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CR Flamengo

Clube de Regatas do Flamengo (lit. 'Rowing Club of Flamengo'), more commonly referred to as simply Flamengo, is a Brazilian multi sports club based in Rio de Janeiro, in the neighborhood of Gávea, best known for their professional football team. They are one of two clubs to have never been relegated from the top division, along with São Paulo. Flamengo is the most popular team in Brazil with more than 46.9 million fans, equivalent to 21.9% of the population that supports a team in Brazil.

The club was first established in 1895 specifically as a rowing club in the Flamengo neighborhood and did not play their first official football match until 1912. Flamengo's traditional uniform features red and black striped shirts with white shorts, and red and black striped socks. Flamengo has typically played their home matches in the Maracanã (which is also Brazil's national stadium) since its completion in 1950, with some exceptions in recent years. Since 1969, the vulture (Portuguese: urubu) has been the mascot of Flamengo.

Flamengo established themselves as one of Brazil's most successful sports clubs in the 20th century during the era of state leagues in Brazil when they won several Campeonato Carioca (Rio de Janeiro state league) titles prior to the establishment of the first Brazilian national football championship in 1959. Since then, they have remained successful in Brazilian football, having won 8 Campeonato Brasileiro Série A, 4 Copa do Brasil, and a record 38 Campeonato Carioca. In South American and worldwide competitions, the club's highest achievements are their conquests of the 1981, 2019 and 2022 Copa Libertadores, and 1981 Intercontinental Cup against Liverpool, led by the club's most iconic player, Zico.

The name "Flamengo", first referring to the Flamengo Neighborhood and later to the club´s name, is a reference to the Dutch navigator Olivier Van Noort, who tried to invade the city of Rio de Janeiro in the 16th century from Flamengo Beach. "Flamengo" is a direct portuguese translation from the word "flemish".

Flamengo's fiercest and longest-standing rivalries are with the other "Big Four" of Rio de Janeiro: Fluminense, Botafogo and Vasco da Gama; as well as interstate rivalries with Atletico MG and Palmeiras.

It´s Brazil's richest and most valuable football club with an annual revenue of R$1,2 billion (€ 218 million) and a valuation of over R$3.8 billion (€691 million). Flamengo became the non-European football club with the most followers on social media with 49 million followers across all platforms as of 18 June 2023.

Flamengo have also been well represented in the Brazil national football team; At the 1938 FIFA World Cup, forward Leônidas, a Flamengo player at the time, was the Golden Boot winner with 7 goals and won the Golden Ball, thus becoming the first Brazilian player ever to win those two awards. Twelve years later at the 1950 World Cup, Zizinho, who was a midfielder for Flamengo, also won the Golden Ball after he was voted best player; 4 out of the 10 top scorers for the Brazil National Team have all been Flamengo players at one point in their careers, seven players have won the World Cup whilst playing for Flamengo, and Flamengo player Màrio Zagallo scored Brazil's third goal in the 1958 World Cup final.

Flamengo's youth academy is one of the most prolific in Brazil and in the world, and have developed a number of Brazilian internationals such as Zico, Zizinho, Vinícius Júnior, Lucas Paquetá, Júlio César, Adriano, Mário Zagallo, Júnior and Leonardo.

Flamengo's training center, officially known as "Ninho do Urubu" (which translates to "Vulture's Nest" in English), is located in Vargem Grande, Rio de Janeiro. It serves as the primary training facility for the Flamengo football club, housing their professional teams as well as youth academy.

Establishment of the club (1895–1912)
Flamengo was founded on 17 November 1895, by a group of rowers gathered at club member Nestor de Barros's manor on Flamengo Beach in Rio de Janeiro. In the late 19th century, rowing was the elite, upper middle class sport in the region and the group hoped to impress the young women of the city's high society by establishing a rowing club. Previously, they could only afford a used boat named Pherusa, which had to be completely rebuilt before it could be used in competition. The team debuted on October 6, 1895, when they sailed off the Caju Point toward Flamengo Beach. However, strong winds turned over the boat and the rowers nearly drowned. They were rescued by a fishing boat named Leal (Loyal). Later as the Pherusa was undergoing repairs, it was stolen and never found again. The group saved money to buy a new boat, the Etoile, renamed Scyra.

On the night of 17 November, the group gathered at Nestor de Barros's manor on Flamengo beach and founded the Grupo de Regatas do Flamengo (English: Flamengo Rowing Group) and elected its first board and president (Domingos Marques de Azevedo). The name was changed a few weeks later to its current title of Clube de Regatas do Flamengo (Flamengo Rowing Club). The founders decided that the anniversary of the club's foundation should be commemorated on 15 November to coincide with Republic Proclamation Day, a national holiday.

Flamengo's football team was only established after a group of ten dissatisfied players from Fluminense broke away from that club following a board dispute. The players decided to join Flamengo because Alberto Borgerth, the team's captain, was also a rower for Flamengo. Also, establishing a land sports department at Flamengo was preferable to joining football rivals Botafogo or the all-English club Paissandu. The new members were admitted on 8 November 1911. A motion against the club taking part in football tournaments was put to a vote but was defeated, and as a result the members officially established the club's new football department on 24 December 1911.

Football in the amateur era (1912–1933)
The new team trained on Russel Beach and gradually gained the support of the locals, who closely watched their practice matches. The first official match was played on 3 May 1912, and marked, to this day, the largest margin of victory in the club's history, as they defeated Mangueira 16–2. Flamengo's first ever match against Fluminense, the start of the Fla-Flu rivalry, was played on 7 July of that year and was won by Fluminense by a score of 3–2. That same year, Flamengo finished as runners-up of the Campeonato Carioca, the Rio de Janeiro State Championship. The team's first uniform was nicknamed the "papagaio vintém", due to its similarity to a particular type of kite.

In 1914 the club won the Campeonato Carioca for the first time, dressed in a red, black, and white-striped shirt nicknamed the "cobra coral" (coral snake) was worn until 1916. Flamengo won the Campeonato Carioca again the following year, in 1915, and secured their first back-to-back championship; something they also did with their titles in 1920 and 1921.

In 1925, the team won the Campeonato Carioca and five other tournaments, a record at the time. In 1927 the prominent Rio newspaper Jornal do Brasil, in partnership with a mineral water company, held a mail-in contest to find "the most beloved club in Brazil." Though Flamengo enjoyed their largest increase in fan support after the club professionalized in the 1930s, they still defeated popular rivals Vasco da Gama in the vote. This was the first of many times that Flamengo would be polled as the nation's most popular club, originating the nickname "O mais querido do Brasil" ("the most beloved of Brazil"). In 1933 the team went on its first tour outside Brazil (to Montevideo and Buenos Aires ) and on 14 May of the same year played its final match as an amateur team, defeating River Futebol Clube by a score of 16–2. After this, the club's football department became professional.

