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Flash suppressor

A flash suppressor, also known as a flash guard, flash eliminator, flash hider, or flash cone, is a device attached to the muzzle of a rifle that reduces its visible signature while firing by cooling or dispersing the burning gases that exit the muzzle, a phenomenon typical of carbine-length weapons. Its primary intent is to reduce the chances that the shooter will be blinded in low-light shooting conditions. Contrary to popular belief, it is only a minor secondary benefit if a flash suppressor reduces the intensity of the flash visible to the enemy.

A flash suppressor is different from a muzzle brake, although they are typically mounted in the same position and sometimes confused with each other. While the former is intended to reduce visible flash, a muzzle brake is designed to reduce recoil inherent to large cartridges and typically does not reduce visible flash.

Rationale
Pre-20th century rifle designs tended to have longer barrels than modern rifles. A beneficial side effect of the long barrel is that the propellant is completely burned before the bullet leaves the barrel, usually resulting only in a puff of smoke from the muzzle. However, if the same weapon's barrel is "cut down" (shortened), as is common in cavalry and jungle-combat adapted versions, the bullet would often leave the barrel before the powder was completely consumed, resulting in a bright flash from the muzzle.

When barrel lengths were dramatically decreased with the introduction of various shorter-barreled rifles and carbines, the flash became a serious problem during night-time combat, as the flash would impair the shooter's night vision and would also make the shooter's position more apparent. Originally limited to "special purpose" roles, it was now expected that all infantry weapons with shorter barrels would experience this problem, and thereby be of limited use in low-light situations. Flash suppressors became common on late-World War II and later assault rifle designs, and are almost universal on these weapons today. Some designs such as those found on the AKS-74U serve a dual-role as a gas expansion chamber helping the shortened weapon's gas system function properly.

Military flash suppressors are designed to reduce the muzzle flash from the weapon to preserve the shooter's night vision, usually by diverting the incandescent gases to the sides, away from the line of sight of the shooter, and to secondarily reduce the flash visible to the enemy. Military forces engaging in night combat are still visible when firing, especially with night vision gear, and must move quickly after firing to avoid receiving return fire.

Limiting the amount of powder to what the length of a barrel can burn is one possible solution, but differences between individual cartridges mean that some cartridges will always have too much powder to be completely consumed, and the reduced powder load produces a lower projectile velocity. Muzzle flash can be controlled by using cartridges with a faster-burning propellant, so that the propellant gases will already have begun to cool by the time they exit the barrel, reducing flash intensities. Faster-burning powders, however, produce less projectile velocity, which reduces the accuracy, due to introducing a more parabolic bullet flight path in place of a "flat" trajectory, while also reducing the lethality of the weapon by reducing the distance of the projectile's penetration of the target.

Flash suppressors reduce, or in some cases eliminate, the flash by rapidly cooling the gases as they leave the end of the barrel. Although the overall amount of burning propellant is unchanged, the density and temperature are greatly reduced, as is the brightness of the flash.

Types

A number of different flash suppressing designs have been used over the years. The simplest is a cone placed on the end of the barrel, which was used on the late-World War II jungle-combat versions of the Lee–Enfield, the Rifle No. 5 Mk I variant, intended for use in the Pacific (the jungles of Malaya). More modern solutions tend to use a "basket" with several slits or holes cut in it, as seen on the M16 and other small-bore weapons. Cone-shaped flash eliminators are also evident on the ZB vzor 26 machine gun, and on the turret-mounted aircraft machine guns of British WWII heavy bombers, which were used mostly at night.

Duckbill flash suppressors have upper and lower "prongs" and direct gases to the sides. Early M60 machine guns and some Armalite AR-10, Armalite AR-15 and early M16 models featured this type of flash suppressor. One disadvantage is that the prongs can become entangled with vines or other natural vegetation and objects in the field.

"Birdcage type" flash suppressors still have prongs, but feature a ring on the front to prevent vegetation entanglement between the prongs. The closed bottom port of the M16A2 design makes the device function as a compensator. Both designs require indexing with a crush washer which unfortunately contributes to flash signature.

The Vortex Flash Hider is a design developed in 1984, with a patent secured in 1995. The Vortex is somewhat reminiscent of the original "three-prong flash hider" found on the original Vietnam-era M16. However, the Vortex is more robust and makes use of four solid tines, which are equally spaced and angled 6° from a centerline, while the slots of the body incorporate a 5-, 10-, and 15-degree twisted helix design, which eliminates up to 99% of visible muzzle flash by having the flash break up at multiple locations and angles.

The Noveske Rifleworks KX-3 is a flash suppressor intended for use on shorter barreled rifles and aids in reliability. The back pressure generated through this type of flash suppressor helps to cycle the rifle. Noveske patterned this design on the muzzle brake found on the Soviet AKS-74U carbine, where it was explicitly used for this purpose. Essentially it is the cone-shaped suppressor of the AKS-74U within a chamber. Some other examples of cone-shaped hiders are found on the Bren machine gun, the .303 Rifle No 5 Mk 1 "Jungle Carbine" and some models of the RPK and German MG3.

The XM177 Commando variant of the M16 rifle used a unique flash suppressor sometimes called a flash or sound moderator for its 10-inch barrel. This device is 4.2 inches long and was designed primarily as a counterbalance measure, as the shorter barrel made the weapon unwieldy. This device reduced flash signature greatly and sound signature slightly, making the normally louder short barreled rifle sound like a longer barreled M16A1. Although it has no internal baffles and does not completely reduce the sound signature to subsonic levels, because it alters the sound level of the weapon, the US Bureau of Alcohol Tobacco Firearms and Explosives has declared this device to be a sound suppressor and regulates its civilian purchase in the United States.

There are also devices referred to as hybrids that function as both flash suppressors and muzzle rise/recoil compensators, such as the White Sound Defense FOSSA-556. The U.S. military A2 muzzle device is technically a hybrid device, as it has vents that are biased upwardly to reduce muzzle rise.

New Zealand
Flash suppressors are seen as a "military" feature, and semi-automatic long guns with flash suppressors were defined as Military-Style Semi-Automatics in 1992, requiring a permit. Such weapons have since been prohibited.

United States
Flash suppressors were seen as "military" features and were on the list of federally defined features that could cause a rifle to be defined as illegal if the lower receiver was manufactured after the effective date of the Federal Assault Weapons Ban that went into effect in 1994 in the United States. This ban expired in 2004, although some states, such as California, Massachusetts, Maryland, New York, and New Jersey, have similar bans in place restricting the use of flash suppressors.

Germany and Australia
Flash suppressors and muzzle brakes can be legally acquired and used on all types of weapons, unless they are designed to significantly or predominantly reduce the sound.

title: Flash suppressor


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Hersonissos

Hersonissos (Χερσόνησος, meaning “peninsula”, Chersónisos, ), also transliterated as Chersonissos and Hersónisos, is a town and a local government unit in the north of Crete, bordering the Mediterranean / Aegean Sea. The town is about 25 kilometers east of Heraklion and west of Agios Nikolaos. What is usually called Hersonissos is in fact its peninsula and harbour. It is part of the Heraklion regional unit. It is situated 25 km from the Heraklion airport and 27 km from the Heraklion port. The seat of the local government unit is the village of Gournes.

Geography
The seaside resort of Hersonissos is officially the Port of Hersonissos (Λιμένας Χερσόνησου, Liménas Chersónissou) in distinction to the village of Upper Hersonissos (Άνω Χερσόνησος, Ano Chersónissos) further inland. Through tourism, the port town developed from the small harbour which served the original village, now known as Old Hersonissos.

History
The ancient town of Chersonasus was important enough in the Roman province of Creta et Cyrenaica early to become a Christian bishopric, a suffragan of the metropolitan see of Gortyna.

The names of some of its bishops appear in extant documents: Anderius took part in the Council of Ephesus in 431; Longinus in the Robber Council of 449; Euphratas was a signatory of the letter sent by the bishops of the province to the emperor Leo I the Thracian in 458 after the killing of Proterius of Alexandria; Sisinnius was at the Trullan Council in 692; and another Sisinnius at the Second Council of Nicaea in 787.

Latin bishopric
After the Venetian conquest of Crete in 1212, the existing dioceses, such as Chersonesus, were administered by Latin Church bishops.

The line of residential Latin bishops of Chersonesus ended with the conquest of Crete by the Ottomans in 1669.

Titular see
No longer a residential bishopric, Chersonnesus in Creta is today listed by the Catholic Church as a titular bishopric, as such nominally restored in 1787 under the name ‘Chersonesus’, changed in 1933 to Chersonesus in Creta, avoiding confusing with other Latin sees called Chersonesus.

