title: G2 Esports

text: On 18 March 2021, during RLCS X, Rizzo announced his plans to retire from professional Rocket League competition, revealing the upcoming Regional Event would be his last event on the roster before leaving the G2 Esports organization entirely on 29 June 2021. Following Rizzo's decision to step down, 15-year-old Andres "Dreaz" Jordan played as a stand-in for the remainder of the season.


title: G2 Esports

text: The announcement that G2 Esports acquired the full roster of PENTA Sports, all five players and two coaches came a few days before the kick-off of the Six Major Paris group stage. These players, winners of the Six Invitational 2018 and multiple Pro League champions, represented the colors of G2 from 10 August 2018. Niclas "Pengu" Mouritze was considered the most experienced player in both the team and the wider Rainbow Six Siege scene, having been in the Year 1 Season 1 PENTA roster. Fabian "Fabian" Hällsten was the in-game leader of the team to whom the strategic success and flexibility of the team was often pointed towards, as one of the best IGLs in the European Pro League. Daniel "Goga" Mazorra Romero was the only non-Nordic player on the team, and the only Spanish player in the whole of Pro League at the time. He was often praised for his ability on the games hard breachers, particularly Thermite. JNSzki was one of the 2 Finnish players on the team, being acquired from PENTA's Year 1 rival of GiFu, he has been reputed throughout the Pro League's history as one of the best aimers and Bandit players in all of Siege.


title: G2 Esports

text: The team quickly proved to be a beneficial pick-up by G2, winning the Six Major Paris and its $350,000 prize pool immediately following the purchase by defeating their rivals Evil Geniuses 3–0.


title: G2 Esports

text: jNSzki was released by G2 Esports on 27 May 2019, replaced by UUNO from LeStream (Now Rogue). Juhani "Kantoraketti" Toivonen was originally a loan to PENTA from ENCE for the LAN finals of Season 7 Pro League. Following the departure of Ville "SHA77E" Palola, Kantoraketti officially became the 5th member of PENTA, that would go on to be G2 Esports. UUNO had played for the PENTA Academy being coached by G2's own coach, Thomas "Shas[O]Uas" Lee. Shas is one of the longest working coaches in Siege, originally coaching for Team Fenix, a team which had also featured Fabian and previous roster teammate of Niklas "KS" Massierer, and is still the head coach for the team. Kevin "Sua" Stahnke was the secondary coach and analyst of the roster, brought in to replace Daniel "Ferral" Rotheram, G2's original analyst.


title: G2 Esports

text: After signing Aleksi "UUNO" Työppönen and Joonas "jNSzki" Savolainen retired, G2 lost the Six Major Raleigh on 18 August 2019 after losing 3–1 to Russian rivals, Team Empire.


title: G2 Esports

text: On 22 November 2019, Goga was replaced by the German player of Pascal "Cry1NNN" Alouane. Right before Six Invitational 2020 Cry1NNN was benched and was replaced by Ferenc "SirBoss" Mérész on loan from PENTA. After the event, SirBoss left G2.


title: G2 Esports

text: On 3 March 2020, G2 Esports announced their new "superteam", picking up Ben "CTZN" McMillan from Natus Vincere and Jake "Virtue" Grannan from Fnatic while benching long time player Fabian in the process, who would eventually leave officially on 6 June 2020.


title: G2 Esports

text: At the start of March 2021, Pengu announced his retirement at the age of 23. After few days, G2 Esports announced the addition of Jordan “Kayak” Morley into the roster.


title: G2 Esports

text: After underwhelming performances at the Six Invitational 2021, finishing 8th in Group A during the Group Stage and being eliminated in the first round of the lower bracket, the organization decided to revamp their roster. On 10 June 2021, it was announced that both remaining Finnish players Kantoraketti and UUNO were benched. On the same day, G2 introduced two new players: Lucas "Hungry" Reich, coming back from a break from the competitive scene, and Jonas "Jonka" Kaczmarzyk from MnM Gaming.


title: G2 Esports

text: G2 Esports' debut into Fortnite saw Brand Manager and Hearthstone Manager Jakub "Lothar" Szygulski transition back into a full-time streamer and became the first competitive Fortnite player under the organization. A second player, Dominik "RazZzero0o" Beckmann, was signed on 12 September 2018. Following the conclusion of G2: Making the Squad, the top four contestants were offered contracts, with Kevin "Tohaj" Batic later transitioning into a professional player role in January 2020.


title: G2 Esports

text: Leading up to the reveal of G2 Atlantis on 31 May 2021, various Fortnite players in both Europe and North America were signed. The first signing was Sean "Coop" Cooper on 13 October 2020, followed by Kevin "LeTsHe" Fedjuschkin, Zach "smqcked" Ebersole, Jesus "Jelty" Navarez Espinoza and Mack "MackWood" Aesoph to complete the all-new lineup. G2 said goodbye to Coop on 6 July 2021.


title: G2 Esports

text: G2 Esports first entered the "Valorant" scene by signing former CS:GO player Oscar "mixwell" Cañellas Colocho as the team's captain on 16 June 2020. The following week saw Patryk "paTiTek" Fabrowski and Jacob "pyth" Mourujärvi also join the roster on 24 and 26 June 2020 respectively. Following the addition of a fourth player in Ardis "ardiis" Svarenieks on 3 July 2020, the G2 VALORANT team would then sign David "Davidp" Prins, who had been standing in for the first two successful event runs, on 31 July 2020 before going on to win a further four tournaments.


title: G2 Esports

text: First Strike Europe saw G2 fall in the semi-finals to eventual champions Team Heretics which led to the benching of Davidp and the arrival of Aleksander "zeek" Zygmunt. The first half of 2021 was a contrast to the early domination and further struggles for the team saw them part ways with zeek, ardiis and paTiTek. These departures saw Žygimantas "nukkye" Chmieliauskas, Auni "AvovA" Chahade and Jose Luis "koldamenta" Aranguren Herrero added to the roster in their place. Three weeks later, a new fifth, Cista "keloqz" Wassim, was announced on 25 June 2021 following pyth's decision to bench himself two weeks previously.


title: G2 Esports

text: In October 2021, G2 announced the organization's first-ever all-female team, led by former "CS:GO" professional player Julia "Juliano" Kiran, which would compete in "Valorant" as G2 Gozen. G2 Esports failed to secure a slot in one of the three partnered competitions, despite being in discussion with various players and staff members ahead of the announcement. In November 2022, the women's team won the Valorant Championship Tournament (VCT) Game Changers Championship in Berlin, beating Shopify Rebellion in the grand finals to become the first team to win a championship in both Valorant and CS:GO.


title: G2 Esports

text: Initially fielding Apex Legends streamers, G2 Esports went on to sign an all-Finnish lineup of Sebastian "Mimu" Vesala, Aaro "rette" Hälli and Niko "ZeroNothing" Suominen in September 2019. The organization temporarily left the Apex scene and released its former players in April 2020.


title: G2 Esports

text: G2 Esports returned to the Apex Legends scene with the signing of the former AimAssist roster on 1 June 2021 alongside new manager Christopher "BixLe" Dunbar.


title: G2 Esports

text: On 13 November 2017, G2 Esports signed Sim Racer Cem Bölükbaşı and Racing Team Manager Danny Engels. A joint venture saw the launch of new Sim Racing team FA Racing G2 Logitech G between G2 Esports and Formula One driver Fernando Alonso later that same month.


title: G2 Esports

text: G2 would go on to launch a multi-year partnership with Red Bull Racing in the form of Red Bull Racing Esports Team, with drivers competing across multiple Sim Racing titles.


title: G2 Esports

text: During the game's beta and while still known as G2.Kinguin, an Overwatch roster that was composed of retired European Team Fortress 2 players briefly competed under G2.


title: G2 Esports

text: G2 Esports signed Team CryptiK's Paladins roster on 31 August 2017. The team went on to win Paladins Premier League North America Summer 2018 and the Paladins Premier League Summer Finals 2018. G2 left the Paladins scene in early 2019.


title: G2 Esports

text: G2 Esports signed Weston "Westballz" Dennis on 11 July 2016, but Dennis and G2 parted ways on 31 March 2019.


title: Tony Cavalero

text: Anthony Cavalero (born October 14, 1983) is an American actor and comedian. He is known for his role as Dewey Finn on the Nickelodeon's "School of Rock", Keefe Chambers on the HBO television series "The Righteous Gemstones" (2019–present), and for playing Ozzy Osbourne in the film "The Dirt".


title: Tony Cavalero

text: Cavalero was born in Northern Virginia, not far from Washington, DC. He attended Poe Middle School and graduated from Annandale High School, where he lettered in varsity football, wrestling and lacrosse. He is an Eagle Scout and a Black Belt in Tae Kwon Do. He is a graduate of Virginia Military Institute where he was a four-year varsity lacrosse player. He moved to Los Angeles in 2006 and studied theater at CalStLA. He is a main company member of The Groundlings.


title: Tony Cavalero

text: Cavalero began acting in 2006. In 2014, he was cast as Dewey Finn on the Nickelodeon remake of "School of Rock", replacing Jack Black from the original 2003 film. The series premiered in 2016 and ran for three seasons.


title: Dave Cowens

text: David William Cowens ( ; born October 25, 1948) is an American former professional basketball player and NBA head coach. At , he played the center position and occasionally played power forward. Cowens spent most of his playing career with the Boston Celtics. He was the 1971 NBA Rookie of the Year and the 1973 NBA Most Valuable Player. Cowens won NBA championships as a member of the Celtics in 1974 and 1976. He was inducted into the Naismith Memorial Basketball Hall of Fame in 1991. Cowens has also held coaching positions in the NBA, CBA, and WNBA.


title: Dave Cowens

text: After starring in high school at Newport Catholic High in his hometown of Newport, Kentucky, Cowens played his collegiate basketball at Florida State University from 1967 to 1970 for coach Hugh Durham. He scored 1,479 points in 78 games at Florida State, at 19.0 points per game, and ranks among Florida State's top 10 all-time scoring leaders.


title: Dave Cowens

text: Cowens is the all-time Florida State leading rebounder with 1,340 rebounds (17.2 rebounds per game). He holds the team record for best seasonal rebound average (17.5 in the 1968–1969 season). He once grabbed 31 rebounds (second-best all-time) against LSU in the 1968–69 season.


title: Dave Cowens

text: Cowens was named to the"The Sporting News" All-America second team in 1970. His number hangs in the rafters of the Donald L. Tucker Center.