Early professional era (1934–1955)
Local advertiser José Bastos Padilha was elected club president in 1934 and served until 1937. Under his tenure, the club massively improved its popularity in both Rio de Janeiro and the entirety of Brazil. For publicity, he organized a contest for students in schools to create phrases describing Flamengo, from which the phrase uma vez Flamengo, Flamengo até morrer ("Once you are Flamengo, you are Flamengo 'til you die") was developed and would later be adopted as part of the club's anthem. In 1936 Padilha signed excellent players such as Domingos da Guia and Leônidas da Silva (who would go on to be the leading goalscorer in the 1938 FIFA World Cup as a Flamengo player). These beloved players endeared Flamengo to the public and it is believed that by this time Flamengo was the most popular club in the country. In 1937 Flamengo hired Hungarian coach Izidor "Dori" Kürschner, who introduced the WM system to Brazil and other innovations from Europe such as training without the use of the ball and playing a more defensive, controlled style. Padilha facilitated the construction of Flamengo's new stadium and current training center, the Estádio da Gávea. The stadium was inaugurated on 4 September 1938, when Vasco da Gama defeated Flamengo 2–0 and Kürschner was promptly fired.

In 1938, the five-year split in Rio de Janeiro football over the dispute between professionalism and amateurism was resolved with the merger of the two competing leagues (Flamengo had been a member of the professional LCF - Liga Carioca de Football). In 1939, after twelve years without winning any titles, Flamengo conquered the state championship with a team that would become the basis of the three-time state champions in the 1940s.

In 1941, the group played its first international competition, the Hexagonal Tournament of Argentina. In 1942, the first organized supporters group in all of Brazil, Charanga Rubro-Negra, was founded in support of Flamengo. Flamengo's popularity grew incidentally during World War II when Brazil's allies, the United States, installed two high-powered antennas in Natal and Belém in the north of Brazil to intercept enemy radio signals. They also allowed residents in the North and Northeast regions to receive the radio broadcasts of football matches. As Rio de Janeiro was the national capital at the time and Flamengo was highly successful in the war years with Zizinho and Domingos da Guia, nationwide support increased. In 1944, Flamengo completed their first tricampeonato Carioca: three consecutive Rio de Janeiro state titles (winning the 1942, 1943, and 1944 competitions). The key player of this squad was Zizinho, a player developed at Flamengo and considered the first ever "idol" of the club. Zizinho was transferred to Bangu just before the start of the 1950 World Cup in Brazil, where he scored twice and the Seleção finished runners-up. From 1953 to 1955, Flamengo once again won the Rio de Janeiro State League three consecutive times.

Zico and the world champions (1974–1983)
Flamengo won their 18th Campeonato Carioca state championship in 1978. The following five years would come to represent the club's most glorious era. Brazilian stars like Júnior, Carpegiani, Adílio, Cláudio Adão and Tita were led by Zico to become state champions three times in a row - the club's third tri-championship. This run of sustained excellent play pushed Flamengo towards its first Brazilian Championship in 1980. As national champions, the club qualified to play in the South American continental tournament, the 1981 Copa Libertadores, for the first time.

The 1981 season is a benchmark year in Flamengo's history. They advanced through the semi-final group stage of the Copa Libertadores with four victories in four matches. In the final they encountered Chilean club Cobreloa, also a debutante club in the tournament. In the first final at the Maracanã, Flamengo prevailed (2–1) with two goals from Zico. In the National Stadium in Santiago the following week, the Brazilian team received a violent reception on the field and fell 1–0 from a free kick. Equal on goals, a third match was played at the neutral venue of the Estadio Centenario in Montevideo. Zico scored twice in the first half, sealing the game and the championship. Flamengo were crowned champions of South America on November 23 and qualified for the Intercontinental Cup, a single match to be played in Tokyo's Olympic Stadium against European Champions' Cup winner Liverpool F.C..

On December 13, 1981, Zico, Tita, and Nunes took the field for the most important match in the club's history. Two goals by Nunes and one by Adílio (all in the first half) along with a brilliant midfield performance by Zico earned Flamengo the title of first Brazilian World Champions since Pelé's Santos, shutting out Liverpool 3–0.

The following two years were also marked with success. One more Rio de Janeiro State Championship in 1981 and two back-to-back Brazilian Championships – 1982 and 1983 – closed Flamengo's "Golden Age."

National success and the return of Zico (1984–1994)
After spending two years in Italy playing for Udinese, Zico returned to Flamengo in 1986 and won his last state championship. Only one month after returning, he suffered a severe knee injury after a violent tackle from Bangu defender Marcio Nunes, which interrupted his career for several months and affected his form in the 1986 FIFA World Cup.

In 1987, Zico was a major contributor to Flamengo's victory in the first edition of the Copa União. That year, the CBF was experiencing serious financial and institutional crises and was unable to secure sponsorship to organize the national championship as in years prior. As a result, the thirteen biggest clubs in Brazil (which included Flamengo) reacted and created a new entity named the Club of 13 to organize a championship of their own. The CBF originally supported the decision by the Club of 13, but were pressured by other clubs to create a larger national tournament. As a result, CBF placed three additional clubs into the Copa União, regarded the Copa União as the "Green Module," and organized a second "Yellow Module" of 16 other teams. CBF then decided that for the 1987 Brazilian Championship, the winners and runners-up of both modules would face each other in a knockout-style cup to determine the national champion and qualification for the Copa Libertadores, although this decision was made after the beginning of the championship, without Club of 13 agreement. With strong performances from Zico, Zé Carlos, Renato Gaúcho and Bebeto, Flamengo conquered the Copa União with major victories over Internacional and Atlético Mineiro. However, there was a dispute over whether Flamengo and Internacional of the Green Module would dispute the quadrangular against Sport Recife and Guarani of the Yellow Module. The Club of 13 clubs had agreed to not participate in the final set up by the CBF, since it was decided while the matches were already being played, but Eurico Miranda, a representative of Vasco, Flamengo's archi-rival and member of the Club of 13, had already signed an agreement with CBF regarding the final, without the board consent. Flamengo still did not participate in the final under the understanding that it would only determine the entrants of the Copa Libertadores and not the Brazilian national champion. CBF officially recognized Sport as the sole champion in 1987 and they qualified to the Copa Libertadores. In 2011, CBF retroactively declared Flamengo champion of 1987. However, Sport later appealed the decision to a Common Justice Tribunal, which is prohibited by FIFA, and CBF ultimately declared Sport as the sole champion of that year, pending appeals from Flamengo, all of which were unsuccessful, and a few years later Sport was officially declared as the champion of the 1987 season.

Throughout his career at Flamengo, Zico scored 508 goals and was the top scorer in club history before retiring in 1990.

Even without its biggest star, the early years of the post-Zico era were successful for Flamengo. They achieved national victory in the second edition of the Copa do Brasil in 1990, defeating Goiás in the finals. In 1992, Flamengo won their fifth Campeonato Brasileiro, defeating Botafogo across two legs in the final (3–0, 2–2). The team's key player was again Júnior at 38 years old.

End of title drought (2006–2018)
In 2006, Flamengo reached the Copa do Brasil final for a fifth time, finally managing to conquer the title after losing three previous finals, this time beating rivals Vasco da Gama. From 2007 to 2009 Flamengo completed their fifth tricampeonato in the Campeonato Carioca, and became sole owners of the record for most Carioca titles with 31 (Fluminense had 30 at the time).

On 9 March 2007, Flamengo received a commemorative date on the Rio de Janeiro official calendar. Governor Sérgio Cabral Filho declared 17 November (the day the club was founded) "Flamengo Day".