It is vacant, having had the following incumbents, all of the lowest (episcopal) rank:
 * Karel Otčenášek (1950.03.30 – 1989.12.21) (later Archbishop)*
 * Titular Bishop: Bishop Antonio Cardona Riera (later Archbishop) (1928.03.10 – 1950.02.02)
 * Titular Bishop: Bishop Rafael Balanzá y Navarro (1923.08.13 – 1928.03.02)
 * Titular Bishop: Bishop Marc Chatagnon (沙), M.E.P. (1887.01.25 – 1920.11.26)
 * Titular Bishop: Bishop Johann Theodor Laurent (1839.09.17 – 1884.02.20)
 * Titular Bishop: Bishop Viktor Franz Anton von Glutz-Ruchti (1820.05.29 – 1824.10.09)
 * Titular Bishop: Bishop Ambrosi de Magistris (1818.10.02 – ?)
 * Titular Bishop: Bishop Johann Casimir von Häffelin (later Cardinal)* (1787.09.28 – 1818.04.06)

Municipality of Hersonissos
The municipality of Hersonissos was formed at the 2011 local government reform by the merger of the following 4 former municipalities, that became municipal units. These were Episkopi, Gouves, Hersonissos and Malia.

The municipality has an area of 272.17 km2, the municipal unit 70.98 km2.

Ancient remains
At the modern settlement of Hersonissos is the site of the ancient town of Chersonesos, an important seaport from Classical Greece through Byzantine times that served the city of Lyttos. The contemporaneous pleasure port is built over the remains of the Roman port. Some traces of those remains, most of them submerged, are still visible in some places. On the seaside street there is a pyramidal Roman fountain with mosaics of fishing scenes. On the top of the rocky hill behind the port stand the ruins of an early Christian basilica with floor mosaics.

The vicinity of Hersonissos is noted for its prehistoric archaeological finds. On the coast approximately one kilometer to the east of Hersonissos was an ancient temple dedicated to the goddess Britomartis.

William Smith’s Dictionary of Greek and Roman Geography states: "'CHERSONE’SUS (Χερσόνησος) … the haven of Lyctus, with a temple of Britomartis. 16 M P. from Cnossus. Robert Pashley found ruins close to a little port on the shore, and the actual names of the villages Khersónesos and Episcopianó, indicate that here is to be found what was once the ancient port of Lyctus, and afterwards became an Episcopal city."

The episcopal see associated with this town is now a titular see (“Chersonesus in Creta”) of the Catholic Church.

Tourism
Hersonissos is a resort area in Crete, which also hosts the only golf club on the island. Tourist sites include; the Hersonissos Aquarium, Labyrinth Theme Park, and the Dinosauria Park in Gournes. There are several beaches in Hersonissos, some with blue flag status. These include Potamos (blue flag) Karteros, Tobruk, Arina (municipal beach), Vathianos Kampos, Kokkini Hani, Gournes, Gouves, Apolselemis, Analipsi, Anissara (blue flag), Sarantaris (municipal beach), Hersonissos, Stalida, Klotsani, Malia and Potamos (municipal beach and blue flag).

Sources and external links

 * GCatholic.org
 * GCatholic.org

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

title: Hersonissos


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Computer lab

A computer lab is a space where computer services are provided to a defined community. These are typically public libraries and academic institutions. Generally, users must follow a certain user policy to retain access to the computers. This usually consists of rules such as no illegal activity during use or attempts to circumvent any security or content-control software while using the computers.

Computer labs are often subject to time limits in order to allow more people access to use the lab. It is also common for personal login credentials to be required for access. This allows institutions to track the user's activities for any possible fraudulent use. The computers in computer labs are typically equipped with internet access, scanners, and printers and are typically arranged in rows. This is to give the workstation a similar view to facilitate lecturing or presentations, and also to facilitate small group work.

For some academic institutions, student laptops or laptop carts take place of dedicated computer labs. However, computer labs still have a place in applications requiring special software or hardware which are not easily accessible in personal computers.

Purposes
While computer labs are generally multipurpose, some labs may contain computers with hardware or software optimized for certain tasks or processes, depending on the needs of the institution operating the lab. These specialized purposes may include video editing, stock trading, 3-D computer-aided design, programming, and GIS. Increasingly, these have become the main purposes for the existence of traditional desktop-style computer labs, due to rising ownership of inexpensive personal computers making use of the lab only necessary when the expensive, specialized software and more powerful computers needed to run it are required.

Alternatives
In some settings, traditional desktop computer labs are impractical due to the requirement of a dedicated space. Because of this, some labs use laptop carts instead of desktop setups, in order to both save space and give the lab some degree of mobility. In the context of academic institutions, some traditional desktop computer labs are being phased out in favor of other solutions judged to be more efficient given that most students own personal laptops. One of these solutions is a virtual lab, which can allow users to install software from the lab server onto their own laptops or log into virtual machines remotely, essentially turning their own laptops into lab machines.

Academic software bundles
Many universities purchase and maintain discounted academic software bundles and software suites, or free open-source software for their computer labs, such as programming text editors, programming languages, CAx software, rendering engines, Adobe Creative Cloud, Microsoft Office Suite, productivity software, statistical software, music software, video editing software, 3D animation software, and photo editing software.

Media lab
A media lab (often referred to as "new media lab" or "media research lab") is a term used for interdisciplinary organizations, collectives or spaces with the main focus on new media, digital culture and technology. The MIT Media Lab is a well-known example of a media lab.

Internet café
An Internet café differs from a computer lab in that usage of a computer lab is generally free for those with access, while Internet cafés charge for computer use. The term 'Internet café' is often used interchangeably with 'computer lab' but may differ from a computer lab in that users can also connect to the Internet using their own computer or device, and users of a computer lab generally do not need any equipment of their own.

title: Computer lab


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Colonial National Historical Park

Colonial National Historical Park is a large national historical park located in the Hampton Roads region of Virginia operated by the National Park Service. It protects and interprets several sites relating to the Colony of Virginia and the history of the United States more broadly. These range from the site of the first English settlement at Jamestown, to the battlefields of Yorktown where the British Army was defeated in the American Revolutionary War. Over 3 million people visit the park each year.

Colonial Parkway
The park includes the Colonial Parkway, a scenic 23 mi parkway linking the three points of Virginia's Historic Triangle: Jamestown and Yorktown and running through the historic district of Colonial Williamsburg. The Colonial Parkway is located in James City County, York County, and the city of Williamsburg.

Jamestown
The park includes the original site of Jamestown, known in modern times as Historic Jamestowne in James City County at the southern end of the Colonial Parkway. It encompasses the area of Jamestown Island, including the Jamestown Glasshouse. Adjacent to it is the Commonwealth of Virginia's complementary attraction known as Jamestown Settlement.

Yorktown Battlefield
The park operates the Yorktown Battlefield at the eastern end of the Colonial Parkway in York County at Yorktown. The Thomas Nelson House was built around 1724 and served as Cornwallis's headquarters during the final battle of the Revolutionary War.

The battlefield was the site of the British defeat. Both the house and the historic siege earthworks were restored in 1976. The Moore House is where surrender negotiations took place in 1781, located in the eastern part of the park.

Nearby are the state-operated American Revolution Museum at Yorktown and the Yorktown Riverwalk Landing area.

Green Spring Plantation
William Berkeley held the colonial governorship during the longest periods of any individual. He used his Green Spring Plantation as an experimental farm to develop sources of income for the colony other than cultivated tobacco and traded furs.

Cape Henry Memorial
The Cape Henry Memorial is at the site of the landing of Captain Christopher Newport and the Jamestown colonists in 1607. It is located in the city of Virginia Beach, Virginia at Cape Henry. It open to the public and is located off U.S. Route 60 on the Navy's Joint Expeditionary Base East.

Administrative history
Colonial National Monument was authorized on July 3, 1930. It was established on December 30, 1930. On June 5, 1936, it was redesignated a National Historical Park. The cemetery at Yorktown was transferred from the War Department to the National Park Service on August 10, 1933.

Jamestown National Historic Site is co-owned by the National Park Service and Preservation Virginia (formerly known as the Association for the Preservation of Virginia Antiquities) and administered by the NPS, was designated on December 18, 1940. Preservation Virginia owns 22 acre containing the remains of the original 1607 fort. The National Park Service owns the remaining 1178 acre of the island which contains the archeological remains of the expanded towne and its island plantation sites.

