doesn't belong on VfD. If it is a real term presented poorly, it is still clearly a encyclopedic topic and doesn't belong on VfD.  On the other hand, if the person who posted the VfD request doesn't understand the topic well enough to determine if it is "quackery", it doesn't belong on VfD.  Keep. ElBenevolente 21:16, 27 May 2004 (UTC)
 * That's perfectly OK with me. It's not that I didn't understand the topic.  It was so badly written that I simply couldn't comprehend what I was reading.  There was a patently nonsensical article here last week that was couched in pseudo-scientific mumbo-jumbo.  I wasn't certain if this was the same sort of thing, hence my electing to bring it here.  It's already on "pages needing attention," so by all means, keep.  And let's try and keep the personal attacks to a minimum, OK? - Lucky 6.9 21:34, 27 May 2004 (UTC)
 * Comment - Mikkalai has revised the article. It's certainly more readable now, anyway. Average Earthman 17:48, 28 May 2004 (UTC)


text:
Karlovy Vary Region

The Karlovy Vary Region (Karlovarský kraj) is an administrative unit (kraj) of the Czech Republic, located in the westernmost part of the country. It is named after its capital Karlovy Vary. It is known for spas, which include Karlovy Vary and Mariánské Lázně.

The Karlovy Vary Region, as a higher territorial self-governing unit, was created in 2000 in the northern part of the West Bohemian Region. The seat of the region is Karlovy Vary. In terms of size, number of municipalities, and population, it ranks among the smaller regions of the Czech Republic. Its area (3,314 km²) covers 4.25% of the territory of the Czech Republic. The Karlovy Vary Region is the third smallest region by area, right after Prague and the Liberec Region. By population, the Karlovy Vary Region is the smallest region in the Czech Republic, with approximately 295,000 inhabitants.

Administrative divisions
The Karlovy Vary Region is divided into three districts:

At a lower level, the region has 134 municipalities, comprising 56 in the Karlovy Vary District, 40 in the Cheb District and 38 in the Sokolov District.

Population
Karlovy Vary Region is the smallest region in the Czech Republic with a population of less than 300,000. Only 11 municipalities have populations greater than 5,000. The largest municipality of the region is Karlovy Vary with a population of around 50,000. The table below shows the municipalities in Karlovy Vary Region with the largest population (as of 1 January 2024):

Other significant towns in Karlovy Vary Region are Nejdek, Kraslice, Františkovy Lázně and Horní Slavkov.

Spas
The region is responsible over half of the county's spa industry. Twelve spas are in the city of Karlovy Vary. Other spa towns in the region include Františkovy Lázně, Mariánské Lázně, Lázně Kynžvart and Jáchymov. The spas are visited by Czechs as well as by people from the rest of Europe, Russia, Israel and North America. The Karlovy Vary spa wafer, a local food item, was awarded protected designation of origin (PDO) status by the European Commission in 2011.

The water from the region is used in locally produced beverages including Mattoni from Karlovy Vary and Aquila from the village of Kyselka.

Black Triangle
The region is the home of two power stations, Vřesová and Tisová, both in the Sokolov District. The region is also part of the so-called Black Triangle, an area of heavy industrialization and environmental damage on the three-way border of Poland, Germany, and the Czech Republic.

Transport
The Karlovy Region is served by Karlovy Vary Airport, which handled more than 100,000 passengers in 2012. The region is also home to two other airports, neither of which are used for passenger flights. These are Cheb Airport, the oldest airport in the country, and Mariánské Lázně Airport.

The region lacks any motorways. The unfinished R6 expressway passes through the region, linking Cheb and Karlovy Vary to Prague. The length of operated railway lines in the region is 493 km.

Education
The Czech University of Life Sciences Prague opened a centre in the village of Dalovice in the Karlovy Vary District in 2007. The private College of Karlovy Vary is also located in the region, in addition to regional centres of the Banking Institute / College of Banking in Karlovy Vary and the University of West Bohemia in Cheb and Sokolov.

title: Karlovy Vary Region


text:
User:Benzh~enwiki

I am from Berlin and 23 years old. Currently I am studying physics at ETH Zurich. My main interests are condensed matter physics, progressive rock and the philosophy of Ludwig Wittgenstein.

title: User:Benzh~enwiki


text:
The Way of The Vaselines: A Complete History

The Way of the Vaselines: A Complete History is a compilation album by the indie rock band The Vaselines. It was released in May 1992 on Sub Pop Records, catalogue SP145b. The album compiles every previous release by the band, the two EP's Son of a Gun and Dying For It, as well as their first long-playing album Dum-Dum, in chronological order of release. Three additional tracks are included: "Dying for It (The Blues)", "Let's Get Ugly", and the previously unreleased "Bitch."