In the 2007 Campeonato Brasileiro Série A, Flamengo won many games at home, avoided the relegation zone and climbed to second place before being defeated by Náutico 1–0 in the final round and ultimately ending the season third. This marked a dramatic improvement in league outcome from previous seasons. Flamengo finished fifth the following year, and in 2009 despite being in tenth place in midseason, Flamengo won the league after seventeen years. With this victory Flamengo became five-time Campeonato Brasileiro Série A champions, seventeen seasons after their last title in 1992. The 2009 championship team finished the season with 67 points, the lowest winning point total in Brazil since the current league format was established in 2003. Flamengo were champions despite spending only two rounds at the top of the league: the final two. The title was won after a dramatic 2–1 comeback victory against Grêmio in the final round. International success continued to elude Flamengo through the 21st century. After finishing runners-up in the 2001 Copa Mercosur to San Lorenzo on penalties, the club made the quarter-finals only one time in their following twelve competitions (both Copa Libertadores and Copa Sudamericana).

In 2007, the club was eliminated from the Libertadores by Uruguayan minnows Defensor Sporting 3–2 on aggregate. In 2008, in Flamengo's first official tournament tie against a club from Mexico, they defeated Club América 4–2 in the Estadio Azteca before losing polemically 3–0 at home and being eliminated in the Copa Libertadores round of 16; the second leg was also manager Joel Santana's final match with the club.

Flamengo experienced a poor run in Série A from 2010 to 2015, finishing better than tenth only once. Following the success of 2009, the club gambled on winning several titles and signed striker Vágner Love to form a pair with Adriano. The dream of repeating as state champions four times in a row was foiled by Botafogo in 2010. After narrowly qualifying out of the group stage in the Copa Libertadores, manager Andrade was still fired. In their first quarter-final appearance since 1993, after disposing of Corinthians, Flamengo were eliminated by Universidad de Chile on away goals. Shortly after, Vágner Love and Adriano left the team. A series of coaching changes during the troublesome domestic league saw Flamengo survive relegation, avoiding defeat in their final nine matches, and claim the final berth to the Copa Sudamericana under manager Vanderlei Luxemburgo.

The blockbuster signing of 2011 was 30-year-old superstar Ronaldinho from A.C. Milan. He was joined by Argentine Darío Bottinelli and Fluminense idol Thiago Neves. Flamengo won the Campeonato Carioca outright in an undefeated campaign, but captured no other trophies that season: eliminations in the Copa do Brasil by Ceará, a heavy 5–0 loss in the Sudamericana by Universidad de Chile, and a fourth-place finish in the league left fans feeling that a strong roster had been squandered. The season saw the retirement of Serbian club idol Dejan Petković as well. In 2012 Ronaldinho sued Flamengo claiming lack of payment for four months and canceled his contract with the club, Thiago Neves returned to Fluminense after a drawn-out negotiation with contract-holders Al-Hilal, and defender Alex Silva was loaned to Cruzeiro after threatening Flamengo with a lawsuit. Vágner Love and Ibson returned for a 2012 campaign that yielded no trophies and a group-stage exit from the Copa Libertadores.

At the end of 2012, Flamengo elected Eduardo Bandeira de Mello as club president for three years. The goal of his term was to improve the club's finances, after an independent audit assessed Flamengo's debt at R$750 million. After a typical series of managerial changes, Jayme de Almeida was appointed as interim manager during which he fought off relegation and won the 2013 Copa do Brasil final against Atlético Paranaense. It was Flamengo's third Copa title, after 1990 and 2006.

Flamengo's Copa do Brasil title-defense fell short to Atlético Mineiro in the semi-final. However, by 2014, Flamengo was the only club that successfully reduced their debt over the year (down to R$600 million) and recorded the highest annual profit. In 2015 after an inconsistent start to the Carioca and national league seasons, multiple managers were dismissed and Flamengo failed to qualify for the Libertadores. However, Flamengo had signed Paolo Guerrero and Ederson and were the most valuable club in Brazil with debt now reduced to R$495 million. As a result, president Bandeira was re-elected. The club signed fan-favorite Diego in the mid-season and mounted a strong campaign, but could not catch Palmeiras in 2016.

2017 was characterized as the year Flamengo played two major finals at the end of the season but failed to win either. After going undefeated in the 2017 Campeonato Carioca, they were eliminated in the Copa Libertadores group stage, failing to win a single match away from home but qualifying for the Copa Sudamericana in third place. In the Copa do Brasil, the club reached the final where they lost in a penalty shootout to Cruzeiro. Less than three months later, they reached an unprecedented Copa Sudamericana final. They lost away to Independiente and drew at home 1–1, losing the title. After the match, a group of Flamengo supporters rioted outside the hotel where Independiente were staying. CONMEBOL punished the club with two closed-door home matches in the following Copa Libertadores. In the league, the club finished sixth and qualified for the following year's Libertadores.

Nine years after their last Campeonato Brasileiro victory, Flamengo made a title run but fell just short. In 2018 they spent the most rounds as league leader (thirteen) and broke their points record from 2016 (72), but finished runners-up behind Palmeiras. In the Libertadores they finished runner-up behind eventual champion River Plate and qualified to the round of 16, where they were eliminated by Cruzeiro. That season, the club recorded their two highest outgoing transfer fees in history: 18-year-old winger Vinícius Júnior moved to Real Madrid in July for €46 million, and 20-year-old midfielder Lucas Paquetá transferred to A.C. Milan for a reported €35 million at the end of the year. Both were products of Flamengo's youth academy.

2019 season
On the morning of 8 February 2019 a fire erupted at Flamengo's Ninho do Urubu training center, popular name for Centro de Treinamento George Helal (Vulture's Nest training center) (Flamengo training ground fire). The fire resulted in the deaths of ten academy players between the ages of 14 and 17 training with the club. Three others were injured. The cause of the fire was a malfunctioning air-conditioning unit that caught fire in the room of one of the victims close to 5:00 am. President Rodolfo Landim described it as "the worst tragedy the club has ever experienced in its 123 years." The governor of the state of Rio de Janeiro declared a three-day period of mourning following the tragedy. Since then, Flamengo fans sing in memory of those kids, usually referred to as the "Garotos do Ninho". It happens every tenth minute of Flamengo home games, since 10 kids died in the tragedy. The 2019 season marked the most successful one in the club's footballing history. At the end of 2018, Rodolfo Landim was elected club president for a three-year term. Flamengo paid the most expensive incoming transfer fee for a player in Brazilian football history, signing Giorgian de Arrascaeta from Cruzeiro for R$63 million (€14.5 million). In January the club signed forward Bruno Henrique from Santos and secured the loan of striker Gabriel Barbosa from Inter Milan.

After advancing out of the Copa Libertadores group stage, manager Abel Braga resigned and Flamengo hired Portuguese manager Jorge Jesus. Europe-based players Rafinha, Filipe Luís, Pablo Marí and Gerson were added to play alongside Flamengo's other record signings. After qualifying to their first Copa Libertadores semi-final since 1984, Flamengo defeated Grêmio 5–0 in their home leg at the Maracanã to advance their first Copa Libertadores final since 1981. For the first time in Copa Libertadores history, the final was played as a single match in a neutral venue. On 23 November 2019, at the Estadio Monumental in Lima, Peru against defending champions River Plate, Flamengo trailed 0–1 in the final minutes before Gabriel scored twice to secure the 2–1 victory.