As with all historical areas administered by the National Park Service, Colonial National Historical Park and Jamestown National Historic Site are listed on the National Register of Historic Places of the U.S. Department of the Interior.

title: Colonial National Historical Park


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Talk:Netware Core Protocol

I removed the statement about "present in the Network Layer of" because if it uses IPX (which is a network layer protocol) then it can't be network layer itself. I don't know much about Novell protocols, so if someone knows what's up, feel free to fix it. Noel 23:31, 9 Nov 2003 (UTC)

title: Talk:Netware Core Protocol


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Urban Male Magazine

Urban Male Magazine (a.k.a. UMM) was a Canadian men's interest magazine created and operated by Abbis Mahmoud, an Ontario entrepreneur that also operates several nightclubs like Lobby, Mansion, Tila Tequila, Buddha Bar, Tequila Jacks and the Brunswick House. The magazine was launched in 1998 and published its last issue in 2013.

title: Urban Male Magazine


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Battle of Kirksville

The Battle of Kirksville took place during the American Civil War and was fought in the town of Kirksville, Missouri, on August 6, 1862. The Union victory helped consolidate Federal control over northeastern Missouri.

Battle

Confederate Col. Joseph C. Porter had been recruiting in the Macon area, to the south of Kirksville. He had assembled a brigade of between 1,500 and 2,500 ill-trained and poorly equipped troops, but his irregulars had harried and recruited as far north as Memphis, Missouri. Confederate sympathies in the Kirksville area were high (though Union sentiment was stronger than in surrounding counties), due to the Southern heritage of most of the residents. Porter had been urged to come to Kirksville by Confederate Captain Tice Cain, an Adair County farmer who claimed to be holding Kirksville with 500 fresh recruits. (In one of the battle's mysteries, Cain disappeared and was never heard from again, according to a descendant.)

Union Colonel John McNeil of the 2nd Missouri Cavalry Regiment and his troops, totalling about 1,000, had been pursuing Porter for more than a week. Before noon on August 6, McNeil attacked Porter in the town of Kirksville, where the Confederates had concealed themselves in homes and stores and among the crops in the nearby fields, especially in the county courthouse and the commercial buildings on the square. Their presence was discovered by a Union detachment that volunteered to ride around the square in order to draw fire and cause the Confederates to reveal themselves — an act of courage which cost two Union soldiers their lives. McNeil deployed his artillery before moving in a broad line towards the town square. The subsequent cannon fire demoralized the defenders, some of whom retreated behind a rail fence, west of the square.

The Union troops then advanced in two wings, with Lt. Col. William F. Shaffer of the 2nd Missouri in command of the Union right wing and Major Henry Clay Caldwell of the 3rd Iowa Cavalry Regiment in charge of the left. As the two wings met, they succeeded in driving the Confederates from the courthouse. Porter's remaining forces yielded ground and joined the others behind the rail fence. From this position, the Confederates poured heavy fire into McNeil's men, but were ultimately overwhelmed. The battle began at 11 a.m. and was over by 2 p.m.

The Federals then secured the town, capturing numerous prisoners, and driving away the remaining Confederates. Three days later, another Union force arrived and finished the work begun at Kirksville, virtually destroying Porter's command.

Aftermath
According to a letter by resident J. Martin, written a week after the battle, Confederate dead numbered about 200; Union 30. McNeill's official tally was 150 Confederates killed (300-400 wounded) against 6 Union deaths (32 wounded). Two civilian casualties were noted: James Dye, a sixty-year-old farmer with two sons in the Union army, was held overnight by Porter during his approach to the town, then told to be on his way, but shot as he left. The other was Mrs. Elizabeth Cutts (also given as "Kutz" and "Coots"). Most Kirksville residents had heeded Porter's warning to depart, but Cutts was shot when two Confederate soldiers attempted to enter the cellar where she was hiding, and she was hit by a Union bullet meant for them as she ran out.

John L. Porter, a prominent local citizen (no relation to the Confederate leader), asked for and was granted permission to treat the Confederate wounded. McNeil supplied a surgeon and instruments, the departed Porter having previously commandeered all medical equipment. The Confederate dead were deposited in several mass graves in Forest Llewellen Cemetery; a monument now marks the spot. Some were later recovered by their families. Fifteen Confederates were quickly court-martialed on McNeil's orders and executed for having violated previous parole agreements not to take up arms again until exchanged. Although the execution was permissible within military norms, it was seldom done and McNeil has been criticized for both the justice and necessity of the proceedings, by John L. Porter (see Kirksville Daily Express, 1912, below) and Joseph Mudd (see references to Palmyra massacre), among others.

A number of other questionable shootings followed, including those of Dr. John Davis (said by some to have been told to run and then shot when he did) and Lt. Col. Frisby McCullough — a subordinate of Porter who was tried and sentenced to death as a bushwhacker, even though he was captured wearing a regular Confederate uniform and carrying letters authorizing him to recruit troops. He was granted permission to give the order to fire, and his final words were, "May God forgive you for this cold-blooded murder. Aim at the heart. Fire!" A second volley was necessary.

McNeil's reputation would be darkened further by the "Palmyra Massacre" on October 18, but he would go on to serve two terms as Sheriff of St. Louis County, dying June 7, 1891. Porter died February 18, 1863, of wounds received in an engagement at Hartville.

The victory at Kirksville helped consolidate Union dominance in northeastern Missouri.

Memorial Park (the approximate location of the Union artillery) commemorates the battle.

Sources, references and links

 * National Park Service account
 * A Book of Adair County History, Kirksville, The Kirksville-Adair County Bicentennial Committee, 1976.
 * A History of Lewis, Clark, Knox and Scotland Counties, Missouri (detailed account from 1887)
 * County history
 * Contemporary news dispatches
 * Eyewitness accounts, and E.M. Violette's detailed history, from the Kirksville Daily Express Fiftieth Anniversary coverage
 * List of casualties
 * CWSAC Report Update

title: Battle of Kirksville


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Order theory

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary.

Background and motivation
Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.g. "2 is less than 3", "10 is greater than 5", or "Does Tom have fewer cookies than Sally?". This intuitive concept can be extended to orders on other sets of numbers, such as the integers and the reals. The idea of being greater than or less than another number is one of the basic intuitions of number systems (compare with numeral systems) in general (although one usually is also interested in the actual difference of two numbers, which is not given by the order). Other familiar examples of orderings are the alphabetical order of words in a dictionary and the genealogical property of lineal descent within a group of people.

The notion of order is very general, extending beyond contexts that have an immediate, intuitive feel of sequence or relative quantity. In other contexts orders may capture notions of containment or specialization. Abstractly, this type of order amounts to the subset relation, e.g., "Pediatricians are physicians," and "Circles are merely special-case ellipses."

Some orders, like "less-than" on the natural numbers and alphabetical order on words, have a special property: each element can be compared to any other element, i.e. it is smaller (earlier) than, larger (later) than, or identical to. However, many other orders do not. Consider for example the subset order on a collection of sets: though the set of birds and the set of dogs are both subsets of the set of animals, neither the birds nor the dogs constitutes a subset of the other. Those orders like the "subset-of" relation for which there exist incomparable elements are called partial orders; orders for which every pair of elements is comparable are total orders.

Order theory captures the intuition of orders that arises from such examples in a general setting. This is achieved by specifying properties that a relation ≤ must have to be a mathematical order. This more abstract approach makes much sense, because one can derive numerous theorems in the general setting, without focusing on the details of any particular order. These insights can then be readily transferred to many less abstract applications.

Driven by the wide practical usage of orders, numerous special kinds of ordered sets have been defined, some of which have grown into mathematical fields of their own. In addition, order theory does not restrict itself to the various classes of ordering relations, but also considers appropriate functions between them. A simple example of an order theoretic property for functions comes from analysis where monotone functions are frequently found.

Basic definitions
This section introduces ordered sets by building upon the concepts of set theory, arithmetic, and binary relations.

Partially ordered sets
Orders are special binary relations. Suppose that P is a set and that ≤ is a relation on P ('relation on a set' is taken to mean 'relation amongst its inhabitants', i.e. ≤ is a subset of the cartesian product P x P). Then ≤ is a partial order if it is reflexive, antisymmetric, and transitive, that is, if for all a, b and c in P, we have that:

 * a ≤ a (reflexivity)
 * if a ≤ b and b ≤ a then a = b (antisymmetry)
 * if a ≤ b and b ≤ c then a ≤ c (transitivity).

A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these properties, one immediately sees that the well-known orders on natural numbers, integers, rational numbers and reals are all orders in the above sense. However, these examples have the additional property that any two elements are comparable, that is, for all a and b in P, we have that:

 * a ≤ b or b ≤ a.