title: Dave Cowens

text: Cowens was selected as the fourth overall pick by the Boston Celtics in the 1970 NBA draft. Former Celtics center Bill Russell's recommendation of Cowens influenced the selection. While some critics believed that Cowens was too small to play center, Russell said: "No one is going to tell that kid he can't play center".


title: Dave Cowens

text: During his rookie year, Cowens averaged 17.0 points per game and 15.0 rebounds per game. He was named to the NBA All-Rookie First Team and shared the NBA's Rookie of the Year honors with Portland's Geoff Petrie. He also led the league in personal fouls that same year.


title: Dave Cowens

text: In the 1972–73 season, Cowens averaged 20.5 ppg, 16.2 rpg and 4.1 apg while helping the Celtics to a league-best 68–14 record. In that season also, Cowens scored 20 points, grabbed a career-high 32 rebounds and dished out 9 assists in a home win over the Houston Rockets. He carried the Celtics to the semifinals, where they met the New York Knicks. They won Game 1 of that best-of-7 series after Cowens recorded 15 points and 18 rebounds. However, they bowed out to the Knicks in Game 7. Cowens was chosen the NBA MVP as well as MVP of the All-Star Game that same season. Cowens and fellow Celtic Bill Russell both have the distinction of being named MVP of the league but not being included on the All-NBA First Team.


title: Dave Cowens

text: The following season, Cowens averaged 19.0 PPG, 15.7 RPG, 4.4 APG and 1.3 BPG while guiding the Celtics to a record of 56–26. Cowens was instrumental in bringing the Celtics into the playoffs, where they defeated the Buffalo Braves in six games and the New York Knicks in five. In the finals, the Celtics faced the top-seeded Milwaukee Bucks. The teams split the first six games, with each team winning at least once on their home court. This led to a decisive Game 7, where the Celtics faced the Bucks in Milwaukee. The Celtics prevailed thanks to a strong performance by Cowens, who recorded 28 points and 14 rebounds as the Celtics took their 12th NBA championship.


title: Dave Cowens

text: Cowens won his second NBA championship ring as a member of the 1975–1976 Celtics team that defeated the Phoenix Suns, 4–2, in the NBA Finals.


title: Dave Cowens

text: Eight games into the 1976–77 season on November 10, 1976, and with the Celtics on a four-game losing streak, Cowens left the team for "undisclosed reasons". Speculations included that Cowens was upset that the team didn't offer Paul Silas a new contract after the previous season and traded him to the Denver Nuggets. Other speculations were that he was unhappy with coach Tom Heinsohn and also his involvement in a lawsuit from the previous season where he allegedly struck a fan during a game against the Houston Rockets. Cowens returned to the team in January 1977 and led them to the playoffs, where they lost in the second round to the Philadelphia 76ers.


title: Dave Cowens

text: Cowens averaged 18.6 points and 14 rebounds a game in the 1977–78 season, but the Celtics missed the playoffs for the first time since his 1970–71 rookie season.


title: Dave Cowens

text: After Coach Satch Sanders was fired following a 2–12 start to the 1978–1979 season, Cowens served as player-coach for the remainder of the season. The team finished the year with a 29–53 record.


title: Dave Cowens

text: In his final season with the Celtics (1979–80), Cowens helped the team to a 61–21 record. Cowens averaged 14.2 points, 8.1 rebounds and 3.1 assists during the season. Cowens and the Celtics defeated the Houston Rockets 4–0 in the Eastern Conference playoffs before losing to the Philadelphia 76ers 4–1 in the Eastern Conference finals.


title: Dave Cowens

text: Cowens retired as a player in 1980, as Boston drafted Kevin McHale and traded for Robert Parish to replace him at center. Boston then won the 1981 NBA Championship. "I have sprained my ankle at least 30 times over the duration of my career, broken both legs and fractured a foot," Cowens said upon retiring. "Two years ago, a team of foot and bone specialists said they were amazed that I could play up to that point without sustaining serious injuries."


title: Dave Cowens

text: In 1982–83, Cowens felt the desire to play again and approached the Celtics about trading him, as they still held his rights. Cowens said, "The Celtics are set up front (with Bird, McHale and Parish). They could trade me, work something out. No disrespect to Bill Fitch. I'd advise any younger players to play for him, but I'd probably be better off somewhere else". After first negotiating with the Phoenix Suns, the Celtics traded Cowens to the Milwaukee Bucks, who were coached by former Celtic teammate Don Nelson. The Celtics received Quinn Buckner from Milwaukee as compensation. Cowens averaged 8.1 points, 6.9 rebounds and 2.1 assists in 25 minutes per game with the Bucks. He was injured in the final game of the regular season and was unable to play in the playoffs for Milwaukee. Cowens retired for good after the season.


title: Dave Cowens

text: During his NBA career, Cowens averaged a double-double of 17.6 points and 13.6 rebounds. with 3.8 assists and 1.1 steals in 766 career NBA games. Cowens was selected to eight All-Star Games, was named to the All-NBA Second Team three times, and was named to the All-NBA Defensive First Team in 1976 and All-NBA Defensive Second Team in 1973 and 1980. He was a member of the Celtics' 1974 and 1976 NBA Championship teams.


title: Dave Cowens

text: Cowens' playing credo was all-out intensity at both ends of the court, a style that never wavered during his 11-year NBA career. "He was quick, fast, strong and skilled, and played hard," Knicks Hall of Fame center Willis Reed said of Cowens.


title: Dave Cowens

text: Cowens was the fourth center in NBA history to average five assists per game in a single season, joining Wilt Chamberlain, former Celtic center, Bill Russell, and Kareem Abdul-Jabbar. His career average is 3.8 assists per game. As of the end of the 2018–19 season, Cowens ranked 27th overall for most point-rebound-assist triple-doubles by a center in NBA history.


title: Dave Cowens

text: As evidence to his all-around ability, only five other players (Scottie Pippen, Kevin Garnett, LeBron James, Giannis Antetokounmpo and Nikola Jokić) have led their teams in all five major statistical categories for a season: points, rebounds, assists, blocks, and steals. He accomplished the feat in the 1977–78 season, averaging 18.6 points, 14.0 rebounds, 4.6 assists, 0.9 blocks and 1.3 steals as Boston finished 32–50.


title: Dave Cowens

text: In 1996, Cowens was honored as one of the league's greatest players of all time by being named to the NBA 50th Anniversary Team. In October 2021, Cowens was again honored as one of the league's greatest players of all time by being named to the NBA 75th Anniversary Team.


title: Dave Cowens

text: He began his coaching career by serving as a player-coach for the Boston Celtics during the 1978–79 season, but he quit coaching after the season and returned as a full-time player before retiring in 1980.


title: Dave Cowens

text: Cowens returned to the NBA coaching ranks as an assistant coach for the San Antonio Spurs in 1994–96 and was considered for the coaching job of the Boston Celtics during the 1995 offseason. He served as head coach of the Charlotte Hornets from 1996 to 1999 and was the head coach of the Golden State Warriors from 1999 to 2001, a tenure of 105 games.


title: Dave Cowens

text: In 2005–06 Cowens was head coach of the Chicago Sky of the Women's National Basketball Association (WNBA).


title: Dave Cowens

text: In 1990, Cowens, a former Democrat, ran as a Republican for Massachusetts Secretary of the Commonwealth. However, because he did not register by June 5, 1989, he was unable to appear on the primary ballot. Cowens considered running a sticker campaign for the Republican nomination, but decided to drop out of the race.


title: Dave Cowens

text: Cowens married his wife, Deby, in 1978. They have two daughters and several grandchildren. In 1977, Cowens spent a day driving a taxi cab for the Independent Taxi Operators Association (ITOA) in Boston. "Nobody even knew who I was," Cowens told ESPN. "I put my cap on and just you know drove around. I got decent tips, though."


title: Charisma

text: Scholars in sociology, political science, psychology, and management reserve the term for a type of leadership seen as extraordinary; in these fields, the term "charisma" is used to describe a particular type of leader who uses "values-based, symbolic, and emotion-laden leader signaling".


title: Charisma

text: In Christian theology, the term appears as "charism", an endowment or extraordinary power given by the Holy Spirit.


title: Charisma

text: The English term "charisma" is from the Greek ("khárisma"), which means "favor freely given" or "gift of grace". The term and its plural ("charismata") derive from ("charis"), which means "grace" or indeed "charm" with which it shares the root. Some derivatives from that root (including "grace") have similar meanings to the modern sense of "personality charisma", such as "filled with attractiveness or charm", "kindness", "to bestow a favor or service", or "to be favored or blessed". Moreover, the ancient Greek dialect widely used in Roman times employed these terms without the connotations found in modern religious usage. Ancient Greeks applied personality charisma to their gods; for example, attributing charm, beauty, nature, human creativity or fertility to goddesses they called "Charites" ().


title: Charisma

text: Theologians and social scientists have expanded and modified the original Greek meaning into two distinct senses: "personality charisma" and "divinely conferred charisma".


title: Charisma

text: The meaning of "charisma" has become greatly diffused from its original "divinely conferred" meaning, and even from the "personality charisma" meaning in modern English dictionaries, which reduces to a mixture of charm and status. John Potts, who has extensively analyzed the term's history, sums up meanings beneath this diffused common usage:Contemporary charisma maintains, however, the irreducible character ascribed to it by Weber: it retains a mysterious, elusive quality. Media commentators regularly describe charisma as the "X-factor". …The enigmatic character of charisma also suggests a connection – at least to some degree – to the earliest manifestations of charisma as a spiritual gift.


title: Charisma

text: The Hebrew Bible and the Christian Bible record the development of "divinely conferred charisma". In the Hebrew text the idea of charismatic leadership is generally signaled by the use of the noun "hen" (favor) or the verb "hanan" (to show favor). The Greek term for "charisma" (grace or favor), and its root "charis" (grace) replaced the Hebrew terms in the Greek translation of the Hebrew Bible (the Septuagint). Throughout, "the paradigmatic image of the charismatic hero is the figure who has received God's favor". In other words, "divinely conferred charisma" applied to highly revered figures.


title: Charisma

text: Thus, Eastern Mediterranean Jews in the had notions of "charis" and "charisma" that embraced the range of meanings found in Greek culture and the spiritual meanings from the Hebrew Bible. From this linguistic legacy of fused cultures, in 1 Corinthians, Paul the Apostle introduced the meaning that the Holy Spirit bestowed "charism" and "charismata", "the gift of God's grace," upon individuals or groups. For Paul, "[t]here is a clear distinction between charisma and "charis"; charisma is the direct result of divine "charis" or grace."