The band had broken up around the time that Dum-Dum was issued, and had never gained a huge following. However, covers of their songs by Nirvana had brought them new exposure, which prompted Sub Pop to put together this compilation. Production credits are to The Vaselines in collaboration with Stephen Pastel on the tracks from Son of A Gun and Dying for It, and with Jamie Watson on the remainder.

Critical reception
Entertainment Weekly wrote that "in The Way of the Vaselines: A Complete History, these recovering Catholics tackle subjects as complex as atheism and murder and as mundane as a particularly chafing bike seat, all with lyrics so simple a 6-year-old could have written them." Pitchfork said, "The 19-track collection that Sub Pop released at Cobain's suggestion has long been the best way to listen in on Kelly and McKee's flirty chaos." Robert Christgau called it, "one of those punk miracles that makes you think anyone can do it".

Track listing
All songs by Eugene Kelly and Frances McKee except "You Think You're a Man" by Geoff Deane.

 * 1) "Son of a Gun" – 3:46
 * 2) "Rory Rides Me Raw" – 2:28
 * 3) "You Think You're a Man" – 5:43
 * 4) "Dying for It" – 2:22
 * 5) "Molly's Lips" – 1:44
 * 6) "Teenage Superstars" – 3:28
 * 7) "Jesus Wants Me for a Sunbeam" – 3:31
 * 8) "Sex Sux (Amen)" – 3:10
 * 9) "Slushy" – 2:00
 * 10) "Monsterpussy" – 1:43
 * 11) "Bitch" – 2:42
 * 12) "No Hope" – 3:21
 * 13) "Oliver Twisted" – 2:49
 * 14) "The Day I Was a Horse" – 1:29
 * 15) "Dum-Dum" – 1:57
 * 16) "Hairy" – 1:48
 * 17) "Lovecraft" – 5:37
 * 18) "Dying for It (The Blues)" – 3:09
 * 19) "Let's Get Ugly" – 2:19

Personnel

 * Eugene Kelly — vocals, guitars. harmonica
 * Frances McKee — vocals, guitars, synthesizer on "You Think You're A Man"
 * James Seenan — bass
 * Charlie Kelly — drums

Additional personnel

 * Aggi Wright — keyboards on "Son of A Gun"
 * David Keegan — lead guitar on "Dying for It"
 * Sophie Pragnell — viola on "Jesus Doesn't Want Me for A Sunbeam", "Dying for It" and "Oliver Twisted"
 * Jamie Watson — slide guitar on "Bitch," "The Day I Was A Horse," and "Dying for It (The Blues)"
 * Stephen Pastel — production, additional guitar. backing vocals on "You Think You're A Man"
 * Gordon Rintoul, Ian Beveridge, Peter Haigh, Jamie Watson — engineers
 * Jane Higgins — design


text:
Magenta (disambiguation)

Magenta is a color.

Magenta may also refer to:

Places

 * Magenta, Lombardy, Italy
 * Magenta, Marne, France
 * Magenta, New South Wales, Australia

Media and entertainment

 * Magenta (comics), a DC Comics character, enemy of the Flash
 * Magenta (EP), a 2020 EP by South Korean singer/songwriter Kang Daniel
 * Magenta (film), a 1996 film by Gregory Haynes
 * "Magenta" (The Flash), an episode of The Flash
 * Magenta (Norwegian band), an alternative rock group
 * Magenta (Welsh band), a progressive rock group
 * Magenta, a character in The Rocky Horror Show
 * Magenta, a character from Blue's Clues and Blue's Clues & You!
 * Magenta Telekom, an Austrian subsidiary of T-Mobile

Other uses

 * Peristrophe bivalvis, also known as the magenta plant
 * MAGENTA, a block cipher
 * Magenta (Paris RER) rail station
 * Magenta Air, a Peruvian airline
 * A.S. Magenta, a New Caledonian football team
 * Battle of Magenta, an 1859 during the Second Italian War of Independence

People

 * Magenta Devine (1957–2019), British TV presenter and journalist
 * Giovanni Magenta (1565–1635), Italian architect
 * Guy Magenta (1927–1967), French composer
 * Muriel Magenta, visual artist

title: Magenta (disambiguation)


text:
VEP

Vep may refer to:

 * vep, the ISO 639-3 code for the Veps language
 * Vép, a town in Vas County, Hungary

VEP may refer to:

 * Variable electro-precipitator, a waste water remediation unit using electrocoagulation
 * Visual evoked potential, a nervous response to light
 * Venus Entry Probe, the former name of the European Venus Explorer
 * Voluntary Euthanasia Party, in Australia
 * Voter Education Project, a 1960s U.S. organisation for distributing funds to the civil rights movement
 * Signature of Victor E. Pazmiño, an American cartoonist
 * British Rail Class 423, aka "4Vep", "4VEP" or simply "VEP"
 * , a bioinformatic tool
 * Vulnerabilities Equities Process, used by the U.S. government to determine its response to security vulnerabilities

title: VEP