Less than 24 hours later, Flamengo became champions of the Campeonato Brasileiro Série A for the first time since 2009 with four matches in hand after a loss by Palmeiras to Grêmio in the 34th round. Flamengo became only the second Brazilian club to win their state championship (2019 Campeonato Carioca), Campeonato Brasileiro, and Copa Libertadores in the same season, after Pelé's 1962 Santos team. Flamengo's 2019 campaign under Jorge Jesus' leadership broke a number of records in the Campeonato Brasileiro's 20-team double round-robin era (2006–present): most points (90), most wins (28), most goals scored (86), best goal differential (+49), longest undefeated streak (24 matches), most points clear of runners-up (16) and most goals by a single player (25 from Gabriel Barbosa).

Flamengo participated in the FIFA Club World Cup for the first time in the club's history in 2019 in Qatar. The club defeated Al Hilal SFC 3–1 in the semi-final, but lost 0–1 to Liverpool in the final.

2020 season
After winning the revived Supercopa do Brasil against Athletico Paranaense, then the Recopa Sudamericana against Copa Sudamericana champions Independiente del Valle, and the 2020 Campeonato Carioca, in July 2020 Jorge Jesus departed from Flamengo to return to Benfica, having won five titles in Brazil. Jesus's successor was former Pep Guardiola assistant Domènec Torrent, but his tenure was brief and he was replaced with Rogério Ceni in November 2020. Ceni led Flamengo to a second consecutive Campeonato Brasileiro championship, finishing one point ahead of Internacional.

2021 season
In 2021 Ceni led Flamengo to a third consecutive Campeonato Carioca, but was released after four losses in Flamengo's first ten Campeonato Brasileiro Série A matches. The club signed Renato Gaúcho as manager, who brought strong results in league play and took Flamengo back to the Copa Libertadores Final against Palmeiras, but lost 2–1 in extra time on 27 November 2021. He and the club parted ways after.

2022 season
In 2022, after a difficult start to the year under manager Paulo Sousa (runners-up in the Campeonato Carioca and Supercopa do Brasil), Dorival Júnior returned to Flamengo and brought another wave of glory. The team advanced to the finals of the Copa do Brasil against Corinthians. In the second leg in the Maracanã, tied 1–1 on aggregate, Flamengo were victorious in the penalty shootout with Rodinei scoring the winner. This was Flamengo's fourth Copa do Brasil championship and first since 2013. Later that month on 29 October 2022, Flamengo faced Athletico Paranaense in Guayaquil, Ecuador for the final of the Copa Libertadores. Gabriel Barbosa scored the only goal of the match and Flamengo claimed their second Copa Libertadores in four years, and third overall.

Crest
Flamengo's crest has changed slightly throughout the club's history. Most of the changes has been changes to the interlocked letters monogram, with the latest redesign being unveiled in 2018.

The club uses three crests in different situations: the full crest is used as the club's official logo, the rowing crest is used for all rowing related uniforms and equipment, and the white "CRF" monogram is typically the only component of the crest worn on the primary football uniform. It remarkably resembles the "RFC" monogram traditionally used by Scottish club Rangers F.C..

Beginning in 1980, Flamengo wore three white stars aligned vertically along the side of their monogram crest to indicate their three state league tri-championships (1942–43–44, 1953–54–55, and 1978–79–79 Special). When Nike became Flamengo's kit provider in 2000, their first kit featured the full shield crest with three stars above it for the first time. After the fourth state league tri-championship (1999-2000-2001) and to commemorate the 20th anniversary of the 1981 Copa Libertadores and Intercontinental Cup championships, a fourth white star and a gold star were introduced above the crest. Since 2005 the club uses only the gold star above the "CRF" monogram crest on their shirts.

Uniforms
At the 1895 meeting which established the Flamengo rowing club, the club's official colors were decided as blue and gold to symbolized the sky of Rio de Janeiro and the riches of Brazil. The team adopted a uniform of thick blue and gold horizontal stripes. However Flamengo failed to win a single regatta in their first year and gained the nickname of "bronze club." The team colors were perceived as bad luck, and the colored fabric was expensive to import from England. One year after the club's establishment, the official colors were replaced with the current red and black.

In 1912, at the request of the Flamengo rowing team (who opposed the use of their same uniform by the newly established football team), the football players dressed in shirts divided into red and black quarters which became known as the papagaio de vintém uniform, named after a particular style of kite. However the shirt became synonymous with bad luck and was replaced in 1913 by a shirt with red and black horizontal stripes and thinner white bands. This uniform was nicknamed the cobra coral due to its similarity to the pattern of a coral snake. This was the uniform worn when Flamengo won their first Campeonato Carioca title in 1914. The white bands were removed from the shirt in 1916 as the pattern was very similar to the flag of Germany at the time, who Brazil was allied against in World War I. The rowing team permitted the football team to use their same uniform, and Flamengo's traditional football uniform of a red and black striped shirt, white shorts and red-black socks was born.

In 1938, Flamengo manager Dori Kruschner suggested the creation of a secondary white uniform to "improve the visibility in night matches." The new uniform was approved by the club, and Flamengo became a pioneer of secondary uniforms in Brazil. The white shirt had two red and black stripes across the chest until 1979 when it was changed to a plain white chest with stripes on the sleeves. This was the shirt worn by the team that won the 1981 Intercontinental Cup.

Beginning in the 1990s the club began to experiment with their second and third alternative uniforms, sometimes wearing all black or all red shirts. In 1995 for the club's centenary, a "papagaio de vintém" shirt was worn in friendlies. In 2010 uniform supplier Olympikus introduced a blue and gold alternative uniform which paid homage to Flamengo's original colors and regatta uniform, however it was not well received by fans who likened it to the uniform worn by the fictional satirical team "Tabajara" on the popular comedy program Casseta & Planeta Urgente. In the first half of the 2009 season, the team wore a uniform without sponsorship for the first time in 25 years. Flamengo have continued to traditionally wear red and black striped shirts with white shorts as their primary uniform.

Kit suppliers and shirt sponsors
The following is a list of Flamengo's sponsors and uniform suppliers.

Scarlet-Black Nation
Since the early 1990s, surveys have shown that Flamengo is consistently the most supported club in Brazil with an estimated more than 40 million fans. In a 2019 survey, 20 percent of adult football fans in Brazil consider themselves supporters of Flamengo, with high levels of support in all states of the country, including the North and Northeast regions, in addition to Rio de Janeiro. Flamengo supporters are known as Nação Rubro-Negra (en: Scarlet-Black Nation).

The first organized supporters group in all of Brazil, Charanga Rubro-Negra (Scarlet-Black Charanga Band), was founded in support of Flamengo in 1942. Since then, a large number of additional organized supporters groups have formed around Flamengo, notably Torcida Jovem-Fla (Young-Fla), Urubuzada (Vultures), Flamanguaça (FlaBooze), and Raça Rubro-Negra (Scarlet-Black Race).

In 2007 Flamengo supporters were declared as part of the cultural heritage of the city of Rio de Janeiro, along with bossa nova and Bola Preta, the oldest Carnival block in Rio.

In the 1983 Campeonato Brasileiro Série A final, Flamengo played against Santos in the Maracanã in front of an official crowd of 155,523 with some estimates of over 160,000 people in attendance.