title: Charisma

text: In the New Testament Epistles, Paul refers to "charisma" or its plural "charismata" seven times in 1 Corinthians, written in Koine (or common) Greek around . He elaborates on his concepts with six references in Romans (c. 56). He makes 3 individual references in 2 Corinthians (c. 56), 1 Timothy, and 2 Timothy (c. 62 – c. 67). The seventeenth and only other mention of "charisma" is in 1 Peter.


title: Charisma

text: The gospels, written in the late first century, apply "divinely conferred charisma" to revered figures. Examples are accounts of Jesus' baptism and of his transfiguration, in which disciples see him as radiant with light, appearing together with Moses and Elijah. Another example is Gabriel's greeting to Mary as "full of grace". In these and other instances early Christians designated certain individuals as possessing "spiritual gifts", and these gifts included "the ability to penetrate the neighbour to the bottom of his heart and spirit and to recognize whether he is dominated by a good or by an evil spirit and the gift to help him to freedom from his demon".


title: Charisma

text: Believers characterized their revered religious figures as having "a higher perfection… a special "Charisma"". Then, with the establishment of the Christian Church, "the old charismatic gifts and free offerings were transformed into a hierarchical sacerdotal system". The focus on the institution rather than divinely inspired individuals increasingly dominated religious thought and life, and that focus went unchanged for centuries.


title: Charisma

text: Additional changes began in the 17th century when church leaders, notably in the Latin tradition, accented "individual gifts [and] particular talents imparted by God or the Holy Spirit." The 19th century brought an increasing shift in emphasis toward individual and spiritual aspects of charisma; Protestant and some Catholic theologians narrowed the concept to superlative, out-of-the-ordinary, and virtuoso gifts. Simultaneously, the term became alienated from the much wider meaning that early Christians had attached to it. Still, the narrowed term projected back to the earlier period "A systematically reflected and highly differentiated understanding of charisma was often unconsciously infused into the Scriptures and writings of the church fathers, so that these texts were no longer read through the eyes of the authors".


title: Charisma

text: These dialectic meanings influenced notable changes in Pentecostalism in the late 19th century, and charismatic movements in some mainline churches in the mid-20th century. The discussion in the 21st Century Religion section explores what "charisma" means in these and other religious groups.


title: Charisma

text: The basis for modern secular usage comes from German sociologist Max Weber. He discovered the term in the work of Rudolph Sohm, a German church historian whose 1892 "Kirchenrecht" was immediately recognized in Germany as an epoch-making work. It also stimulated a debate between Sohm and leading theologians and religion scholars, which lasted more than twenty years and stimulated a rich polemical literature. The debate and literature had made "charisma" a popular term when Weber used it in "The Protestant Ethic and the Spirit of Capitalism" and in his "Sociology of Religion". Perhaps because he assumed that readers already understood the idea, Weber's early writings lacked definition or explanation of the concept. In the collection of his works, "Economy and Society" edited by his wife, he identified the term as a prime example of action he labeled "value-rational," in distinction from and opposition to action he labeled "Instrumentally rational." Because he applied meanings for "charisma" similar to Sohm, who had affirmed the purely charismatic nature of early Christianity, Weber's "charisma" would have coincided with the "divinely conferred charisma" sense defined above in Sohm's work.


title: Charisma

text: Weber introduced the "personality charisma" sense when he applied "charisma" to designate a form of authority. To explain charismatic authority he developed his classic definition:Charisma is a certain quality of an individual personality by virtue of which he is set apart from ordinary men and treated as endowed with supernatural, superhuman, or at least specifically exceptional powers or qualities. These as such are not accessible to the ordinary person, but are regarded as of divine origin or as exemplary, and on the basis of them the individual concerned is treated as a leader.


title: Charisma

text: Here Weber extends the concept of charisma beyond supernatural to superhuman and even to exceptional powers and qualities. Sociologist Paul Joosse examined Weber's famous definition, and found that:through simple yet profoundly consequential phrases such as “are considered” and “is treated,” charisma becomes a relational, attributable, and at last a properly sociological concept... For Weber, the locus of power is in the led, who actively (if perhaps unconsciously) invest their leaders with social authority.


title: Charisma

text: In other words, Weber indicates that it is followers who attribute powers to the individual, emphasizing that "the recognition on the part of those subject to authority" is decisive for the validity of charisma.


title: Charisma

text: Weber died in 1920, leaving "disordered, fragmentary manuscripts without even the guidance of a plan or table of the proposed contents". One unfinished manuscript contained his above quoted definition of "charisma". It took over a quarter century for his work to be translated into English. With regard to charisma, Weber's formulations are generally regarded as having revived the concept from its deep theological obscurity. However, even with the admirable translations and prefaces of his entire works, many scholars have found Weber's formulations ambiguous. For the past half-century they have debated the meaning of many Weberian concepts, including the meaning of "charisma," the role of followers, and the degree of a supernatural component.


title: History of Wales

text: The history of what is now Wales () begins with evidence of a Neanderthal presence from at least 230,000 years ago, while "Homo sapiens" arrived by about 31,000 BC. However, continuous habitation by modern humans dates from the period after the end of the last ice age around 9000 BC, and Wales has many remains from the Mesolithic, Neolithic, and Bronze Age. During the Iron Age the region, like all of Britain south of the Firth of Forth, was dominated by the Celtic Britons and the Brittonic language. The Romans, who began their conquest of Britain in AD 43, first campaigned in what is now northeast Wales in 48 against the Deceangli, and gained total control of the region with their defeat of the Ordovices in 79. The Romans departed from Britain in the 5th century, opening the door for the Anglo-Saxon invasion. Thereafter, the Brittonic language and culture began to splinter, and several distinct groups formed. The Welsh people were the largest of these groups, and are generally discussed independently of the other surviving Brittonic-speaking peoples after the 11th century.


title: History of Wales

text: In the post-Roman period, a number of Welsh kingdoms formed in present-day Wales, including Gwynedd, Powys, Deheubarth, Brycheiniog, Ergyng and Gwent. While the most powerful ruler was acknowledged as King of the Britons (later "Tywysog Cymru": "Leader" or "Prince of Wales"), and some rulers extended their control over other Welsh territories and into western England, none were able to unite Wales for long. Internecine struggles and external pressure from the English and later, the Norman conquerors of England, led to the Welsh kingdoms coming gradually under the sway of the English crown. In 1282, the death of Llywelyn ap Gruffudd led to the conquest of the Principality of Wales by King Edward I of England; afterwards, the heir apparent to the English monarch has borne the title "Prince of Wales". The Welsh launched several revolts against English rule, the last significant one being that led by Owain Glyndŵr in the early 15th century. In the 16th century Henry VIII, himself of Welsh extraction as a great-grandson of Owen Tudor, passed the Laws in Wales Acts aiming to fully incorporate Wales into the Kingdom of England.


title: History of Wales

text: Under England's authority, Wales became part of the Kingdom of Great Britain in 1707 and then the United Kingdom of Great Britain and Ireland in 1801. Yet, the Welsh retained their language and culture despite heavy English dominance. The publication of the extremely significant first complete Welsh translation of the Bible by William Morgan in 1588 greatly advanced the position of Welsh as a literary language. The 18th century saw the beginnings of two changes that would greatly affect Wales, the Welsh Methodist revival, which led the country to turn increasingly nonconformist in religion, and the Industrial Revolution. During the rise of the British Empire, 19th century Southeast Wales in particular experienced rapid industrialisation and a dramatic rise in population as a result of the explosion of the coal and iron industries. Wales played a full and willing role in World War One. The industries of the Empire in Wales declined in the 20th century with the end of the British Empire following the Second World War, while nationalist sentiment and interest in self-determination rose. The Labour Party replaced the Liberal Party as the dominant political force in the 1920s. Wales played a considerable role during World War Two along with the rest of the United Kingdom of Great Britain and Northern Ireland and the Allies, and its cities were bombed extensively during the Blitz. The nationalist party Plaid Cymru gained momentum from the 1960s. In a 1997 referendum, Welsh voters approved the devolution of governmental responsibility to a National Assembly for Wales which first met in 1999. In May 2020, the National Assembly for Wales was officially renamed Senedd Cymru or the Welsh Parliament (simply Senedd), to reflect significantly increased devolution and administrative power.


title: History of Wales

text: The earliest known human remains discovered in modern-day Wales is a Neanderthal jawbone, found at the Bontnewydd Palaeolithic site in the valley of the River Elwy in North Wales, whose owner lived about 230,000 years ago in the Lower Palaeolithic period. The Red Lady of Paviland, a human skeleton dyed in red ochre, was discovered in 1823 in one of the Paviland limestone caves of the Gower Peninsula in Swansea, South Wales. Despite the name, the skeleton is that of a young man who lived about 33,000 years ago at the end of the Upper Paleolithic Period (old Stone Age). It is considered to be the oldest known ceremonial burial in Western Europe. The skeleton was found along with jewellery made from ivory and seashells and a mammoth's skull.


title: History of Wales

text: Following the last ice age, Wales became roughly the shape it is today by about 8000 BC and was inhabited by Mesolithic hunter-gatherers. The earliest farming communities are now believed to date from about 4000 BC, marking the beginning of the Neolithic period. This period saw the construction of many chambered tombs, particularly dolmens or "cromlechs". The most notable examples of megalithic tombs include Bryn Celli Ddu and Barclodiad y Gawres on Anglesey, Pentre Ifan in Pembrokeshire, and Tinkinswood Burial Chamber in the Vale of Glamorgan.


title: History of Wales

text: Metal tools first appeared in Wales about 2500 BC, initially copper followed by bronze. The climate during the Early Bronze Age (c. 2500–1400 BC) is thought to have been warmer than at present, as there are many remains from this period in what are now bleak uplands. The Late Bronze Age (c. 1400–750 BC) saw the development of more advanced bronze implements. Much of the copper for the production of bronze probably came from the copper mine on the Great Orme, where prehistoric mining on a very large scale dates largely from the middle Bronze Age. Radiocarbon dating has shown the earliest hillforts in what would become Wales, to have been constructed during this period. Historian John Davies, theorises that a worsening climate after around 1250 BC (lower temperatures and heavier rainfall) required more productive land to be defended.


title: History of Wales

text: The earliest iron implement found in Wales is a sword from Llyn Fawr which overlooks the head of the Vale of Neath, which is thought to date to about 600 BC. Hillforts continued to be built during the British Iron Age. Nearly 600 hillforts are in Wales, over 20% of those found in Britain, examples being Pen Dinas near Aberystwyth and Tre'r Ceiri on the Llŷn peninsula. A particularly significant find from this period was made in 1943 at Llyn Cerrig Bach on Anglesey when the ground was being prepared for the construction of a Royal Air Force base. The cache included weapons, shields, chariots along with their fittings and harnesses, and slave chains and tools. Many had been deliberately broken and seem to have been votive offerings.