A partial order with this property is called a total order. These orders can also be called linear orders or chains. While many familiar orders are linear, the subset order on sets provides an example where this is not the case. Another example is given by the divisibility (or "is-a-factor-of") relation |. For two natural numbers n and m, we write n|m if n divides m without remainder. One easily sees that this yields a partial order. For example neither 3 divides 13 nor 13 divides 3, so 3 and 13 are not comparable elements of the divisibility relation on the set of integers. The identity relation = on any set is also a partial order in which every two distinct elements are incomparable. It is also the only relation that is both a partial order and an equivalence relation because it satisfies both the antisymmetry property of partial orders and the symmetry property of equivalence relations. Many advanced properties of posets are interesting mainly for non-linear orders.

Visualizing a poset
Hasse diagrams can visually represent the elements and relations of a partial ordering. These are graph drawings where the vertices are the elements of the poset and the ordering relation is indicated by both the edges and the relative positioning of the vertices. Orders are drawn bottom-up: if an element x is smaller than (precedes) y then there exists a path from x to y that is directed upwards. It is often necessary for the edges connecting elements to cross each other, but elements must never be located within an edge. An instructive exercise is to draw the Hasse diagram for the set of natural numbers that are smaller than or equal to 13, ordered by | (the divides relation).

Even some infinite sets can be diagrammed by superimposing an ellipsis (...) on a finite sub-order. This works well for the natural numbers, but it fails for the reals, where there is no immediate successor above 0; however, quite often one can obtain an intuition related to diagrams of a similar kind.

Special elements within an order
In a partially ordered set there may be some elements that play a special role. The most basic example is given by the least element of a poset. For example, 1 is the least element of the positive integers and the empty set is the least set under the subset order. Formally, an element m is a least element if:

 * m ≤ a, for all elements a of the order.

The notation 0 is frequently found for the least element, even when no numbers are concerned. However, in orders on sets of numbers, this notation might be inappropriate or ambiguous, since the number 0 is not always least. An example is given by the above divisibility order |, where 1 is the least element since it divides all other numbers. In contrast, 0 is the number that is divided by all other numbers. Hence it is the greatest element of the order. Other frequent terms for the least and greatest elements is bottom and top or zero and unit.

Least and greatest elements may fail to exist, as the example of the real numbers shows. But if they exist, they are always unique. In contrast, consider the divisibility relation | on the set {2,3,4,5,6}. Although this set has neither top nor bottom, the elements 2, 3, and 5 have no elements below them, while 4, 5 and 6 have none above. Such elements are called minimal and maximal, respectively. Formally, an element m is minimal if:

 * a ≤ m implies a = m, for all elements a of the order.

Exchanging ≤ with ≥ yields the definition of maximality. As the example shows, there can be many maximal elements and some elements may be both maximal and minimal (e.g. 5 above). However, if there is a least element, then it is the only minimal element of the order. Again, in infinite posets maximal elements do not always exist - the set of all finite subsets of a given infinite set, ordered by subset inclusion, provides one of many counterexamples. An important tool to ensure the existence of maximal elements under certain conditions is Zorn's Lemma.

Subsets of partially ordered sets inherit the order. We already applied this by considering the subset {2,3,4,5,6} of the natural numbers with the induced divisibility ordering. Now there are also elements of a poset that are special with respect to some subset of the order. This leads to the definition of upper bounds. Given a subset S of some poset P, an upper bound of S is an element b of P that is above all elements of S. Formally, this means that

 * s ≤ b, for all s in S.

Lower bounds again are defined by inverting the order. For example, -5 is a lower bound of the natural numbers as a subset of the integers. Given a set of sets, an upper bound for these sets under the subset ordering is given by their union. In fact, this upper bound is quite special: it is the smallest set that contains all of the sets. Hence, we have found the least upper bound of a set of sets. This concept is also called supremum or join, and for a set S one writes sup(S) or $$\bigvee S$$ for its least upper bound. Conversely, the greatest lower bound is known as infimum or meet and denoted inf(S) or $$\bigwedge S$$. These concepts play an important role in many applications of order theory. For two elements x and y, one also writes $$x\vee y$$ and $$x\wedge y$$ for sup({x,y}) and inf({x,y}), respectively.

For example, 1 is the infimum of the positive integers as a subset of integers.

For another example, consider again the relation | on natural numbers. The least upper bound of two numbers is the smallest number that is divided by both of them, i.e. the least common multiple of the numbers. Greatest lower bounds in turn are given by the greatest common divisor.

Duality
In the previous definitions, we often noted that a concept can be defined by just inverting the ordering in a former definition. This is the case for "least" and "greatest", for "minimal" and "maximal", for "upper bound" and "lower bound", and so on. This is a general situation in order theory: A given order can be inverted by just exchanging its direction, pictorially flipping the Hasse diagram top-down. This yields the so-called dual, inverse, or opposite order.

Every order theoretic definition has its dual: it is the notion one obtains by applying the definition to the inverse order. Since all concepts are symmetric, this operation preserves the theorems of partial orders. For a given mathematical result, one can just invert the order and replace all definitions by their duals and one obtains another valid theorem. This is important and useful, since one obtains two theorems for the price of one. Some more details and examples can be found in the article on duality in order theory.

Constructing new orders
There are many ways to construct orders out of given orders. The dual order is one example. Another important construction is the cartesian product of two partially ordered sets, taken together with the product order on pairs of elements. The ordering is defined by (a, x) ≤ (b, y) if (and only if) a ≤ b and x ≤ y. (Notice carefully that there are three distinct meanings for the relation symbol ≤ in this definition.) The disjoint union of two posets is another typical example of order construction, where the order is just the (disjoint) union of the original orders.

Every partial order ≤ gives rise to a so-called strict order <, by defining a < b if a ≤ b and not b ≤ a. This transformation can be inverted by setting a ≤ b if a < b or a = b. The two concepts are equivalent although in some circumstances one can be more convenient to work with than the other.

Functions between orders
It is reasonable to consider functions between partially ordered sets having certain additional properties that are related to the ordering relations of the two sets. The most fundamental condition that occurs in this context is monotonicity. A function f from a poset P to a poset Q is monotone, or order-preserving, if a ≤ b in P implies f(a) ≤ f(b) in Q (Noting that, strictly, the two relations here are different since they apply to different sets.). The converse of this implication leads to functions that are order-reflecting, i.e. functions f as above for which f(a) ≤ f(b) implies a ≤ b. On the other hand, a function may also be order-reversing or antitone, if a ≤ b implies f(a) ≥ f(b).

An order-embedding is a function f between orders that is both order-preserving and order-reflecting. Examples for these definitions are found easily. For instance, the function that maps a natural number to its successor is clearly monotone with respect to the natural order. Any function from a discrete order, i.e. from a set ordered by the identity order "=", is also monotone. Mapping each natural number to the corresponding real number gives an example for an order embedding. The set complement on a powerset is an example of an antitone function.

An important question is when two orders are "essentially equal", i.e. when they are the same up to renaming of elements. Order isomorphisms are functions that define such a renaming. An order-isomorphism is a monotone bijective function that has a monotone inverse. This is equivalent to being a surjective order-embedding. Hence, the image f(P) of an order-embedding is always isomorphic to P, which justifies the term "embedding".

A more elaborate type of functions is given by so-called Galois connections. Monotone Galois connections can be viewed as a generalization of order-isomorphisms, since they constitute of a pair of two functions in converse directions, which are "not quite" inverse to each other, but that still have close relationships.

Another special type of self-maps on a poset are closure operators, which are not only monotonic, but also idempotent, i.e. f(x) = f(f(x)), and extensive (or inflationary), i.e. x ≤ f(x). These have many applications in all kinds of "closures" that appear in mathematics.

Besides being compatible with the mere order relations, functions between posets may also behave well with respect to special elements and constructions. For example, when talking about posets with least element, it may seem reasonable to consider only monotonic functions that preserve this element, i.e. which map least elements to least elements. If binary infima ∧ exist, then a reasonable property might be to require that f(x ∧ y) = f(x) ∧ f(y), for all x and y. All of these properties, and indeed many more, may be compiled under the label of limit-preserving functions.

Finally, one can invert the view, switching from functions of orders to orders of functions. Indeed, the functions between two posets P and Q can be ordered via the pointwise order. For two functions f and g, we have f ≤ g if f(x) ≤ g(x) for all elements x of P. This occurs for example in domain theory, where function spaces play an important role.

Special types of orders
Many of the structures that are studied in order theory employ order relations with further properties. In fact, even some relations that are not partial orders are of special interest. Mainly the concept of a preorder has to be mentioned. A preorder is a relation that is reflexive and transitive, but not necessarily antisymmetric. Each preorder induces an equivalence relation between elements, where a is equivalent to b, if a ≤ b and b ≤ a. Preorders can be turned into orders by identifying all elements that are equivalent with respect to this relation.