The largest attendance for a football match in the world's history was the derby between Flamengo and Fluminense in 1963, with 194,603 spectators. Flamengo matches in the Maracanã have broken the 150,000 attendance mark thirteen times.

In July 2020, their YouTube channel FLATV passed Liverpool F.C. as the club with the third-most subscriptions for a soccer channel only behind Barcelona and Real Madrid. Flamengo's channel reached over 5 million subscriptions.

Mascot
Flamengo's first mascot was Popeye the Sailor Man, a comic book and cartoon character from the 1940s. The idea for the mascot came from Argentine cartoonist Lorenzo Molas, who saw in Popeye the strength and persistence of Flamengo, in addition to its obvious connection with the sea. However, such a mascot was never very popular among the club's supporters.

In the 1960s, rival fans began to call Flamengo fans urubus (English: "vultures"), a racist allusion to the large mass of Afro-descendant and poor suporters. Such an offensive nickname was never well received by Flamengo fans, until May 31, 1969. It was on a Sunday, when a Scarlet-Black fan decided to take a vulture to a game between Flamengo and Botafogo at Maracanã. At the time, the two clubs were playing the classic with the greatest post-Garrincha rivalry. And Flamengo hadn't beaten the rival for four years. In the stands, Botafogo fans shouted, as always, that Flamengo was a urubu team.

The vulture was released in the stands with a Flamengo´s flag tied to its feet and, when it landed on the field, just before the game started, the crowd cheered and shouted: É urubu, é urubu. (English: "it's a vulture, it's a vulture"). Flamengo won the game 2-1 and, from there, the new mascot was consecrated, taking Popeye's place. The cartoonist Henfil, tried to humanize him in his sports cartoons in newspapers and magazines, and the Urubu became a popular mascot.

In 2000, Flamengo's mascot received an official design and a name: Samuca. However, this name did not become popular among the supporters, who continue to call him simply Urubu.

On May 25, 2008, debuted at Maracanã in a match between Flamengo and Internacional, valid for the 2008 Campeonato Brasileiro Série A. Since then, they have been present in several Flamengo games and events.

Anthem
Flamengo has two anthems: the official one, called Hymno Rubro-Negro (English: "Scarlet-Black Anthem"), which was created in 1920 with lyrics and music by Paulo Magalhães (former goalkeeper of the club), recorded in 1932 by singer Castro Barbosa and registered in 1937 at the Instituto Nacional de Música, with the refrain "Flamengo! Flamengo! Tua glória é lutar, Flamengo! Flamengo! Campeão de terra e mar" (in English: "Flamengo! Flamengo! Your glory is to fight, Flamengo! Flamengo! Champion of land and sea"); and the popular one, with lyrics and music by Lamartine Babo, recorded for the first time by Gilberto Alves in 1945. The latter is the best known and the one that sings the glories of the club, whose refrain is "Uma vez Flamengo, sempre Flamengo" (English: "Once you are Flamengo, always Flamengo").

Rua Paysandu
Flamengo's first official home ground was the Estádio da Rua Paysandu ("Paysandu Street Stadium"). The ground formerly belonged to Paissandu Atlético Clube before they ceased playing football in 1914. The owners of the ground rented the field to Flamengo where they played their home matches from 1915 to 1932. Between 1912 and 1915 (and later between 1932 and 1938), the club played all their matches on the grounds of Botafogo or Fluminense. The first Flamengo match at Rua Paysandu was played on October 31, 1915, in the Campeonato Carioca against Bangu. Crowds of 15,000 watched Flamengo face Fluminese at the park in 1918 and 1919.

Estádio da Gávea

Flamengo's home stadium is nominally the Estádio da Gávea (officially named the Estádio José Bastos Padilha at Flamengo's Gávea Headquarters), which was inaugurated on September 4, 1938, and has a capacity of 4,000 people. The stadium is named after José Bastos Padilha, Flamengo's president at the time of the stadium's construction, from 1933 to 1937. Even though Flamengo no longer play their matches at Gávea, the site serves as the club's administrative headquarters. Since the 1990s, the stadium has been used almost exclusively for the club's youth and women's teams' matches, and as the training ground for the senior team. Most matches are played at the significantly larger Maracanã Stadium, considered by supporters as the real Flamengo home ground. Gávea Stadium is not actually located in the neighborhood of Gávea but rather in Leblon.

During the 2014 FIFA World Cup, the Dutch National Team used the Estádio da Gávea and all of its facilities as their training ground in preparation for the competition.

Maracanã
Since its construction for the 1950 World Cup, the Maracanã has primarily served as the home ground for the four biggest Rio de Janeiro clubs. The stadium was officially completed in 1965, 17 years after construction began. In 1963, more than 194,000 people attended a match between Flamengo and Fluminense at the Maracanã. The capacity of the stadium allowed Flamengo to have the largest support of any clubs in Brazil for much of the 20th century. In 1989 Zico scored his final goal in the historic stadium, setting the current unbroken record for goals in the Maracanã at 333. An upper stand in the stadium collapsed on July 19, 1992, in the second match of the finals of 1992 Campeonato Brasileiro Série A between Botafogo and Flamengo, leading to the death of three spectators and injuring 50 others. Following the disaster, the stadium's capacity was greatly reduced as it was converted to an all-seater stadium in the late 1990s. Following its 50th anniversary in 2000, the stadium underwent renovations which would increase its full capacity to around 103,000. After years of planning and nine months of closure between 2005 and 2006 (during which Flamengo played their home matches at Volta Redonda's Estádio Raulino de Oliveira and Portuguesa's Estádio Luso Brasileiro), the stadium was reopened in January 2007 with an all-seated capacity of 87,000. For the 2014 World Cup and 2016 Olympics and Paralympics, a major reconstruction project was initiated in 2010. The original seating bowl, with a two-tier configuration, was demolished, giving way to a new one-tier seating bowl.

The stadium is officially under the management of Brazilian conglomerate Odebrecht as of 2013. This has resulted in unfavorable rental agreements for Flamengo who do not officially administer the stadium and often owe rental fees for matches in excess of their ticket revenue, even for matches with high attendance. The most recent rental agreement was signed in 2018 and is valid through 2020. In April 2019, Flamengo and Fluminense came to an agreement with the state and the operators of the Maracanã to serve as joint-managers of the venue for the following six months, a deal which allowed the clubs to pay a fixed monthly fee and receive a higher share of matchday revenue than was granted under the previous deal.

Ilha do Urubu
In 2017, Flamengo played their home matches at the Estádio Luso Brasileiro of Portuguesa while disputing their stadium situation with the Rio de Janeiro state government and Complexo Maracanã Entretenimento S.A. (composed of Odebrecht, IMX, AEG), the operator of the Maracanã Stadium. A three-year agreement was signed with Portuguesa over management of Estádio Luso Brasileiro, named Ilha do Urubu ("Vulture's Island") by Flamengo supporters in a poll. The park was renovated to fit 20,500 spectators. Flamengo started playing at the arena in March 2017, but after several delays and administrative issues and a new contract with the Maracanã, Flamengo broke their lease with the Ilha do Urubu in July 2018.