title: History of Wales

text: Until recently, the prehistory of Wales was portrayed as a series of successive migrations. The present tendency is to stress population continuity; the Encyclopedia of Wales suggests that Wales had received the greater part of its original stock of peoples by c.2000 BC. Recent studies in population genetics have argued for genetic continuity from the Upper Paleolithic, Mesolithic or Neolithic eras. According to historian John Davies, the Brythonic languages spoken throughout Britain resulted from an indigenous "cumulative Celticity", rather than from migration.


title: History of Wales

text: The Roman conquest of Wales began in AD 48 and took 30 years to complete; the occupation lasted over 300 years. The most famous of resistance was led by Caradog of the Celtic Catuvellauni tribe (modern day Essex), which were defeated by the Romans. Now leading the Celtic tribes of the Ordovices and Silures (of present day Monmouthshire), Caradog led a successful guerilla war against the Romans. His armies were eventually defeated at the Battle of Caer Caradog on the Anglo-Welsh border in AD 50. Caradog was later taken to Rome and gave a speech, impressing the Roman emperor to the extent that he was pardoned and allowed to live peacefully in Rome.


title: History of Wales

text: The Roman conquest was completed in 78, with Roman rule lasting until 383. Roman rule in Wales was a military occupation, save for the southern coastal region of South Wales east of the Gower Peninsula, where there is a legacy of Romanisation. The only town in Wales founded by the Romans, Caerwent, is located in South Wales. Both Caerwent and Carmarthen, also in southern Wales, would become Roman "civitates". During the occupation, both the region that would become Wales and its people were a mostly autonomous part of Roman Britain.


title: History of Wales

text: By AD 47, Rome had invaded and conquered all of southernmost and southeastern Britain under the first Roman governor of Britain. As part of the Roman conquest of Britain, a series of campaigns to conquer Wales was launched by his successor in 48 and would continue intermittently under successive governors until the conquest was completed in 78. It is these campaigns of conquest that are the most widely known feature of Wales during the Roman era due to the spirited but unsuccessful defence of their homelands by two native tribes, the Silures and the Ordovices.


title: History of Wales

text: The Demetae of southwestern Wales seem to have quickly made their peace with the Romans, as there is no indication of war with Rome, and their homeland was not heavily planted with forts nor overlaid with roads. The Demetae would be the only Welsh tribe to emerge from Roman rule with their homeland and tribal name intact.


title: History of Wales

text: Wales was a rich source of mineral wealth and the Romans used their engineering technology to extract large amounts of gold, copper, and lead, as well as modest amounts of some other metals such as zinc and silver. When the mines were no longer practical or profitable, they were abandoned. Roman economic development was concentrated in southeastern Britain, with no significant industries located in Wales. This was largely a matter of circumstance, as Wales had none of the needed materials in suitable combination, and the forested, mountainous countryside was not amenable to development.


title: History of Wales

text: Subsequent medieval Welsh lore developed a series of legends around Macsen Wledig, a literary and mythical figure derived from Magnus Maximus, a historical Roman general who revolted and became Emperor in the west from 383 to 388. Magnus Maximus was based in Britain in the early 380s, immediately prior to his usurpation of the throne. Several medieval Welsh dynasties claimed that they were descended from Macsen, thereby linking their origins to the legitimacy and prestige of a Roman past. Later Welsh genealogies, medievial poetry, for example the "Mabinogion", and chronicles such as the "Historia Brittonum" and "Annales Cambriae", used myths and legends to give roles in Welsh history to historical and quasi-historical figures from the Roman and Sub-Roman periods. Aside from Macsen Wledig, other examples include St Helena, the Emperor Constantine and Coel Hen.


title: History of Wales

text: When the Roman garrison of Britain was withdrawn in 410, the various British states were left self-governing. Evidence for a continuing Roman influence after the departure of the Roman legions is provided by an inscribed stone from Gwynedd dated between the late 5th century and mid 6th century commemorating a certain Cantiorix who was described as a citizen ("cives") of Gwynedd and a cousin of Maglos the magistrate ("magistratus"). There was considerable Irish colonisation in Dyfed in southwest Wales, where there are many stones with Ogham inscriptions. Wales had become Christian, and the "age of the saints" (approximately 500–700) was marked by the establishment of monastic settlements throughout the country, by religious leaders such as Saint David, Illtud and Teilo.


title: History of Wales

text: One of the reasons for the Roman withdrawal was the pressure put upon the empire's military resources by the incursion of barbarian tribes from the east. These tribes, including the Angles and Saxons, who later became the English, were unable to make inroads into Wales except possibly along the Severn Valley as far as Llanidloes. However, they gradually conquered eastern and southern Britain.


title: History of Wales

text: At the Battle of Chester in 616 AD, the forces of Powys and other British kingdoms were defeated by the Northumbrians under Æthelfrith, with king Selyf ap Cynan among the dead. It has been suggested that this battle finally severed the land connection between Wales and the kingdoms of the Hen Ogledd ("Old North"), the Brythonic-speaking regions of what is now southern Scotland and northern England, including Rheged, Strathclyde, Elmet and Gododdin, where Old Welsh was also spoken. From the 8th century on, Wales was by far the largest of the three remnant Brythonic areas in Britain, the other two being the Hen Ogledd and Cornwall.Wales was divided into a number of separate kingdoms, the largest of these being Gwynedd in northwest Wales and Powys in east Wales. Gwynedd was the most powerful of these kingdoms in the 6th century and 7th century, under rulers such as Maelgwn Gwynedd (died 547) and Cadwallon ap Cadfan (died 634/5), who in alliance with Penda of Mercia was able to lead his armies as far as Northumbria in 633, defeat the local ruler Edwin and control it for approximately one year. When Cadwallon was killed in battle by Oswald of Northumbria, his successor Cadafael ap Cynfeddw also allied himself with Penda against Northumbria, but thereafter Gwynedd, like the other Welsh kingdoms, was mainly engaged in defensive warfare against the growing power of Mercia.


title: History of Wales

text: Powys as the easternmost of the major kingdoms of Wales came under the most pressure from the English in Cheshire, Shropshire and Herefordshire. This kingdom originally extended east into areas now in England, and its ancient capital, Pengwern, has been variously identified as modern Shrewsbury or a site north of Baschurch. These areas were lost to the kingdom of Mercia. The construction of the earthwork known as Offa's Dyke (usually attributed to Offa, King of Mercia in the 8th century) may have marked an agreed border.


title: History of Wales

text: For a single man to rule the whole country during this period was rare. This is often ascribed to the inheritance system practised in Wales. All sons received an equal share of their father's property (including illegitimate sons), resulting in the division of territories. However, the Welsh laws prescribe this system of division for land in general, not for kingdoms, where there is provision for an "edling" (or heir) to the kingdom to be chosen, usually by the king. Any son, legitimate or illegitimate, could be chosen as edling and there were frequently disappointed candidates prepared to challenge the chosen heir.


title: History of Wales

text: The first to rule a considerable part of Wales was Rhodri Mawr (Rhodri The Great), originally king of Gwynedd during the 9th century, who was able to extend his rule to Powys and Ceredigion. Upon his death, his realms were divided between his sons. Rhodri's grandson, Hywel Dda (Hywel the Good), formed the kingdom of Deheubarth by joining smaller kingdoms in the southwest and had extended his rule to most of Wales by 942. He is traditionally associated with the codification of Welsh law at a council which he called at Whitland, the laws from then on usually being called the "Laws of Hywel". Hywel followed a policy of peace with the English. On his death in 949 his sons were able to keep control of Deheubarth but lost Gwynedd to the traditional dynasty of this kingdom.


title: History of Wales

text: Wales was now coming under increasing attack by Viking raiders, particularly Danish raids in the period between 950 and 1000. According to the chronicle "Brut y Tywysogion", Godfrey Haroldson carried off two thousand captives from Anglesey in 987, and the king of Gwynedd, Maredudd ab Owain is reported to have redeemed many of his subjects from slavery by paying the Danes a large ransom.


title: History of Wales

text: Gruffydd ap Llywelyn was the only ruler to be able to unite Wales under his rule. In 1055 Gruffydd ap Llywelyn killed his rival Gruffydd ap Rhydderch in battle and recaptured Deheubarth.


title: History of Wales

text: Originally king of Gwynedd, by 1057 he was the ruler of Wales and had annexed parts of England around the border. He ruled Wales with no internal battles His territories were again divided into the traditional kingdoms.


title: History of Wales

text: Historian John Davies stated that Gruffydd was, "the only Welsh king ever to rule over the entire territory of Wales... Thus, from about 1057 until his death in 1063, the whole of Wales recognised the kingship of Gruffudd ap Llywelyn. For about seven brief years, Wales was one, under one ruler, a feat with neither precedent nor successor." During this time, between 1053 and 1063, Wales lacked any internal strife and was at peace.


title: History of Wales

text: At the time of the Norman conquest of England in 1066, the dominant ruler in Wales was Bleddyn ap Cynfyn, who was king of Gwynedd and Powys. The initial Norman successes were in the south, where William Fitz Osbern overran Gwent before 1070. By 1074, the forces of the Earl of Shrewsbury were ravaging Deheubarth.


title: History of Wales

text: The killing of Bleddyn ap Cynfyn in 1075 led to civil war and gave the Normans an opportunity to seize lands in North Wales. In 1081 Gruffudd ap Cynan, who had just won the throne of Gwynedd from Trahaearn ap Caradog at the Battle of Mynydd Carn was enticed to a meeting with the Earl of Chester and Earl of Shrewsbury and promptly seized and imprisoned, leading to the seizure of much of Gwynedd by the Normans. In the south William the Conqueror advanced into Dyfed founding castles and mints at St David's and Cardiff. Rhys ap Tewdwr of Deheubarth was killed in 1093 in Brycheiniog, and his kingdom was seized and divided between various Norman lordships. The Norman conquest of Wales appeared virtually complete.In 1094, however, there was a general Welsh revolt against Norman rule, and gradually territories were won back. Gruffudd ap Cynan was eventually able to build a strong kingdom in Gwynedd. His son, Owain Gwynedd, allied with Gruffydd ap Rhys of Deheubarth won a crushing victory over the Normans at the Battle of Crug Mawr in 1136 and annexed Ceredigion. Owain followed his father on the throne of Gwynedd the following year and ruled until his death in 1170. He was able to profit from disunity in England, where King Stephen and Empress Matilda were engaged in a struggle for the throne, to extend the borders of Gwynedd further east than ever before.