Several types of orders can be defined from numerical data on the items of the order: a total order results from attaching distinct real numbers to each item and using the numerical comparisons to order the items; instead, if distinct items are allowed to have equal numerical scores, one obtains a strict weak ordering. Requiring two scores to be separated by a fixed threshold before they may be compared leads to the concept of a semiorder, while allowing the threshold to vary on a per-item basis produces an interval order.

An additional simple but useful property leads to so-called well-founded, for which all non-empty subsets have a minimal element. Generalizing well-orders from linear to partial orders, a set is well partially ordered if all its non-empty subsets have a finite number of minimal elements.

Many other types of orders arise when the existence of infima and suprema of certain sets is guaranteed. Focusing on this aspect, usually referred to as completeness of orders, one obtains:

 * Bounded posets, i.e. posets with a least and greatest element (which are just the supremum and infimum of the empty subset),
 * Lattices, in which every non-empty finite set has a supremum and infimum,
 * Complete lattices, where every set has a supremum and infimum, and
 * Directed complete partial orders (dcpos), that guarantee the existence of suprema of all directed subsets and that are studied in domain theory.
 * Partial orders with complements, or poc sets, are posets with a unique bottom element 0, as well as an order-reversing involution $$*$$ such that $$a \leq a^{*} \implies a = 0.$$

However, one can go even further: if all finite non-empty infima exist, then ∧ can be viewed as a total binary operation in the sense of universal algebra. Hence, in a lattice, two operations ∧ and ∨ are available, and one can define new properties by giving identities, such as

 * x ∧ (y ∨ z) =  (x ∧ y) ∨ (x ∧ z), for all x, y, and z.

This condition is called distributivity and gives rise to distributive lattices. There are some other important distributivity laws which are discussed in the article on distributivity in order theory. Some additional order structures that are often specified via algebraic operations and defining identities are

 * Heyting algebras and
 * Boolean algebras,

which both introduce a new operation ~ called negation. Both structures play a role in mathematical logic and especially Boolean algebras have major applications in computer science. Finally, various structures in mathematics combine orders with even more algebraic operations, as in the case of quantales, that allow for the definition of an addition operation.

Many other important properties of posets exist. For example, a poset is locally finite if every closed interval [a, b] in it is finite. Locally finite posets give rise to incidence algebras which in turn can be used to define the Euler characteristic of finite bounded posets.

Subsets of ordered sets
In an ordered set, one can define many types of special subsets based on the given order. A simple example are upper sets; i.e. sets that contain all elements that are above them in the order. Formally, the upper closure of a set S in a poset P is given by the set {x in P | there is some y in S with y ≤ x}. A set that is equal to its upper closure is called an upper set. Lower sets are defined dually.

More complicated lower subsets are ideals, which have the additional property that each two of their elements have an upper bound within the ideal. Their duals are given by filters. A related concept is that of a directed subset, which like an ideal contains upper bounds of finite subsets, but does not have to be a lower set. Furthermore, it is often generalized to preordered sets.

A subset which is - as a sub-poset - linearly ordered, is called a chain. The opposite notion, the antichain, is a subset that contains no two comparable elements; i.e. that is a discrete order.

Related mathematical areas
Although most mathematical areas use orders in one or the other way, there are also a few theories that have relationships which go far beyond mere application. Together with their major points of contact with order theory, some of these are to be presented below.

Universal algebra
As already mentioned, the methods and formalisms of universal algebra are an important tool for many order theoretic considerations. Beside formalizing orders in terms of algebraic structures that satisfy certain identities, one can also establish other connections to algebra. An example is given by the correspondence between Boolean algebras and Boolean rings. Other issues are concerned with the existence of free constructions, such as free lattices based on a given set of generators. Furthermore, closure operators are important in the study of universal algebra.

Topology
In topology, orders play a very prominent role. In fact, the collection of open sets provides a classical example of a complete lattice, more precisely a complete Heyting algebra (or "frame" or "locale"). Filters and nets are notions closely related to order theory and the closure operator of sets can be used to define a topology. Beyond these relations, topology can be looked at solely in terms of the open set lattices, which leads to the study of pointless topology. Furthermore, a natural preorder of elements of the underlying set of a topology is given by the so-called specialization order, that is actually a partial order if the topology is T0.

Conversely, in order theory, one often makes use of topological results. There are various ways to define subsets of an order which can be considered as open sets of a topology. Considering topologies on a poset (X, ≤) that in turn induce ≤ as their specialization order, the finest such topology is the Alexandrov topology, given by taking all upper sets as opens. Conversely, the coarsest topology that induces the specialization order is the upper topology, having the complements of principal ideals (i.e. sets of the form {y in X | y ≤ x} for some x) as a subbase. Additionally, a topology with specialization order ≤ may be order consistent, meaning that their open sets are "inaccessible by directed suprema" (with respect to ≤). The finest order consistent topology is the Scott topology, which is coarser than the Alexandrov topology. A third important topology in this spirit is the Lawson topology. There are close connections between these topologies and the concepts of order theory. For example, a function preserves directed suprema if and only if it is continuous with respect to the Scott topology (for this reason this order theoretic property is also called Scott-continuity).

Category theory
The visualization of orders with Hasse diagrams has a straightforward generalization: instead of displaying lesser elements below greater ones, the direction of the order can also be depicted by giving directions to the edges of a graph. In this way, each order is seen to be equivalent to a directed acyclic graph, where the nodes are the elements of the poset and there is a directed path from a to b if and only if a ≤ b. Dropping the requirement of being acyclic, one can also obtain all preorders.

When equipped with all transitive edges, these graphs in turn are just special categories, where elements are objects and each set of morphisms between two elements is at most singleton. Functions between orders become functors between categories. Many ideas of order theory are just concepts of category theory in small. For example, an infimum is just a categorical product. More generally, one can capture infima and suprema under the abstract notion of a categorical limit (or colimit, respectively). Another place where categorical ideas occur is the concept of a (monotone) Galois connection, which is just the same as a pair of adjoint functors.

But category theory also has its impact on order theory on a larger scale. Classes of posets with appropriate functions as discussed above form interesting categories. Often one can also state constructions of orders, like the product order, in terms of categories. Further insights result when categories of orders are found categorically equivalent to other categories, for example of topological spaces. This line of research leads to various representation theorems, often collected under the label of Stone duality.

History
As explained before, orders are ubiquitous in mathematics. However, the earliest explicit mentionings of partial orders are probably to be found not before the 19th century. In this context the works of George Boole are of great importance. Moreover, works of Charles Sanders Peirce, Richard Dedekind, and Ernst Schröder also consider concepts of order theory.

Contributors to ordered geometry were listed in a 1961 textbook: "It was Pasch in 1882, who first pointed out that a geometry of order could be developed without reference to measurement. His system of axioms was gradually improved by Peano (1889), Hilbert (1899), and Veblen (1904)."

In 1901 Bertrand Russell wrote "On the notion of order" exploring the foundations of the idea through generation of series. He returned to the topic in part IV of The Principles of Mathematics (1903). Russell noted that binary relation aRb has a sense proceeding from a to b with the converse relation having an opposite sense, and sense "is the source of order and series". (p 95) He acknowledges Immanuel Kant was "aware of the difference between logical opposition and the opposition of positive and negative". He wrote that Kant deserves credit as he "first called attention to the logical importance of asymmetric relations."

The term poset as an abbreviation for partially ordered set is attributed to Garrett Birkhoff in the second edition of his influential book Lattice Theory.

title: Order theory


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Triforce

The Triforce (トライフォース) is a fictional artifact and icon of Nintendo's The Legend of Zelda video game franchise. It first appeared in the original The Legend of Zelda video game (1986) and has appeared in every subsequent game in the series. It consists of three equilateral triangles that are joined to form a large equilateral triangle. In the fictional history of the series, it represents the essence of the Golden Goddesses named Din, Nayru and Farore who create Hyrule. Imbued with divine power, it is capable of granting any wish to anyone who possesses it.

The three pieces of the Triforce are in the possession of the three main characters of the series, Ganon, Zelda and Link, who each embody one of its virtues: Power, Wisdom and Courage. The Triforce has frequently been the main objective in the series, requiring the player to search for its shards and protect it from Ganon, who seeks its power for evil purposes.

The Triforce is a central motif of The Legend of Zelda series, frequently appearing in Zelda iconography and merchandise. It has appeared in related media, including manga, video games and an animated television series. Due to its prominence and significance within the mythology of the Zelda series, the Triforce has become a widely recognisable symbol in gaming.