Rivalry with Botafogo
The match became known as the Clássico da Rivaldade (English: "Rivalry Classic") in the 1960s, is the traditional Brazilian derby between Botafogo and Flamengo, both from Rio de Janeiro.The first confrontation between Rio de Janeiro rivals Flamengo and Botafogo occurred in 1913. Flamengo's mascot of the vulture originated during the June 1, 1969, match against Botafogo when Flamengo supporters released a vulture onto the field in response to the racist cheers of urubu (vulture) from Botafogo and other teams' supporters. Flamengo's top scorer in the derby is Zico and Botafogo's top scorer is Heleno de Freitas.

Rivalry with Fluminense
The Fla-Flu or Clássico das Multidões (English: "Derby of the Crowds") is the traditional Brazilian derby between Flamengo and Fluminense, both from Rio de Janeiro. It is considered by football experts and much of the sports media as one of the greatest classics in the world. According to writer Nelson Rodrigues, the classic was generated by resentment. On the tricolor side, the fact that their starting players deserted and went to form Flamengo's football department, and on the red-black side, the fact that Fluminense still won the first match, circumstances that would have been fundamental in generating the derby mystique.

The rivalry between these two clubs began in October 1911, when a group of dissatisfied players from Fluminense left their club and joined rowing club of Flamengo, establishing the football department at their new club. The first Fla–Flu ever was played the following year on July 7. Fluminense won the match 3–2, with 800 people in attendance.

Over time Flamengo and Fluminense became powerhouses of Brazilian football, although with common origins, the clubs became very distinct and in some cases antagonistic. Soon Flamengo became the most popular team in Brazil, with fans mainly in the working and lower classes across the country. While Fluminense becomes a club linked to the rich class of Rio de Janeiro, especially in the south of the city.

In 1950, the Maracanã stadium was built to host the FIFA World Cup, although the four big clubs of Rio de Janeiro play in the stadium, Flamengo and Fluminense are the teams that played the most matches there and currently manage the stadium, which belongs to the state of Rio de Janeiro. The Fla-Flu holds the world record for attendance in games between clubs: 194,603 spectators were present at the Maracanã stadium, in the final of the 1963 Campeonato Carioca, won by Flamengo after a goalless draw.

Flamengo and Fluminense are the two most successful team in the Campeonato Carioca: as of 2023 Flamengo have 37 state league titles and Fluminense have 33. Since 2012, Fla-Flu has been considered an Intangible Heritage of Rio de Janeiro, being the only football derby to deserve this honor.

Rivalry with Vasco da Gama
The Clássico dos Milhões (English: "Derby of Millions") is the traditional Brazilian derby between Flamengo and Vasco da Gama, both from Rio de Janeiro. Although the rivalries against Botafogo and Fluminense are more traditional, Vasco is the club most hated by Flamengo supporters and vice versa,  with the derby between them being considered one of the biggest rivalries in Brazilian football and in football worldwide. The derby's name originated in the 1920s and refers to the two largest fanbases in the state of Rio de Janeiro. Both clubs were established in the late 19th century as regatta rowing clubs. The first football match between the clubs was played in 1923 when Vasco entered the top division of the Campeonato Carioca.

From the 1972 to 2001, the matchup was elevated as the most important of Flamengo's rivalries and became one of the biggest rivalries in all of Brazil. In this span, Flamengo and Vasco played in or won the final of each of the phases of the state championship nearly every year, frequently facing one another. This also coincided with the beginnings of the national Campeonato Brasileiro and the growth in popularity of both clubs nationwide. The most iconic matches between Flamengo and Vasco featured the idols of both clubs challenging each other: Zico of Flamengo (1971–83; 85–89) and Roberto Dinamite of Vasco da Gama (1971–79; 80–93).

Some of the great players in Brazilian football played for both teams, and with hectic transfers in the 1980s and 1990s. Bebeto revealed by Flamengo, was seen as Zico's successor, but left the red-black team and went to play for Vasco in 1989. Romário revealed for Vasco's youth teams, when he returned to Brazil in 1995, recently champion of the 1994 FIFA World Cup and elected best player of the year by FIFA, he chose to play for Flamengo. Other players like Andrade, Edmundo, Felipe, Jean, Jorginho, Juninho Paulista, Dejan Petković and Tita.

Rivalry with Atlético Mineiro
Flamengo has an inter-state rivalry with Atlético Mineiro of Minas Gerais, developed in the 1980s from numerous controversial encounters between the two clubs in that decade's Campeonato Brasileiro and Copa Libertadores editions. It maintained its high intensity through the following years, and is considered one of the biggest interstate rivalries in Brazilian football.

Youth players with first team numbers
The following players have previously made appearances or have appeared on the substitutes bench for the first team.

Retired numbers

 * 12 – 🇧🇷 Club Supporters (the 12th Man) – Number dedicated to the rubro-negro fans.

Football honours
(1) In 1940 the competition was interrupted with Flamengo and Fluminense in the lead, without the CBD making the title official, however, the clubs and newspapers at the time considered the result definitive and declared the Flamengo and Fluminense as the legitimate champions of the competition. The club currently considers itself champion of the competition and includes this title among its achievements.

Others

 * Torneio do Povo (1): 1972
 * Copa dos Campeões Mundiais (1): 1997
 * Taça Brahma dos Campeões (1): 1992
 * Super Series Manaus (1): 2015
 * Taça Guanabara (24): 1970, 1972, 1973, 1978, 1979, 1980, 1981, 1982, 1984, 1988, 1989, 1995, 1996, 1999, 2001, 2004, 2007, 2008, 2011, 2014, 2018, 2020, 2021, 2024
 * Taça Rio (9): 1983, 1985, 1986, 1991, 1996, 2000, 2009, 2011, 2019
 * Copa Rio (1): 1991
 * Torneio Relâmpago (1): 1943Troféu Copa Libertadores 2019.jpg trophy.|335x335px]]
 * Torneio Extra (1): 1934
 * Torneio Aberto do Rio de Janeiro (1): 1936
 * Other Campeonato Carioca rounds (7): 1974, 1978, 1979, 1979, 1979, 1981, 1987
 * Torneio Super Clássicos (3): 2013, 2014, 2015
 * Campeonato da Capital do Rio de Janeiro Copa Rio stage (2): 1991, 1993
 * Torneio Início (6): 1920, 1922, 1946, 1951, 1952, 1959

Average attendance
Below is Flamengo's average home match average attendance in Campeonato Brasileiro league matches since the current league format was adopted in 2003.

Domestic results
Below are Flamengo's results in domestic competitions since the previous nationwide organized competitions (1959), before the first official Brazilian national championship tournament in 1971.

W = Winners; RU = Runners-up; SF = Semi-finals; QF = Quarter-finals; R16 = Round of 16; R32 = Round of 32; 3R = Third round; 2R = Second round; DNQ = Did Not Qualify; DNP = Did Not Participate
 * Key

International results
Below are Flamengo's results in official international competitions since the club's first qualification to the Copa Libertadores in 1981. Group stage match results are listed with the home match first.

† Defunct competitions

(H) – Home; (A) – Away; (N) – Neutral * Tiebreaker match ** Both matches played at the same stadium

Men's basketball
Flamengo basketball won the Rio de Janeiro City Championship in 1919 and have since grown to be one of the most successful and supported basketball teams in the country. The club have won six Brazilian Championships, a record 44 Rio de Janeiro State Championships, the 1953 South American Championship of Champions Clubs, and the 2009 South American League.