title: History of Wales

text: Powys also had a strong ruler at this time in Madog ap Maredudd, but when his death in 1160 was quickly followed by the death of his heir, Llywelyn ap Madog, Powys was split into two parts and never subsequently reunited. In the south, Gruffydd ap Rhys was killed in 1137, but his four sons, who all ruled Deheubarth in turn, were eventually able to win back most of their grandfather's kingdom from the Normans. The youngest of the four, Rhys ap Gruffydd (Lord Rhys) ruled from 1155 to 1197. In 1171 Rhys met King Henry II and came to an agreement with him whereby Rhys had to pay a tribute but was confirmed in all his conquests and was later named Justiciar of South Wales. Rhys held a festival of poetry and song at his court at Cardigan over Christmas 1176 which is generally regarded as the first recorded Eisteddfod. Owain Gwynedd's death led to the splitting of Gwynedd between his sons, while Rhys made Deheubarth dominant in Wales for a time.


title: History of Wales

text: Out of the power struggle in Gwynedd eventually arose one of the greatest of Welsh leaders, Llywelyn ab Iorwerth, also known as Llywelyn Fawr (the Great), who was sole ruler of Gwynedd by 1200 and by his death in 1240 was effectively ruler of much of Wales. Llywelyn made his 'capital' and headquarters at Abergwyngregyn on the north coast, overlooking the Menai Strait. In 1200 Llywelyn ap Iorwerth (Llywelyn the Great) became King of Gwynedd and agreed to a treaty of peace with King John of England, marrying his illegitimate daughter Joan. 1208 Llywelyn claimed the Kingdom of Powys after the arrest of Gwenwynwyn ap Owain. Powys was left vulnerable following Gwenwynwyn's arrest by King John, who disapproved of his attacks on Marcher Lords of the South. Although John invaded parts of Gwynedd in 1211, these attacks were rebuffed in 1212 by Llywelyn.


title: History of Wales

text: Charters of the Welsh Princes included in the Magna Carta of 1215 was the first document which included English and Welsh law, including reference to common acceptance of the lawful judgement of peers.


title: History of Wales

text: Chapter 56: The return of lands and liberties to Welshmen if those lands and liberties had been taken by English (and vice versa) without a law-abiding judgement of their peers.


title: History of Wales

text: Chapter 57: The return of Gruffydd ap Llywelyn, the illegitimate son of Llywelyn ap Iorwerth (Llywelyn the Great) along with other Welsh hostages who were originally taken for "peace" and "good".


title: History of Wales

text: After the death of John in 1218, Llywelyn and King Henry II agreed to the treaty of Worcester which again confirmed Llywelyn's right to Wales until his death in 1240. His son Dafydd ap Llywelyn followed him as ruler of Gwynedd, but King Henry III of England would not allow him to inherit his father's position elsewhere in Wales. War broke out in 1241 and then again in 1245, and the issue was still in the balance when Dafydd died suddenly at Abergwyngregyn, without leaving an heir in early 1246. Llywelyn the Great's other son, Gruffudd had been killed trying to escape from the Tower of London in 1244. Gruffudd had left four sons, and a period of internal conflict between three of these ended in the rise to power of Llywelyn ap Gruffudd (also known as "Llywelyn Ein Llyw Olaf"; "Llywelyn, Our Last Leader").


title: History of Wales

text: The Treaty of Montgomery in 1267 confirmed Llywelyn in control, directly or indirectly, over a large part of Wales. Edward I disapproved of Llywelyn's alliance with Simon de Montfort, who revolted along with other barons against the English king in the second barons' war of 1264-1267 and war followed in 1277. Llywelyn was obliged to seek terms, and the Treaty of Aberconwy greatly restricted his authority. War broke out again when Llywelyn's brother Dafydd ap Gruffudd attacked Hawarden Castle on Palm Sunday 1282. On 11 December 1282, Llywelyn was lured into a meeting in Cilmeri in Builth Wells castle with unknown Marchers, where he was killed and his army subsequently destroyed. His brother Dafydd ap Gruffudd continued an increasingly forlorn resistance. He was captured in June 1283 and was hanged, drawn and quartered at Shrewsbury. This ended Welsh independence and in effect, Wales became England's first colony until it was finally annexed through the Laws in Wales Acts 1535-1542.


title: History of Wales

text: After the passing of the Statute of Rhuddlan (1284), which restricted Welsh laws, King Edward I's ring of impressive stone castles assisted in the domination of Wales, and he crowned his conquest by giving the title Prince of Wales to his son and heir in 1301. Wales became, effectively, part of England, even though its people spoke a different language and had a different culture. English kings appointed a Council of Wales, sometimes presided over by the heir to the throne. This Council normally sat in Ludlow, now in England but at that time still part of the disputed border area in the Welsh Marches. Welsh literature, particularly poetry, continued to flourish, however, with the lesser nobility now taking over from the princes as the patrons of the poets. Many consider Dafydd ap Gwilym, who flourished in the middle of the 14th century, the greatest of the Welsh poets.


title: History of Wales

text: There were a number of rebellions including ones led by Madog ap Llywelyn in 1294–1295 and by Llywelyn Bren, Lord of Senghenydd, in 1316–1318. In the 1370s, the last representative in the male line of the ruling house of Gwynedd, Owain Lawgoch, twice planned an invasion of Wales with French support. The English government responded to the threat by sending an agent to assassinate Owain in Poitou in 1378.


title: History of Wales

text: In 1400, a Welsh nobleman, Owain Glyndŵr (or "Owen Glendower"), revolted against King Henry IV of England. Owain inflicted a number of defeats on the English forces and for a few years controlled most of Wales. Some of his achievements included holding the first Welsh Parliament at Machynlleth and plans for two universities. Eventually, the king's forces were able to regain control of Wales and the rebellion died out, but Owain himself was never captured. His rebellion caused a great upsurge in Welsh identity and he was widely supported by Welsh people throughout the country.


title: History of Wales

text: As a response to Glyndŵr's rebellion, the English parliament passed the Penal Laws against Wales. These prohibited the Welsh from carrying arms, from holding office and from dwelling in fortified towns. These prohibitions also applied to Englishmen who married Welsh women. These laws remained in force after the rebellion, although in practice they were gradually relaxed.


title: History of Wales

text: In the Wars of the Roses which began in 1455, both sides made considerable use of Welsh troops. The main figures in Wales were the two Earls of Pembroke, the Yorkist Earl William Herbert and the Lancastrian Jasper Tudor. In 1485, Jasper's nephew, Henry Tudor, landed in Wales with a small force to launch his bid for the throne of England. Henry was of Welsh descent, counting princes such as Rhys ap Gruffydd (Lord Rhys) among his ancestors, and his cause gained much support in Wales. Henry defeated King Richard III of England at the Battle of Bosworth with an army containing many Welsh soldiers and gained the throne as King Henry VII of England.


title: History of Wales

text: In 1470 Edward IV formed the Council of Wales and the Marches. Following the defeat of Richard III in battle, the Welsh King of England Henry VII continued the use of Council and it was mostly used for judicial purposes. In 1660, the council of Wales and the Marches was reconstituted but did not carry the same importance as under Henry VII for example. It was abolished in 1689 following the deposition of James II by the Dutch William III of Orange.


title: History of Wales

text: Under his son, Henry VIII of England, the Laws in Wales Acts 1535-1542 were passed, integrating Wales with England in legal terms, abolishing the Welsh legal system, and banning the Welsh language from any official role or status, but it did for the first time define the England-Wales border and allowed members representing constituencies in Wales to be elected to the English Parliament. They also abolished any legal distinction between the Welsh and the English, thereby effectively ending the Penal Code although this was not formally repealed. The Marcher Lordships were abolished, and Wales began electing members of the Westminster parliament.


title: History of Wales

text: Following Henry VIII's break with Rome and the Pope, Wales for the most part followed England in accepting Anglicanism, although a number of Catholics were active in attempting to counteract this and produced some of the earliest books printed in Welsh. In 1588, William Morgan produced the first complete translation of the Welsh Bible. Morgan's Bible is one of the most significant books in the Welsh language, and its publication greatly increased the stature and scope of the Welsh language and literature.


title: History of Wales

text: Bishop Richard Davies and dissident Protestant cleric John Penry introduced Calvinist theology to Wales. Calvinism developed through the Puritan period, following the restoration of the monarchy under Charles II, and within Wales' Methodist movement. However, few copies of Calvin's works were available before the mid-19th century. In 1567, Davies, William Salesbury, and Thomas Huet completed the first modern translation of the New Testament and the first translation of the "Book of Common Prayer" (). In 1588, William Morgan completed a translation of the whole Bible. These translations were as important to the survival of the Welsh language and had the effect of conferring status on Welsh as a liturgical language and vehicle for worship. This had a significant role in its continued use as a means of everyday communication and as a literary language down to the present day despite the pressure of English.


title: History of Wales

text: Wales was overwhelmingly Royalist in the Wars of the Three Kingdoms in the early 17th century, though there were some notable exceptions such as John Jones Maesygarnedd and the Puritan writer Morgan Llwyd. Wales was an important source of men for the armies of King Charles I of England, though no major battles took place in Wales. The Second English Civil War began when unpaid Parliamentarian troops in Pembrokeshire changed sides in early 1648. Colonel Thomas Horton defeated the Royalist rebels at the battle of St. Fagans in May and the rebel leaders surrendered to Cromwell on 11 July after the protracted two-month siege of Pembroke.


title: History of Wales

text: Education in Wales was at a very low ebb in this period, with the only education available being in English while the majority of the population spoke only Welsh. In 1731, Griffith Jones started circulating schools in Carmarthenshire, held in one location for about three months before moving (or "circulating") to another location. The language of instruction in these schools was Welsh. By Griffith Jones' death, in 1761, it is estimated that up to 250,000 people had learnt to read in schools throughout Wales.The 18th century also saw the Welsh Methodist revival, led by Daniel Rowland, Howell Harris and William Williams Pantycelyn.