Background
Although the Triforce has become associated with The Legend of Zelda series, an identical symbol originated nearly 1,000 years before in medieval Japan. The symbol takes historical reference from the Hōjō clan, a family that took control of Japan in the 13th century. Its emblem (mon) was the mitsuuroko, or "three scales". The symbol also appears frequently in contemporary Japanese culture. It appears on the logos for large and small businesses and can be found on temples and family memorials. Since the release of The Legend of Zelda video game in 1986, the Triforce has become a recognisable icon of The Legend of Zelda series, appearing in every game in some form, particularly as part of the heraldry of the Kingdom of Hyrule.

Concept and creation
Shigeru Miyamoto, creator of The Legend of Zelda series, explained his vision for the first game in an interview with Gamekult. He said that the Triforce fragments were originally supposed to be electronic chips, as the game was intended to be set in both the past and the future. This early futuristic concept was abandoned and replaced by a heroic fantasy. In The Legend of Zelda video game, the Triforce was simply described as magical triangles of great power, but its significance was expanded in subsequent games. The first game established it as an object of desire and a central plot device that binds the three characters. Initially comprising two pieces, the third piece, the Triforce of Courage, was introduced in Zelda II: The Adventure Of Link.

Characteristics
The Triforce consists of three equilateral triangles that are joined to create a large equilateral triangle. Its design resembles the Sierpiński triangle. The three pieces are the Triforce of Power, the Triforce of Wisdom, and the Triforce of Courage, which represent the qualities of the Golden Goddesses who create the land of Hyrule, named Din, the Goddess of Power; Nayru, the Goddess of Wisdom; and Farore, the Goddess of Courage. In the creation myth of the series, they create the Triforce and entrust it to the Goddess Hylia. As a divine relic infused with the power of the goddesses, the Triforce is an object of limitless power, capable of granting any wish to anyone who touches it. Its place of origin is known as the Sacred Realm.

The Triforce can only be wielded by someone who possesses a balance of the three virtues in their heart: Power, Wisdom and Courage. Conversely, if held by someone with an imbalanced heart, it splits into three pieces, with each piece bestowed on a person who represents that quality. The three virtues of the Triforce are distributed amongst the three main characters in the series respectively, Ganon, Princess Zelda and Link. In some Zelda games, it manifests as a symbol on the hand of the bearer of one of the pieces. The trinity within the Triforce creates a moral balance, with evil seeking Power, and Wisdom and Courage being the opposing forces for good. A recurring theme of the series is Ganon's plan to steal the Triforce from the Sacred Realm in order to use its power to conquer Hyrule, which is ultimately thwarted by Link and Zelda. This places the three characters in an endless battle that is repeated across the fictional timeline within a reincarnation cycle.

The Legend of Zelda series
The Triforce is a common symbol found in the series. It is connected with the Royal Family of Hyrule and displayed as part of the Hyrule Royal Family's signature crest, which combines the Triforce with a fictional bird called a Crimson Loftwing. It is also found on various objects within the games such as the Master Sword and the Hylian Shield and on sacred sites, such as the Temple of Time.

In 1986, the original The Legend of Zelda video game introduced the Triforce, which consisted of two pieces, as a central plot device. It involves the hero, Link, embarking on a quest to save Hyrule from the evil Ganon, who has stolen the Triforce of Power. After Princess Zelda splits the Triforce of Wisdom into eight fragments and scatters them across the land, Link must search for the fragments and reassemble them to rescue Princess Zelda and defeat Ganon.

Zelda II: The Adventure of Link (1987) established the Triforce of Courage as the third piece of the Triforce. The game's instruction manual tells the backstory of Princess Zelda being placed in a magical sleep by a wizard and sets Link's fate as the hero who will wake her by marking the back of his hand with the Triforce. The story involves Link obtaining six crystals and then claiming the Triforce of Courage from the Great Palace. Using the three pieces of the Triforce, he is able to awaken sleeping Zelda from her curse.

The third game in the series titled A Link to the Past (1991) introduces a detailed fictional lore for the Triforce. In Japan, it was released with the title Triforce of the Gods. The game's instruction booklet provides the creation myth explaining how three Golden Goddesses named Din, Nayru, and Farore descended to create the land of Hyrule and then created the Triforce and imbued it with the essence of their power. In the game's backstory, Ganon enters the Sacred Realm to steal the Triforce and plunges it into darkness, creating the Dark World. To prevent Ganon from escaping and destroying the Light World, Link saves Zelda and the Sages. In the final scenes, he uses the Triforce to wish for the characters in the game to be restored.

Ganon, in his humanoid form of Ganondorf, again pursues his goal of obtaining the Triforce in Ocarina of Time (1998). Ganondorf manages to gain entry to the Sacred Realm and takes over Hyrule, plunging it into chaos. After a seven-year sleep, Link awakens as an adult and sets off to protect the Triforce from Ganondorf by travelling back and forth in time. With the help of Seven Sages, he successfully defeats Ganondorf by sealing him in the Sacred Realm. The game established the trinity of the characters each embodying one of the virtues of the Triforce.

When the game duo titled The Legend of Zelda: Oracle of Seasons and Oracle of Ages (2001) were conceived, they were originally intended to be a trilogy, with each story centred on one of the three virtues of the Triforce. In each game the Triforce initiates the adventure by summoning Link and transporting him to the worlds of Holodrum and Labrynna to collect eight Essences of Nature or Time in order to defeat the games' villains, Onox and Veran.

In The Wind Waker (2002), Link must collect eight pieces of the Triforce of Courage, which are scattered across the islands on the map, before he is ready to confront Ganondorf. The Triforce hunt, which was described by GameSpot as "infamous", is a lengthy process involving finding the chart locations, returning to Tingle and then finding the Triforce shards. Due to the tedious nature of the task, it was later simplified in The Wind Waker HD. In the finale, Ganondorf unites the Triforce, but before he can make his wish to rule Hyrule, the King of Hyrule's spirit touches it and wishes for Hyrule to be destroyed, resulting in a final battle between Ganondorf, Link and Zelda.

The Triforce does not play a major role in Twilight Princess (2006). At the beginning of the game, each of the three main characters is shown to be in possession of their individual component by glowing triangles that appear on their hands, but otherwise the Triforce only appears on murals and buildings.

Skyward Sword (2011) again focuses on the creation of the Triforce by the three Goddesses. In the game's backstory, demonic creatures rise from cracks in the earth led by Demonic King Demise with the intention of claiming the Triforce. To protect it, the goddess Hylia commands an army of the world's people to fight Demise. She seals him away and after becoming mortal, sends the humans to live above the surface world in Skyloft. She hides the Triforce in the sky to await the hero, Link, who recovers the three Triforce pieces from the Sky Keep and uses its powers to defeat Demise.

In A Link Between Worlds (2013), another version of the Triforce was introduced in the fictional universe. In Japan, the game is known as Triforce of the Gods 2, as it is a spiritual sequel to A Link to the Past. It takes place in two mirrored worlds, the Light World (Hyrule) and the Dark World (Lorule). Unlike Hyrule, Lorule has crumbled, caused by its people destroying its own Triforce, due to it being the cause of war. To save her world, Princess Hilda plots to steal Hyrule's Triforce. By the end of the game, she sympathises with Hyrule and allows Link and Zelda to return there with their Triforce. In an act of compassion, the two use the Hyrulean Triforce to recreate Lorule's Triforce.

Nintendo published Tri Force Heroes (2015) for the 3DS, a cooperative multiplayer game involving three Links dressed in red, blue and green. Hiromasa Shikata, the game's director, explained that the concept for the game was a "triangular relationship between three players".

Despite its prominence in the Zelda series, the Triforce plays no part in the storyline of Breath of the Wild (2017). It appears in various places within the game and manifests itself on the hand of Zelda in the battle against Calamity Ganon. The three virtues of the Triforce are present in the form of three springs located in different regions of the map, namely the Spring of Power, the Spring of Wisdom and the Spring of Courage. The Triforce continued to be absent from the series as a plot device with the release of Tears of the Kingdom (2023), although it appears on in-game architecture and as a tattoo on the arm of the character Sonia. This has led to speculation amongst players that it has been abandoned as a major element of the series.

Television series
In The Legend of Zelda animated series the Triforce consists of two pieces, with Ganon possessing the Triforce of Power and Zelda possessing the Triforce of Wisdom. The plot of each episode revolves around Ganon's attempts to gain control of both Triforce pieces so that he can become the ruler of Hyrule. The series gave the Wisdom and Power pieces a voice and a role in the story. Phil Harnage, one of the show's writers explained that this dialogue was used to explain the show's events. The cartoon's voice cast included Elizabeth Hanna as the Triforce of Wisdom and Allen Stewart-Coates as the Triforce of Power.