In 2014, Flamengo won the League of the Americas without a single loss, defeating Pinheiros in the final. This qualified Flamengo to their first Intercontinental Cup against EuroLeague champions Maccabi Tel Aviv. Flamengo won and became the second Brazilian basketball team in history to be world champions. Flamengo, Real Madrid and Barcelona are the only clubs to have won the Intercontinental Cups in both football and basketball.

Flamengo hosted and participated in the 2019 FIBA Intercontinental Cup, falling to BCL champions AEK Athens in the final.

Honours

 * Novo Basquete Brasil (NBB): 7
 * 2009, 2012–13, 2013–14, 2014–15, 2015–16, 2018–19, 2020–21

 * Copa Super 8: 2
 * 2018, 2020–21

 * Campeonato Brasileiro de Basquete: 1
 * 2008

 * Basketball Champions League Americas: 1
 * 2020–21

 * FIBA Americas League: 1
 * 2014

 * FIBA Intercontinental Cup: 2
 * 2014, 2022

Women's football
Between 1995 and 2001, the Flamengo women's football team competed in the Campeonato Carioca. In 2002 the women's Carioca tournament was not organized, and the club ceased operation of the team. Flamengo attempted to re-established their women's professional football department in 2011 through a partnership with the city of Guarujá where the team trained and hoped to sign Marta, but the team never materialized. In 2015 president Eduardo Bandeira de Mello succeeded in establishing the football team through a partnership with the Brazilian Navy. In their first season, the team won the women's Campeonato Carioca state championship and have won it every season from 2015 to 2019. In 2016 Flamengo won the Campeonato Brasileiro de Futebol Feminino for the first time against Rio Preto, become the only club outside the state of São Paulo to win the tournament since its creation in 2013. Flamengo also competed in the 2016 and 2017 Copa do Brasil de Futebol Feminino before the cancellation of the competition in favor of the Campeonato Brasileiro.

Honors

 * Campeonato Brasileiro de Futebol Feminino: 1
 * 2016

 * Campeonato Carioca de Futebol Feminino: 5
 * 2015, 2016, 2017, 2018, 2019

Women's basketball
The Flamengo women's basketball team won back-to-back Brazilian championships in 1954 and 1955. Ten years later with some of the same players, the program won back-to-back Brazilian titles again in 1964 and 1965. Flamengo players Norminha, Angelina, Marlene and Delei were champions of the 1967 Pan American Games in Winnipeg with the Brazil women's national basketball team.

In 1966 Flamengo won the Inter-club Basketball World Championship. The team was led by Angelina, considered one of the best players of her time.

Rowing
The "Flamengo Regatta Group", later renamed the "Flamengo Regatta Club", was established in 1895 as Flamengo's first ever organized athletic department, forming the basis of the club's history and identity to this day. The first regatta victory came in 1898 in the Nautical Championship of Brazil, and the first title was won in 1900, the Regatta of the IV Centenary of the Discovery of Brazil, for which the club was awarded the Jug Tropon trophy. In 1905 the club won a classic event, the South American Cup. By 1908, Flamengo had already won 43 gold, 126 silver and 141 bronze medals. The success of the rowing club made the team famous even before the founding of the football department in 1911. Great rowers such as Everardo Paes de Lima, Arnaldo Voigt, Alfredo Correia ("Boca Larga"), Ângelo Gammaro ("Angelú") and Antônio Rebello Junior ("Engole Garfo") came through Flamengo, the latter three being considered Brazilian sports heroes for completing the Rio-Santos crossing in 1932.

From 1931 to 1937 Flamengo were seven-time champions of Rio de Janeiro, and were four-time repeat state champions from 1940 to 1943. In 1963 the "Buck era" began, which revolutionized Flamengo rowing. The coach brought in athletes from other states and renovated the club's facilities to better accommodate the boats. Buck coached the Brazil national team, directing the team in several international competitions. In the early 1980s, Flamengo won the state championship and won again in 1992. The club has won the men's Brazil Trophy 10 times, and the female once, in addition to 45 Carioca state titles.

Water polo
Water polo is the second oldest sport practiced by the club, after rowing. The team played their first game on May 27, 1913, in Rio de Janeiro, and defeated Clube Internacional de Regatas, 3–2. Flamengo only opened its water sports facility in 1965. Prior to that, athletes played and trained in the Rodrigo de Freitas Lagoon or in the sea. Flamengo's first polo championship in Rio de Janeiro came in 1985 and was the start of a run of nine consecutive championships through 1993. In 1985 the club won the South American Club Championship and the Brazil Trophy (also won four consecutive times). A female water polo team was established in 1987, winning the Brazil Trophy in 1987 and 1991 and the state championship in 1995.

American football
The club launched their American football team in 2013, forming a partnership with the Rio de Janeiro Emperors. The Emperors were established in 2008 and had previously partnered with Fluminense from 2010 to 2013. The team officially goes by the name of the Flamengo Emperors and compete in the BFA (Brasil Futebol Americano).

Tennis
Flamengo began playing tennis championships in 1916 and became three-time Rio champions soon after (1916–18), even with their athletes training at other clubs. Until 1932 the club practiced tennis on their football field at the Rua Paysandu. In 1963 the club inaugurated their own facilities and courts. The biggest idol of Flamengo's tennis department is Thomas Koch.

E-sports
In 2017 the club announced they would be entering the increasingly popular e-sports leagues the following year, beginning with a League of Legends department and eventually establishing a PES team. Because the competitive League of Legends center of Brazil is at the Riot Games studio in São Paulo, Flamengo established a permanent "gaming office" for the team in the city. Flamengo announced that they would not be partnering with an existing team but rather would have their own team. In October 2017 they announced the purchase of Merciless Gaming, a team in the second division of the Brazilian League of Legends championship.

Additional sports departments

 * Artistic gymnastics
 * Auto racing (Flamengo Superleague Formula team)
 * Beach soccer
 * Bocce
 * CP football
 * Futsal
 * Indoor soccer
 * Judo
 * Swimming
 * Synchronized swimming
 * Volleyball

title: CR Flamengo


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Quadratic function

In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before the 20th century, the distinction was unclear between a polynomial and its associated polynomial function; so "quadratic polynomial" and "quadratic function" were almost synonymous. This is still the case in many elementary courses, where both terms are often abbreviated as "quadratic".

For example, a univariate (single-variable) quadratic function has the form

 * $$f(x)=ax^2+bx+c,\quad a \ne 0,$$

where $x$ is its variable. The graph of a univariate quadratic function is a parabola, a curve that has an axis of symmetry parallel to the $y$-axis.

If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros of the corresponding quadratic function.

The bivariate case in terms of variables $x$ and $y$ has the form
 * $$ f(x,y) = a x^2 + bx y+ cy^2 + d x+ ey + f ,$$

with at least one of $a, b, c$ not equal to zero. The zeros of this quadratic function is, in general (that is, if a certain expression of the coefficients is not equal to zero), a conic section (a circle or other ellipse, a parabola, or a hyperbola).