title: History of Wales

text: Nonconformity was a significant influence in Wales from the eighteenth to the twentieth centuries. The Welsh Methodist revival of the 18th century was one of the most significant religious and social movements in the history of Wales. The revival began within the Church of England in Wales and at the beginning remained as a group within it, but the Welsh revival differed from the Methodist revival in England in that its theology was Calvinist rather than Arminian. In the early 19th century the Welsh Methodists broke away from the Anglican church and established their own denomination, now the Presbyterian Church of Wales. This also led to the strengthening of other nonconformist denominations, and by the middle of the 19th century, Wales was largely Nonconformist in religion. This had considerable implications for the Welsh language as it was the main language of the nonconformist churches in Wales. The Sunday schools which became an important feature of Welsh life made a large part of the population literate in Welsh, which was important for the survival of the language as it was not taught in the schools. Welsh Methodists gradually built up their own networks, structures, and even meeting houses (or chapels), which led eventually to the secession of 1811 and the formal establishment of the Calvinistic Methodist Presbyterian Church of Wales in 1823. The Welsh Methodist revival also had an influence on the older nonconformist churches, or dissenters the Baptists and the Congregationalists who in turn also experienced growth and renewal. As a result, by the middle of the nineteenth century, Wales was predominantly a nonconformist country.


title: History of Wales

text: The end of the 18th century saw the beginnings of the Industrial Revolution, and the presence of iron ore, limestone and large coal deposits in south-east Wales meant that this area soon saw the establishment of ironworks and coal mines, notably the Cyfarthfa Ironworks and the Dowlais Ironworks at Merthyr Tydfil.


title: History of Wales

text: The modern history of Wales starts in the 19th century when South Wales became heavily industrialised with ironworks; this, along with the spread of coal mining to the Cynon and Rhondda valleys from the 1840s, led to an increase in population. The social effects of industrialisation resulted in armed uprisings against the mainly English owners. Socialism developed in South Wales in the latter part of the century, accompanied by the increasing politicisation of religious Nonconformism. The first Labour MP, Keir Hardie, was elected as a junior member for the Welsh constituency of Merthyr Tydfil and Aberdare in 1900.


title: History of Wales

text: The first decade of the 20th century was the period of the coal boom in South Wales when population growth exceeded 20 per cent. Demographic changes affected the language frontier; the proportion of Welsh speakers in the Rhondda valley fell from 64 per cent in 1901 to 55 per cent ten years later, and similar trends were evident elsewhere in South Wales.


title: History of Wales

text: The population of Wales doubled from 587,000 in 1801 to 1,163,000 in 1851 and had reached 2,421,000 by 1911. Most of the increase came in the coal mining districts especially Glamorganshire, which grew from 71,000 in 1801 to 232,000 in 1851 and 1,122,000 in 1911. Part of this increase can be attributed to the demographic transition seen in most industrialising countries during the Industrial Revolution, as death rates dropped and birth rates remained steady. However, there was also a large-scale migration of people into Wales during the industrial revolution. The English were the most numerous group, but there were also considerable numbers of Irish and smaller numbers of other ethnic groups, including Italians, migrated to South Wales. Wales received other immigrants from various parts of the British Commonwealth of Nations in the 20th century, and African-Caribbean and Asian communities add to the ethnocultural mix, particularly in urban Wales.


title: History of Wales

text: The 1904–1905 Welsh Revival was the largest full-scale Christian revival of Wales of the 20th century. It is believed that at least 100,000 people became Christians during the 1904–1905 revival, but despite this it did not put a stop to the gradual decline of Christianity in Wales, only holding it back slightly.


title: History of Wales

text: The world wars and interwar period were hard times for Wales, in terms of the faltering economy of antiwar losses. Men eagerly volunteered for war service. The First World War and its aftermath had severe impact on Wales in terms of economic impact as well as war-time casualties. The result was significant social deprivation. The Labour Party replaced the Liberals as the dominant party in Wales, particularly in the industrial valleys of South Wales. Plaid Cymru was formed in 1925, but initially, its growth was slow and it gained few votes at parliamentary elections.


title: History of Wales

text: In the immediate period after the Second World War there was a strong revival in economic growth, accompanied by greater personal material well-being for the poorer elements of society as a result of the new systems of social welfare. Support for political nationalism strengthened with some success for Plaid Cymru and increasing pressure for Welsh devolution. Nevertheless, the coal industry steadily declined after 1945. By the early 1990s, there was only one deep pit still working in Wales. There was a similar catastrophic decline in the steel industry (the steel crisis), and the Welsh economy, like that of other developed societies, became increasingly based on the expanding service sector.


title: History of Wales

text: The Welsh Language Act 1967 repealed a section of the Wales and Berwick Act and thus "Wales" was no longer part of the legal definition of England. This essentially defined Wales as a separate entity legally (but within the UK), for the first time since before the Laws in Wales Acts 1535 and 1542 which defined Wales as a part of the Kingdom of England. The Welsh Language Act 1967 also expanded areas where the use of Welsh was permitted, including in some legal situations.


title: History of Wales

text: In a referendum in 1979, Wales voted against the creation of a Welsh assembly with an 80 per cent majority. In 1997, a second referendum on the same issue secured a very narrow majority (50.3 per cent). The National Assembly for Wales ("Cynulliad Cenedlaethol Cymru") was set up in 1999 (under the Government of Wales Act 1998) with the power to determine how Wales' central government budget is spent and administered, although the UK Parliament reserved the right to set limits on its powers. The governments of the United Kingdom and of Wales almost invariably define Wales as a country. The Welsh Government says: "Wales is not a Principality. Although we are joined with England by land, and we are part of Great Britain, Wales is a country in its own right."


title: History of Wales

text: The proportion of the Welsh population able to speak the Welsh language fell from just under 50% in 1901 to 43.5% in 1911 and continued to fall to a low of 18.9% in 1981.


title: History of Wales

text: In the 2011 census, it was recorded that the proportion of people able to speak Welsh had dropped from 20.8% to 19% (still higher than 1991). Despite an increase in the overall size of the Welsh population this still meant that the number of Welsh speakers in Wales dropped from 582,000 in 2001 to 562,000 in 2011. However, this figure was still much higher than 508,000 or 18.7% of people who said they could speak Welsh in the 1991 census. The Annual Population Survey of April 2020 to March 2021 reported that 29.1% of people aged three and over were able to speak Welsh which equates to 883,300 people. For October 2020 to 30 September 2021, the Annual Population Survey showed that 29.5% of people aged three or older were able to speak Welsh which equates to approximately 892,500 people.


title: History of Wales

text: The Government of Wales Act 2006 (c 32) of the UK Parliament reformed the National Assembly for Wales and allowed further powers to be granted to it more easily. The Act created a system of government with a separate executive drawn from and accountable to the legislature. Following a successful referendum in 2011 on extending the law-making powers of the National Assembly, it was then able to make laws, known as Acts of the Assembly, on all matters in devolved subject areas, without needing the UK Parliament's agreement. In the same year, the International Standards Organisation agreed to apply the description of "country" to Wales in its technical publications, following lobbying from Plaid Cymru AM at the time, Leanne Wood.


title: History of Wales

text: In the 2016 referendum, a majority of Welsh voters supported leaving the European Union, although there were regional differences. According to Danny Dorling, professor of geography at the Oxford University, “If you look at the more genuinely Welsh areas, especially the Welsh-speaking ones, they did not want to leave the EU.”


title: History of Wales

text: In May 2020, the National Assembly for Wales was renamed "Senedd Cymru" or "the Welsh Parliament", commonly known as the "Senedd" in both English and Welsh.


title: History of Wales

text: The results of the 2001 Census showed an increase in the number of Welsh speakers to 21% of the population aged 3 and older, compared with 18.7% in 1991 and 19.0% in 1981. This compares with a pattern of steady decline indicated by census results during the 20th century.


title: 1982 NBA Finals

text: The 1982 NBA World Championship Series was the championship round of the National Basketball Association (NBA)'s 1981–82 season, the top level of competition in men's professional basketball in North America. The series saw the Western Conference champion Los Angeles Lakers face the Eastern Conference champion Philadelphia 76ers. It was a rematch of the 1980 NBA Finals. The Lakers won 4 games to 2.


title: 1982 NBA Finals

text: The 1982 NBA Finals documentary "Something to Prove" recaps all the action of this series. It was the last NBA video documentary to exclusively use film in all on-court action. Dick Stockton narrated the documentary, with the condensed USA Network version narrated by Al Albert.


title: 1982 NBA Finals

text: This was the first Finals to be claimed on the winning team's home court since 1977. The series ended June 8, later than any previous NBA Finals. The previous record was June 7, 1978. This record was eclipsed two years later when the finals ended on June 12, 1984.


title: 1982 NBA Finals

text: The Lakers were stunned in the 1981 NBA Playoffs by the Houston Rockets in a 3-game mini-series. The previous season saw the Lakers in a state of uncertainty, after Magic Johnson missed 45 games due to a knee injury. Their problems continued early in the new season, and with the team at 7–4 the Lakers decided to fire head coach Paul Westhead. Taking over as head coach was Pat Riley, and his promotion to the job led to the birth of the Showtime offense.


title: 1982 NBA Finals

text: With a healthy Johnson and the additions of Kurt Rambis and Bob McAdoo, the Lakers rallied to finish with a 57–25 record, best in the Western Conference. They were even more flawless in the playoffs as they both swept the Phoenix Suns in the Western Conference Semifinals, and the San Antonio Spurs in the Western Conference Finals.


title: 1982 NBA Finals

text: Like the Lakers, the 76ers were coming off a heartbreaking playoff defeat, as they blew a 3–1 lead and lost to the eventual champion Boston Celtics in the Eastern Conference finals. Not much was changed for the 76ers roster-wise and record-wise in the new season, however, as the team finished second behind the Celtics in the Atlantic Division for the third straight year.


title: 1982 NBA Finals

text: Due to a then-existing rule where division winners would earn a first-round bye, the 76ers were forced to play a best-of-three miniseries, even though their 58–24 record was three games better than the Central Division champion Milwaukee Bucks. Nevertheless, Philadelphia easily swept the Atlanta Hawks 2–0 in the first round, then ousted the Bucks in the next round 4–2. In the Eastern Conference finals, the 76ers blew out the Celtics twice at The Spectrum to take a 3–1 lead, only to lose the next two games in a harrowing replay of the 1981 playoffs. But led by Andrew Toney's 34 points, the 76ers exorcised the demons of 1981 by blowing out the Celtics 120–106 in Game 7. As time wound down, the Boston Garden crowd began to chant "Beat L.A.!", encouraging the 76ers to defeat the hated Lakers in the championship round.