Manga and comics
Following the release of The Legend of Zelda video game, a companion manga book titled The Hyrule Fantasy was released in Japan by Wanpaku Comics in September 1986. It follows the game's story, involving the eight fragments of the Triforce. In 1992, a Choose Your Own Adventure-style book was released in Japanese titled The Legend of Zelda: The Triforce of the Gods. It was based on A Link to the Past, though some story elements deviated from the game. Two manga adaptations of A Link to the Past were also published by Ataru Cagiva in 1995 and Akira Himekawa in 2005 with the Japanese title Triforce of the Gods. Akira Himekawa also produced a manga book published by Viz Media, which is based on Ocarina of Time and follows the game's plot involving Link's quest to protect the Triforce from Ganondorf. In the early 1990s, Valiant Comics published The Legend of Zelda comic book based on the animated series. In the third issue, Link is corrupted by the Triforce of Power and attacks Zelda to obtain the Triforce of Wisdom. In the fifth issue, the second storyline is titled "The Day of the Triforce", which involves Link battling without his Triforce power due to its disappearance.

Video games
The Triforce has appeared in various other video games. In the series spin-off hack and slash video game Hyrule Warriors (2014), the Triforce is the objective for one of the main antagonists, Cia. Originally a guardian of the Triforce, she is corrupted by Ganon after displaying affections for Link and builds an army to obtain the Triforce. It also appears in the Super Smash Bros. series. In Super Smash Bros. Brawl Link uses the Triforce in his final smash. In Super Smash Bros for Nintendo 3DS and Wii U, Link's and Toon Link's final smash is the Triforce Slash, which traps enemies in the Triforce before relentlessly slashing at them. In Super Smash Bros. Ultimate, the Triforce Slash appears in Toon Link's and Young Link's "Final Smash" attack. In the same game, Zelda uses the Triforce of Wisdom as her Final Smash, which produces a glowing triangle that sucks in opponents and deals damage. In Sonic Lost World's The Legend of Zelda DLC stage, Sonic the Hedgehog travels through Hyrule in search of the Triforce. In Mario Kart 8's The Legend of Zelda × Mario Kart 8 expansion pack and its enhanced Nintendo Switch port, one of the grand prix cups is known as the "Triforce Cup" with custom vehicle parts including the Triforce Tires. The Triforce was used in Splatoon 3 by Nintendo to promote Tears of the Kingdom prior to its release in May 2023. In the Triforce Splatfest, players were asked to choose Power, Wisdom or Courage as their team. The Tricolor Turf War was fought on a triangular map to represent the shape of the Triforce.

Other media
In 2017, Nintendo rolled out an escape room experience across eight cities in North America titled "Defenders of the Triforce".

"Triforce" is also a name given to an arcade board system that was a joint venture from three companies; Namco, Nintendo and Sega using a combination of Nintendo GameCube and Sega GD-ROM hardware inside a Namco cabinet.

In popular culture
The Triforce has been used as a shibboleth and a meme to embarrass newer users of the imageboard website 4chan. Experienced users write it using Unicode characters, but copying and pasting the Triforce results in the symbol becoming misaligned.

Due to its simple design and popularity with gamers, the Triforce has become one of the most popular gaming tattoos. Professional wrestler Cody Rhodes, a longtime Legend of Zelda fan, formerly had the Triforce on his wrestling boots in his early career with the WWE.

The Triforce has inspired the production of Zelda-themed products, including a beer named Triforce IPA.

In 2023, the British metal band DragonForce released a single titled "Power of the Triforce", which is a tribute to The Legend of Zelda series.

Merchandise
The Triforce regularly appears on official Zelda merchandise, including clothing and accessories. It is prominently displayed on the cover of The Legend of Zelda Encyclopedia, which is published by Dark Horse. In 2023, it was recreated as a logic puzzle for Nintendo by a Japanese toy manufacturer. Images of the Triforce appear on a set of official t-shirts that were released for the Triforce-themed Splatfest.

Reception
The Triforce has become a recognisable icon of The Legend of Zelda series. It has been carved into headstones and used as a family crest. Brian Ashcraft of Kotaku commented that, although the inspiration for the Triforce is unknown, the symbol is found on the grave of Japanese video game designer Gunpei Yokoi, creator of the Game Boy, as his family crest or "kamon" (家紋). Florent Gorges, author of The History of Nintendo, opined that the symbol is so ubiquitous in Japan that Yokoi's protégé, Shigeru Miyamoto, could not have ignored it and had reused the design for the Zelda series. Ashcraft also remarked that the Triforce had such an impact on the younger Japanese generation, that the crest is now widely recognised, not as the mitsuuroko symbol, but as the icon of The Legend of Zelda series. In 1999, the Triforce in Ocarina of Time became the centre of a hoax, where a user account successfully convinced the Zelda fandom that the Triforce could be acquired, by posting a series of fake hints that were eventually debunked. Kotaku described it as "one of the greatest hoaxes in video game history". In 2016, Kate Gray of TechRadar noted that players persisted in their search for the Triforce in Ocarina of Time, using various methods of play in the hope of recovering it.

Stephen Totilo, writing for Kotaku, highlighted that in 2016 Zelda series producer Eiji Aonuma used the Triforce to reinforce the fixed gender roles of the three main characters in the series. Aonuma stated that the concept of creating a female version of Link, "would mess with the balance of the Triforce" and had been rejected by Nintendo for that reason. Jacob Kastrenakes of The Verge strongly disagreed by commenting that, although the three characters possess and embody the three virtues of the Triforce, the pieces could "theoretically be held by others in Hyrule" and that none of the Triforce pieces relate to gender.

The Triforce has been the subject of interpretation with regards to its significance within the Zelda series. Luke Cuddy considered that the Triforce can be interpreted as a lesson in morality that can be applied in the real world, as each of the three Triforce pieces is equal and could be used by the three main characters for good or evil, depending on how they choose to act. Anthony Bean opined that the Triforce is a symbol of the self in Jungian psychology, because it "serves as a connection between Hyrule (the conscious, mortal realm) and the goddesses (the unconscious, divine realm) just as the self serves as a meeting point for the ego and the unconscious". Edge staff commented that the Triforce is the deus ex machina of The Legend of Zelda series, stating that, of all the world-saving devices in gaming, it is "the most visually iconic and symbolically potent one" and noted its Christian similarities: "salvation through a trinity that is also one".

Luke Plunkett of Kotaku opined that the Triforce is "one of the most iconic designs in the history of video games" and "the object that lies at the heart of The Legend of Zelda". Eurogamer staff commented that the Triforce symbolises "Zelda's perpetually cycling legend" and is the blueprint for every game in the series, with Link representing "agency, curiosity, the eternal innocence", Ganon representing "selfishness, megalomania, destruction" and Zelda representing "insight and direction". Nicole Carpenter for Polygon commented that the Triforce has become a ubiquitous symbol that is widely recognised amongst gamers. She highlighted that it creates a sense of community for many isolated gamers and also provides personal significance to those who find comfort and meaning in its symbolism.

title: Triforce


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Toro (magazine)

Toro was a Canadian men's magazine. It was named by its owner, Christopher Bratty. The editorial was overseen by Derek Finkle. Cameron Williamson and Alicia Kowalewski were the creative and art directors, respectively.

Brand lineage
In 2003, TORO magazine entered into the Canadian marketplace as a glossy men's lifestyle publication, distributed by The Globe and Mail as well as by subscription and newsstand. During its four-year run, TORO garnered more than 60 National Magazine Award nominations. In 2007, TORO magazine suspended publication.

A web-only version of TORO launched in May 2008, co-founded by Christopher Bratty and William Morassutti, the founding editor. The digital TORO reached a peak monthly readership of 543,000 unique visitors in October, 2010 (ComScore/October, 2010) and operated for five years, until 2013, at which point publication was suspended.