title: 1982 NBA Finals

text: Fresh from holding off the Celtics in the conference finals, the Sixers worked their offense to precision and held a 15-point lead midway through the third quarter 83-68. But, then, the Lakers began to turn it up on defense and the result was many fast breaks. The Lakers went on a 40–9 run over the game's next 11 minutes. Wilkes scored 10, Kareem and McAdoo scored 8 each, Nixon and Cooper scored 7 each, and Nixon had 4 assists during the run, on the way to a 124-117 Game 1 win, thereby stealing the home-court advantage.


title: 1982 NBA Finals

text: After the game, Sixers coach Billy Cunningham commented that the Sixers weren't affected that much by the trapping Laker defense, just cold shooting and sloppy play. However, he also questioned whether or not it was a "zone defense", which was illegal at the time.


title: 1982 NBA Finals

text: In this game, Laker coach Pat Riley took a different defensive approach, assigning Magic Johnson to cover Julius Erving straight-up on defense. While Magic couldn't match the Doctor's athleticism, the move did keep Erving from the offensive boards.


title: 1982 NBA Finals

text: In Game 2 that wasn't quite enough, as Erving brought the Sixers back with 24 points and 16 rebounds, mostly defensive. Billy Cunningham used all his centers, Caldwell Jones, Darryl Dawkins and Earl Cureton at different points to guard Kareem Abdul-Jabbar. The Sixers got 38 offensive rebounds for 50 second-chance points, while the Lakers only had six offensive boards.


title: 1982 NBA Finals

text: The Sixers used that advantage to take a 110–94 win that evened the series. In a balanced scoring attack, Maurice Cheeks had 19 points and eight assists, Jones added 12 points and 11 rebounds, and Bobby Jones and Clint Richardson each scored 10. This was the Lakers first loss in the 1982 post season.


title: 1982 NBA Finals

text: Back at home at The Forum, the Lakers completely dominated Game 3. Norm Nixon scored 29 points as the Lakers marched to a 129–108 victory. Andrew Toney scored 36 and Julius Erving 21, but no one else came through.


title: 1982 NBA Finals

text: The Lakers controlled the tempo in Game 4 by going to their half-court game, passing down low to Kareem Abdul-Jabbar. On the defensive end, they kept up the pressure with their zone trap. The Lakers went up, three games to one, with a 111–101 win. Jamaal Wilkes and Magic Johnson had 24 points each, while Abdul-Jabbar added 22 and Bob McAdoo 19 off the bench. Hard-charging bruiser Kurt Rambis pulled down 11 rebounds.


title: 1982 NBA Finals

text: Back in Philadelphia, the Sixers took out their frustrations and destroyed the Lakers, 135–102. Kareem Abdul-Jabbar was held to just six points, a career playoff low, thanks to the spirited defense of Darryl Dawkins. In the midst of the offensive explosion, Dawkins also contributed 20 points and nine rebounds to the effort.


title: 1982 NBA Finals

text: This was the Lakers' most lopsided playoff defeat up to this time. It was eclipsed when they were routed 131-92 by the Celtics in the clinching Game 6 of the 2008 Finals.


title: 1982 NBA Finals

text: The Sixers' strong showing in Game 5 gave them hope for Game 6 in the Forum, but the Lakers got the early lead and were up, 66–57, at the half.


title: 1982 NBA Finals

text: In the third period, the Sixers' defense turned it up a notch. They held Los Angeles to 20 points for the quarter and several times cut the lead to one point. Super-sub Bob McAdoo, known more for his offense, made a key defensive play late in the third when he blocked a Julius Erving layup on a breakaway that would have given the Sixers the lead.


title: 1982 NBA Finals

text: The Lakers came back and surged early in the fourth period to boost their lead to 11. Erving, who led all scorers with 30 points, and Andrew Toney, who had 29, responded by trimming the lead to 103–100 with about four minutes left, but then Kareem Abdul-Jabbar scored and was fouled and made the free throw to put Los Angeles up by six. Moments later, Wilkes got a breakaway layup to close it out, 114–104.


title: 1982 NBA Finals

text: Jamaal Wilkes led the Lakers with 27 points, and Magic Johnson, with 13 points, 13 rebounds and 13 assists, was named the series MVP. McAdoo, who had 16 points, nine rebounds and three blocks, was pretty much reborn as a player in this series after being cast off by several teams as a selfish, non-team player.


title: 1982 NBA Finals

text: Aside from the Doctor's and Toney's efforts, no one else stepped up for the Sixers. Darryl Dawkins fouled out and only had 10 points and one rebound in 20 minutes played. Dawkins would soon be shipped to the New Jersey Nets, and the 76ers acquired the final piece of their championship puzzle: Moses Malone, an MVP center from the Houston Rockets.


title: 1982 NBA Finals

text: Unlike previous years, where weeknight games were shown on tape delay, all games in the Finals were televised live by CBS. As a compromise to CBS to allow the live telecasts, the NBA returned the start of its season to late October after starting it earlier in October the previous two seasons, meaning the finals would start after the conclusion of the mid-May sweeps period. The later date also eliminated the back-to-back games on Mother's Day weekend, which was used in 1980 and 1981 to avert another tape delay broadcast.


title: 1982 NBA Finals

text: This was also the first of nine straight NBA finals (1982-1990) that Dick Stockton would call for CBS Sports. Stockton also announced the starting lineups of the 1982 NBA Finals in lieu of P.A. announcers Dave Zinkoff (for the 76ers) and Larry McKay (for the Lakers; McKay would be replaced the next season by Lawrence Tanter).


title: 1982 NBA Finals

text: Both teams would meet in the Finals again in 1983. The Sixers, bolstered by the addition of league MVP Moses Malone, won 65 games, and steamrolled through the playoffs, in which they lost only once (completing Malone's famous "Fo, Fo, Fo" prediction, stating that the Sixers needed to win 4 games in each of the three series) en route to their third NBA title overall (they won in 1955 as the Syracuse Nationals, and in 1967). The Lakers finished the regular season with 58 wins, but were overmatched by the hungrier Sixers in the Finals. Then-rookie and future Hall of Famer James Worthy did not play in the series because of a late-season leg injury.


title: The Great Masturbator

text: The Great Masturbator (1929) is a painting by Salvador Dalí executed during the surrealist epoch, and is currently displayed at Museo Nacional Centro de Arte Reina Sofía, Madrid.


title: The Great Masturbator

text: The centre of the painting has a distorted human face in profile looking downwards, based on the shape of a natural rock formation at Cap de Creus along the sea-shore of Catalonia. A similar profile is seen in Dalí's more famous painting of two years later, "The Persistence of Memory". A nude female figure (resembling Dalí's then-new muse, Gala) rises from the back of the head; this may be the masturbatory fantasy suggested by the title. The woman's mouth is near a thinly clad male crotch, a suggestion that fellatio may take place. The male figure seen only from the waist down has bleeding fresh cuts on his knees. Below the central profile head, on its mouth, is a grasshopper, an insect Dali referred to several times in his writings. A swarm of ants (a popular motif representing sexual anxiety in Dalí's work) gather on the grasshopper's abdomen, as well as on the prone face. In the landscape below, three other figures are arranged, along with an egg (commonly used as a symbol of fertility) and sparse other features. Two of the characters in the landscape are arranged in such a way as to cast a long single shadow, while the other character is seen hurriedly walking into the distance on the peripheries of the canvas. On the back of the central head figure, a formation of two rocks and a potted dry plant can be seen, the pot of the plant placed over the bottom rock while balancing the other rock on top of it in an unrealistic way. This part is thought to represent the escape-of-reality idea found in many of Dalí's other works.


title: The Great Masturbator

text: The painting may represent Dalí's severely conflicted attitudes towards sexual intercourse. In Dalí's youth, his father had left out a book with explicit photos of people suffering advanced untreated venereal diseases to "educate" the boy. The photos of grotesquely damaged diseased genitalia fascinated and horrified young Dalí, and he continued to associate sex with putrefaction and decay into his adulthood.


title: The Great Masturbator

text: The inclusion of the grasshopper and ants crawling on the bottom of the stone head may stem from Dalí's experience with delusional parasitosis. The disease was not first published about until 1937, however Dalí described struggling with sensations of bugs crawling on his skin in his autobiography.


title: The Great Masturbator

text: Comparisons have been made to Hieronymus Bosch's "The Garden of Earthly Delights". "The Great Masturbator" is similar to an image on the right side of the left panel of "The Garden of Earthly Delights" composed of rocks, bushes and little animals resembling a face with a prominent nose and long eyelashes.


title: The Great Masturbator

text: Dalí kept the painting in his personal collection, displayed at the Dalí Theatre and Museum in Figueres, willing it to the national collection of Spain upon his death, when it was removed to the Madrid museum.


title: Delaunay triangulation

text: In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934.


title: Delaunay triangulation

text: For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors.


title: Delaunay triangulation

text: By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean distance. However, in these cases a Delaunay triangulation is not guaranteed to exist or be unique.


title: Delaunay triangulation

text: The Delaunay triangulation of a discrete point set P in general position corresponds to the dual graph of the Voronoi diagram for P.


title: Delaunay triangulation

text: In the 2D case, the Voronoi vertices are connected via edges, that can be derived from adjacency-relationships of the Delaunay triangles: If two triangles share an edge in the Delaunay triangulation, their circumcenters are to be connected with an edge in the Voronoi tesselation.


title: Delaunay triangulation

text: For a set P of points in the ("d"-dimensional) Euclidean space, a Delaunay triangulation is a triangulation DT(P) such that no point in P is inside the circum-hypersphere of any "d"-simplex in DT(P). It is known that there exists a unique Delaunay triangulation for P if P is a set of points in "general position"; that is, the affine hull of P is "d"-dimensional and no set of "d" + 2 points in P lie on the boundary of a ball whose interior does not intersect P.


title: Delaunay triangulation

text: The problem of finding the Delaunay triangulation of a set of points in "d"-dimensional Euclidean space can be converted to the problem of finding the convex hull of a set of points in ("d" + 1)-dimensional space. This may be done by giving each point "p" an extra coordinate equal to |"p"|, thus turning it into a hyper-paraboloid (this is termed "lifting"); taking the bottom side of the convex hull (as the top end-cap faces upwards away from the origin, and must be discarded); and mapping back to "d"-dimensional space by deleting the last coordinate. As the convex hull is unique, so is the triangulation, assuming all facets of the convex hull are simplices. Nonsimplicial facets only occur when "d" + 2 of the original points lie on the same "d"-hypersphere, i.e., the points are not in general position.


title: Delaunay triangulation

text: From the above properties an important feature arises: Looking at two triangles ABD and BCD with the common edge BD (see figures), if the sum of the angles α and γ is less than or equal to 180°, the triangles meet the Delaunay condition.


title: Delaunay triangulation

text: This is an important property because it allows the use of a "flipping" technique. If two triangles do not meet the Delaunay condition, switching the common edge BD for the common edge AC produces two triangles that do meet the Delaunay condition:


title: Delaunay triangulation

text: Many algorithms for computing Delaunay triangulations rely on fast operations for detecting when a point is within a triangle's circumcircle and an efficient data structure for storing triangles and edges. In two dimensions, one way to detect if point "D" lies in the circumcircle of "A", "B", "C" is to evaluate the determinant:


title: Delaunay triangulation

text: When "A", "B" and "C" are sorted in a counterclockwise order, this determinant is positive only if "D" lies inside the circumcircle.


title: Delaunay triangulation

text: As mentioned above, if a triangle is non-Delaunay, we can flip one of its edges. This leads to a straightforward algorithm: construct any triangulation of the points, and then flip edges until no triangle is non-Delaunay. Unfortunately, this can take Ω("n") edge flips. While this algorithm can be generalised to three and higher dimensions, its convergence is not guaranteed in these cases, as it is conditioned to the connectedness of the underlying flip graph: this graph is connected for two-dimensional sets of points, but may be disconnected in higher dimensions.


title: Delaunay triangulation

text: The most straightforward way of efficiently computing the Delaunay triangulation is to repeatedly add one vertex at a time, retriangulating the affected parts of the graph. When a vertex "v" is added, we split in three the triangle that contains "v", then we apply the flip algorithm. Done naïvely, this will take O("n") time: we search through all the triangles to find the one that contains "v", then we potentially flip away every triangle. Then the overall runtime is O("n").


title: Delaunay triangulation

text: If we insert vertices in random order, it turns out (by a somewhat intricate proof) that each insertion will flip, on average, only O(1) triangles – although sometimes it will flip many more.


title: Delaunay triangulation

text: This still leaves the point location time to improve. We can store the history of the splits and flips performed: each triangle stores a pointer to the two or three triangles that replaced it. To find the triangle that contains "v", we start at a root triangle, and follow the pointer that points to a triangle that contains "v", until we find a triangle that has not yet been replaced. On average, this will also take O(log "n") time. Over all vertices, then, this takes O("n" log "n") time. While the technique extends to higher dimension (as proved by Edelsbrunner and Shah), the runtime can be exponential in the dimension even if the final Delaunay triangulation is small.


title: Delaunay triangulation

text: The Bowyer–Watson algorithm provides another approach for incremental construction. It gives an alternative to edge flipping for computing the Delaunay triangles containing a newly inserted vertex.


title: Delaunay triangulation

text: Unfortunately the flipping-based algorithms are generally hard to parallelize, since adding some certain point (e.g. the center point of a wagon wheel) can lead to up to O("n") consecutive flips. Blelloch et al. proposed another version of incremental algorithm based on rip-and-tent, which is practical and highly parallelized with polylogarithmic span.


title: Delaunay triangulation

text: A divide and conquer algorithm for triangulations in two dimensions was developed by Lee and Schachter and improved by Guibas and Stolfi and later by Dwyer. In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time O("n"), so the total running time is O("n" log "n").


title: Delaunay triangulation

text: For certain types of point sets, such as a uniform random distribution, by intelligently picking the splitting lines the expected time can be reduced to O("n" log "n") while still maintaining worst-case performance.


title: Delaunay triangulation

text: A divide and conquer paradigm to performing a triangulation in "d" dimensions is presented in "DeWall: A fast divide and conquer Delaunay triangulation algorithm in E" by P. Cignoni, C. Montani, R. Scopigno.


title: Delaunay triangulation

text: The divide and conquer algorithm has been shown to be the fastest DT generation technique sequentially.


title: Delaunay triangulation

text: Sweephull is a hybrid technique for 2D Delaunay triangulation that uses a radially propagating sweep-hull, and a flipping algorithm. The sweep-hull is created sequentially by iterating a radially-sorted set of 2D points, and connecting triangles to the visible part of the convex hull, which gives a non-overlapping triangulation. One can build a convex hull in this manner so long as the order of points guarantees no point would fall within the triangle. But, radially sorting should minimize flipping by being highly Delaunay to start. This is then paired with a final iterative triangle flipping step.


title: Delaunay triangulation

text: The Euclidean minimum spanning tree of a set of points is a subset of the Delaunay triangulation of the same points, and this can be exploited to compute it efficiently.


title: Delaunay triangulation

text: For modelling terrain or other objects given a point cloud, the Delaunay triangulation gives a nice set of triangles to use as polygons in the model. In particular, the Delaunay triangulation avoids narrow triangles (as they have large circumcircles compared to their area). See triangulated irregular network.


title: Delaunay triangulation

text: Delaunay triangulations can be used to determine the density or intensity of points samplings by means of the Delaunay tessellation field estimator (DTFE).


title: Delaunay triangulation

text: Delaunay triangulations are often used to generate meshes for space-discretised solvers such as the finite element method and the finite volume method of physics simulation, because of the angle guarantee and because fast triangulation algorithms have been developed. Typically, the domain to be meshed is specified as a coarse simplicial complex; for the mesh to be numerically stable, it must be refined, for instance by using Ruppert's algorithm.


title: Delaunay triangulation

text: The increasing popularity of finite element method and boundary element method techniques increases the incentive to improve automatic meshing algorithms. However, all of these algorithms can create distorted and even unusable grid elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. For example, smoothing (also referred to as mesh refinement) is one such method, which repositions nodes to minimize element distortion. The stretched grid method allows the generation of pseudo-regular meshes that meet the Delaunay criteria easily and quickly in a one-step solution.


title: Delaunay triangulation

text: Constrained Delaunay triangulation has found applications in path planning in automated driving and topographic surveying.


title: Special unitary group

text: In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1.


title: Special unitary group

text: The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case.


title: Special unitary group

text: The group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on formula_1. It is itself a subgroup of the general linear group, formula_2.


title: Special unitary group

text: The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics.


title: Special unitary group

text: The groups are important in quantum computing, as they represent the possible quantum logic gate operations in a quantum circuit with formula_3 qubits and thus formula_4 basis states. (Alternatively, the more general unitary group formula_5 can be used, since


title: Special unitary group

text: multiplying by a global phase factor formula_6 does not change the expectation values of a quantum operator.)


title: Special unitary group

text: The simplest case, , is the trivial group, having only a single element. The group is isomorphic to the group of quaternions of norm 1, and is thus diffeomorphic to the 3-sphere. Since unit quaternions can be used to represent rotations in 3-dimensional space (up to sign), there is a surjective homomorphism from to the rotation group whose kernel is . is also identical to one of the symmetry groups of spinors, Spin(3), that enables a spinor presentation of rotations.


title: Special unitary group

text: The special unitary group is a strictly real Lie group (vs. a more general complex Lie group). Its dimension as a real manifold is Topologically, it is compact and simply connected. Algebraically, it is a simple Lie group (meaning its Lie algebra is simple; see below).


title: Special unitary group

text: The center of is isomorphic to the cyclic group formula_7, and is composed of the diagonal matrices for an ‑th root of unity and the identity matrix.


title: Special unitary group

text: Its outer automorphism group for is formula_8 while the outer automorphism group of is the trivial group.


title: Special unitary group

text: A maximal torus of rank is given by the set of diagonal matrices with determinant 1. The Weyl group of SU("n") is the symmetric group , which is represented by signed permutation matrices (the signs being necessary to ensure the determinant is 1).


title: Special unitary group

text: The Lie algebra of , denoted by formula_9, can be identified with the set of traceless anti‑Hermitian complex matrices, with the regular commutator as a Lie bracket. Particle physicists often use a different, equivalent representation: The set of traceless Hermitian complex matrices with Lie bracket given by times the commutator.


title: Special unitary group

text: The Lie algebra formula_9 of formula_11 consists of formula_12 skew-Hermitian matrices with trace zero. This (real) Lie algebra has dimension formula_13. More information about the structure of this Lie algebra can be found below in the section "Lie algebra structure."


title: Special unitary group

text: In the physics literature, it is common to identify the Lie algebra with the space of trace-zero "Hermitian" (rather than the skew-Hermitian) matrices. That is to say, the physicists' Lie algebra differs by a factor of formula_14 from the mathematicians'. With this convention, one can then choose generators that are traceless Hermitian complex matrices, where:


title: Special unitary group

text: where the are the structure constants and are antisymmetric in all indices, while the -coefficients are symmetric in all indices.


title: Special unitary group

text: The factor of formula_14 in the commutation relation arises from the physics convention and is not present when using the mathematicians' convention.


title: Special unitary group

text: In the -dimensional adjoint representation, the generators are represented by × matrices, whose elements are defined by the structure constants themselves:


title: Special unitary group

text: If we consider formula_22 as a pair in formula_23 where formula_24 and formula_25, then the equation formula_26 becomes


title: Special unitary group

text: where formula_29 denotes the set of 2 by 2 complex matrices, is an injective real linear map (by considering formula_23 diffeomorphic to formula_31 and formula_29 diffeomorphic to formula_33). Hence, the restriction of to the 3-sphere (since modulus is 1), denoted , is an embedding of the 3-sphere onto a compact submanifold of formula_29, namely .


title: Special unitary group

text: Therefore, as a manifold, is diffeomorphic to , which shows that is simply connected and that can be endowed with the structure of a compact, connected Lie group.


title: Special unitary group

text: This map is in fact an isomorphism. Additionally, the determinant of the matrix is the square norm of the corresponding quaternion. Clearly any matrix in is of this form and, since it has determinant 1, the corresponding quaternion has norm 1. Thus is isomorphic to the unit quaternions.


title: Special unitary group

text: Every unit quaternion is naturally associated to a spatial rotation in 3 dimensions, and the product of two quaternions is associated to the composition of the associated rotations. Furthermore, every rotation arises from exactly two unit quaternions in this fashion. In short: there is a 2:1 surjective homomorphism from SU(2) to SO(3); consequently SO(3) is isomorphic to the quotient group SU(2)/{±I}, the manifold underlying SO(3) is obtained by identifying antipodal points of the 3-sphere , and SU(2) is the universal cover of SO(3).


title: Special unitary group

text: The Lie algebra of consists of formula_37 skew-Hermitian matrices with trace zero. Explicitly, this means


title: Special unitary group

text: These satisfy the quaternion relationships formula_41 formula_42 and formula_43 The commutator bracket is therefore specified by