Print covers

 * Sam Roberts (April/May 2003)
 * Donald Sutherland (June/July 2003)
 * Ryan Gosling (August/September 2003)
 * Estella Warren (October/November 2003)
 * Melissa Auf der Maur (Winter 2003)
 * Jessica Paré (April 2004)
 * Barry Pepper (March 2004)
 * Ryan Reynolds (Winter 2004)
 * Rachel Blanchard (September 2004)
 * Dita Von Teese (October 2004)
 * Jesse Palmer (November 2004)
 * Daniel Igali (Summer 2004)
 * David Cronenberg (Summer 2004)
 * Sofía Vergara (October 2005)
 * Steve Nash (November 2005)
 * Elisha Cuthbert (May 2005)
 * Kristin Kreuk (Summer 2005)
 * Scott Speedman (April 2005)
 * Wilmer Valderrama (Winter 2005)
 * Paul Walker (March 2006)
 * Gretchen Mol (April 2006)
 * Mía Maestro (May 2006)
 * Jason Bay (Summer 2006)
 * Elizabeth Banks (September 2006)
 * John Cena (October 2006)
 * Ricky Williams (November 2006)
 * Beau Garrett (Winter 2006)
 * Hayden Christensen (March 2007)

Print Talking To's

 * Rick Marin (April/May 2003)
 * Gord Downie (June/July 2003)
 * Bryan Adams (August/September 2003)
 * Phil Esposito (October/November 2003)
 * David Bowie (Winter 2003)
 * Éric Gagné (April 2004)
 * Ed Robertson, Mia Kirshner (March 2004)
 * Chandra West (Winter 2004)
 * Jessalyn Gilsig (September 2004)
 * Brian Wilson (October 2004)
 * Tricia Helfer (May 2004)
 * Julie Delpy, Solitair, Ivana Santilli, Mitchie Mee, Buck 65, Kyprios, Graph Noble, Abs&Fase (Summer 2004)
 * Ashley Scott (September 2005)
 * Sheryl Crow, Jay Baruchel, Tom Green, Will Arnett (October 2005)
 * Franz Ferdinand, Maggie Grace, Benz Antoine (November 2005)
 * Paul Haggis (May 2005)
 * Kate Pierson, Justin Chatwin (May 2005)
 * Joel Plaskett, The Stills, The Dears, Arcade Fire, Melissa George (April 2005)
 * Emilie de Ravin (March 2006)
 * The Streets (May 2006)
 * MSTRKRFT, Josh Dean, Leslie Bibb (Summer 2006)
 * John Lithgow, Justin Timberlake, Emily Haines, Sarah Carter (October 2006)
 * Gordon Moakes (March 2007)

Print TORO Woman

 * Joanne Kelly (April/May 2003)
 * Esthero (June/July 2003)
 * Sarah Polley (August/September 2003)
 * Kristin Booth (October/November 2003)
 * Caroline Dhavernas (Winter 2003)
 * Lindy Booth (April 2004)
 * Feist (March 2004)
 * Erica Durance (Winter 2004)
 * Melyssa Ford (September 2004)
 * Tamara Hope (October 2004)
 * Evelyn Ng (November 2004)
 * Tanya Reid (May 2004)
 * Françoise Yip (Summer 2004)
 * Katheryn Winnick (September 2005)
 * Kristin Adams (October 2005)
 * Sarah Carter (November 2005)
 * Karen Cliche (May 2005)
 * Cobie Smulders (Summer 2005)
 * Emily Van Camp (April 2005)
 * Gina Holden (March 2006)
 * Tania Saulnier (April 2006)
 * Vanessa Lengies, Peregrym (May 2006)
 * Michelle Lombardo (Summer 2006)
 * Natassia Malthe (September 2006)
 * Shelby Fenner (October 2006)
 * Crystal Lowe (Winter 2006)
 * Brooke Nevin (March 2007)

Web TORO Woman

 * Adrienne Kress (January 2009)

title: Toro (magazine)


text:
Maxwell Smart

Maxwell Smart may refer to:

 * Maxwell Smart, fictional character in the television series Get Smart.
 * Maxwell Smart, a Holocaust survivor and subject of the 2023 film The Boy in the Woods.

title: Maxwell Smart


text:
Strut

A strut is a structural component commonly found in engineering, aeronautics, architecture and anatomy. Struts generally work by resisting longitudinal compression, but they may also serve in tension.

Human anatomy
Part of the functionality of the clavicle is to serve as a strut between the scapula and sternum, resisting forces that would otherwise bring the upper limb close to the thorax. Keeping the upper limb away from the thorax is vital for its range of motion. Complete lack of clavicles may be seen in cleidocranial dysostosis, and the abnormal proximity of the shoulders to the median plane exemplifies the clavicle's importance as a strut.

Architecture and construction
Strut is a common name in timber framing for a support or brace of scantlings lighter than a post. Frequently struts are found in roof framing from either a tie beam or a king post to a principal rafter. Struts may be vertically plumb or leaning (then called canted, raking, or angled) and may be straight or curved. In the U.K., strut is generally used in a sense of a lighter duty piece: a king post carries a ridge beam but a king strut does not, a queen post carries a plate but a queen strut does not, a crown post carries a crown plate but a crown strut does not.

Strutting or blocking between floor joists adds strength to the floor system.

Struts provide outwards-facing support in their lengthwise direction, which can be used to keep two other components separate, performing the opposite function of a tie.

In piping, struts restrain movement of a component in one direction while allowing movement or contraction in another direction.

Strut channel made from steel, aluminium, or fibre-reinforced plastic is used heavily in the building industry and is often used in the support of cable trays and other forms of cable management, and pipes support systems.

Aircraft
Bracing struts and wires of many kinds were extensively used in early aircraft to stiffen and strengthen, and sometimes even to form, the main functional airframe. Throughout the 1920s and 1930s they fell out of use in favour of the low drag cantilever construction. Most aircraft bracing struts are principally loaded in compression, with wires taking the tension loads. Lift struts came into increasing use during the changeover period and remain in use on smaller aircraft today where ultimate performance is not an issue. Typically, they are applied to a high wing monoplane and act in tension during flight.

Struts have also been widely used for purely structural reasons to attach engines, landing gear and other loads. The oil-sprung legs of retractable landing gear are still called Oleo struts.

Automobiles
As components of an automobile chassis, struts can be passive braces to reinforce the chassis and/or body, or active components of the suspension. An example of an active unit would be a coilover design in an automotive suspension. The coilover combines a shock absorber and a spring in a single unit.

A common form of automotive suspension strut in an automobile is the MacPherson strut. MacPherson struts are often purchased by the automakers in sets of four completed sub-assemblies: These can be mounted on the car bodies as part of the manufacturers' own assembly operations. A MacPherson strut combines the primary function of a shock absorber (as a damper), with the ability to support sideways loads not along its axis of compression, somewhat similar to a sliding pillar suspension, thus eliminating the need for an upper suspension arm. This means that a strut must have a more rugged design, with mounting points near its middle for attachment of such loads.

Another common type of strut used in air suspension is an air strut which combines the shock absorber with an air spring and can be designed in the same fashion as a coilover device. These come available in most types of suspension setups including beam axle and MacPherson strut style design.

Transportation-related struts are used in "load bearing" applications ranging from both highway and off-road suspensions to automobile hood and hatch window supports to aircraft wing supports. The majority of struts feature a bearing, but only for the cases, when the strut mounts operate as steering pivots. For such struts, the bearing is the wear item, as it is subject to constant impact of vibration and its condition reflects both wheel alignment and steering response. In vehicle suspension systems, struts are most commonly an assembly of coil-over spring and shock absorber. Other variants to using a coil-over spring as the compressible load bearer include support via pressurized nitrogen gas acting as the spring, and rigid (hard tail) support which provides neither longitudinal compression/extension nor damping.

History
Struts were created in the 1970s in which automakers transitioned from large rear-wheeled drive vehicles to more fuel-efficient front-wheeled drive vehicles. The entire suspension system was changed in accordance to meet the new style of vehicles. The new styles of vehicles left less room for the traditional system, which was called the short-arm/ long-arm suspension systems. This caused the MacPherson strut system to become the new standard for all automobiles including front-wheeled and rear-wheeled vehicles. The MacPherson strut system does not require an upper control arm, bushings, or a pivot shaft like previous models.

Options on vehicles
Struts are not necessarily needed components on vehicles which separate the springs and shock absorbers, while the shocks support no weight. There are also some vehicles with the option of only having one pair of struts on one set of wheels while the other pair uses a separate selection of shocks and springs. This singular pair of struts are almost always a MacPherson strut. These choices are made for various reasons including the balance of initial cost, performance, and other elements. Some vehicles use a "double wishbone," suspension system which exclusively uses shock absorbers. Sports cars seem to favor this suspension style; however, the Porsche 911 favors traditional struts.

Maintenance
Struts keeps your suspension aligned, along with numerous other functions. To check if a set of struts is failing; simply walk to each side of the wheel and begin to bounce the car up and down. As the car is pushed down, let it bounce back into position. If it continues to bounce up and down, consider taking your vehicle to a mechanic for replacement. You can also check your strut car to see if it's leaking oil. Bad struts could possibly lead to many issues including the breaking of a wheel, flattening of a tire, damaged power steering, broken springs, broken joints, and many more issues in your suspension system. Keep all of these in mind as you drive your vehicle with bad struts.

title: Strut