A quadratic function in three variables $x$, $y$, and $z$ contains exclusively terms $x^{2}$, $y^{2}$, $z^{2}$, $xy, xz, yz, x, y, z$, and a constant:

 * $$f(x,y,z)=ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz +j,$$

where at least one of the coefficients $a, b, c, d, e, f$ of the second-degree terms is not zero.

A quadratic function can have an arbitrarily large number of variables. The set of its zero form a quadric, which is a surface in the case of three variables and a hypersurface in general case.

Etymology
The adjective quadratic comes from the Latin word quadrātum ("square"). A term raised to the second power like $x^{2}$ is called a square in algebra because it is the area of a square with side $x$.

Coefficients
The coefficients of a quadratic function are often taken to be real or complex numbers, but they may be taken in any ring, in which case the domain and the codomain are this ring (see polynomial evaluation).

Degree
When using the term "quadratic polynomial", authors sometimes mean "having degree exactly 2", and sometimes "having degree at most 2". If the degree is less than 2, this may be called a "degenerate case". Usually the context will establish which of the two is meant.

Sometimes the word "order" is used with the meaning of "degree", e.g. a second-order polynomial. However, where the "degree of a polynomial" refers to the largest degree of a non-zero term of the polynomial, more typically "order" refers to the lowest degree of a non-zero term of a power series.

Variables
A quadratic polynomial may involve a single variable x (the univariate case), or multiple variables such as x, y, and z (the multivariate case).

The one-variable case
Any single-variable quadratic polynomial may be written as
 * $$ax^2 + bx + c,$$

where x is the variable, and a, b, and c represent the coefficients. Such polynomials often arise in a quadratic equation $$ax^2 + bx + c = 0.$$ The solutions to this equation are called the roots and can be expressed in terms of the coefficients as the quadratic formula. Each quadratic polynomial has an associated quadratic function, whose graph is a parabola.

Bivariate and multivariate cases
Any quadratic polynomial with two variables may be written as
 * $$a x^2 + b y^2 + cxy + dx+ e y + f,$$

where $x$ and $y$ are the variables and $a, b, c, d, e, f$ are the coefficients, and one of $a$, $b$ and $c$ is nonzero. Such polynomials are fundamental to the study of conic sections, as the implicit equation of a conic section is obtained by equating to zero a quadratic polynomial, and the zeros of a quadratic function form a (possibly degenerate) conic section. Similarly, quadratic polynomials with three or more variables correspond to quadric surfaces or hypersurfaces.

Quadratic polynomials that have only terms of degree two are called quadratic forms.

Forms of a univariate quadratic function
A univariate quadratic function can be expressed in three formats:

 * $$f(x) = a x^2 + b x + c$$ is called the standard form,
 * $$f(x) = a(x - r_1)(x - r_2)$$ is called the factored form, where $r_{1}$ and $r_{2}$ are the roots of the quadratic function and the solutions of the corresponding quadratic equation.
 * $$f(x) = a(x - h)^2 + k$$ is called the vertex form, where $h$ and $k$ are the $x$ and $y$ coordinates of the vertex, respectively.

The coefficient $a$ is the same value in all three forms. To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots $r_{1}$ and $r_{2}$. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.

Graph of the univariate function

Regardless of the format, the graph of a univariate quadratic function $$f(x) = ax^2 + bx + c$$ is a parabola (as shown at the right). Equivalently, this is the graph of the bivariate quadratic equation $$y = ax^2 + bx + c$$.

 * If $a > 0$, the parabola opens upwards.
 * If $a < 0$, the parabola opens downwards.

The coefficient $a$ controls the degree of curvature of the graph; a larger magnitude of $a$ gives the graph a more closed (sharply curved) appearance.

The coefficients $b$ and $a$ together control the location of the axis of symmetry of the parabola (also the $x$-coordinate of the vertex and the h parameter in the vertex form) which is at
 * $$x = -\frac{b}{2a}.$$

The coefficient $c$ controls the height of the parabola; more specifically, it is the height of the parabola where it intercepts the $y$-axis.

Vertex
The vertex of a parabola is the place where it turns; hence, it is also called the turning point. If the quadratic function is in vertex form, the vertex is $(h, k)$. Using the method of completing the square, one can turn the standard form
 * $$f(x) = a x^2 + b x + c$$

into
 * $$\begin{align}

f(x) &= a x^2 + b x + c \\ &= a (x - h)^2 + k \\ &= a\left(x - \frac{-b}{2a}\right)^2 + \left(c - \frac{b^2}{4a}\right),\\ \end{align}$$ so the vertex, $(h, k)$, of the parabola in standard form is
 * $$ \left(-\frac{b}{2a}, c - \frac{b^2}{4a}\right). $$

If the quadratic function is in factored form
 * $$f(x) = a(x - r_1)(x - r_2)$$

the average of the two roots, i.e.,
 * $$\frac{r_1 + r_2}{2}$$

is the $x$-coordinate of the vertex, and hence the vertex $(h, k)$ is
 * $$ \left(\frac{r_1 + r_2}{2}, f\left(\frac{r_1 + r_2}{2}\right)\right).$$

The vertex is also the maximum point if $a < 0$, or the minimum point if $a > 0$.

The vertical line

 * $$ x=h=-\frac{b}{2a} $$

that passes through the vertex is also the axis of symmetry of the parabola.

Maximum and minimum points
Using calculus, the vertex point, being a maximum or minimum of the function, can be obtained by finding the roots of the derivative:
 * $$f(x)=ax^2+bx+c \quad \Rightarrow \quad f'(x)=2ax+b$$

$x$ is a root of $f '(x)$ if $f '(x) = 0$ resulting in
 * $$x=-\frac{b}{2a}$$

with the corresponding function value
 * $$f(x) = a \left (-\frac{b}{2a} \right)^2+b \left (-\frac{b}{2a} \right)+c = c-\frac{b^2}{4a},$$

so again the vertex point coordinates, $(h, k)$, can be expressed as
 * $$ \left (-\frac {b}{2a}, c-\frac {b^2}{4a} \right). $$

Exact roots
The roots (or zeros), $r_{1}$ and $r_{2}$, of the univariate quadratic function

 * $$\begin{align}

f(x) &= ax^2+bx+c \\ &= a(x-r_1)(x-r_2), \\ \end{align}$$

are the values of $x$ for which $f(x) = 0$.

When the coefficients $a$, $b$, and $c$, are real or complex, the roots are

 * $$r_1=\frac{-b - \sqrt{b^2-4ac}}{2a}, $$

 * $$r_2=\frac{-b + \sqrt{b^2-4ac}}{2a}. $$

Upper bound on the magnitude of the roots
The modulus of the roots of a quadratic $$ax^2+bx+c$$ can be no greater than $$\frac{\max(|a|, |b|, |c|)}{|a|}\times \phi, $$ where $$\phi$$ is the golden ratio $$\frac{1+\sqrt{5}}{2}.$$

The square root of a univariate quadratic function
The square root of a univariate quadratic function gives rise to one of the four conic sections, almost always either to an ellipse or to a hyperbola.

If $$a>0,$$ then the equation $$ y = \pm \sqrt{a x^2 + b x + c} $$ describes a hyperbola, as can be seen by squaring both sides. The directions of the axes of the hyperbola are determined by the ordinate of the minimum point of the corresponding parabola $$ y_p = a x^2 + b x + c .$$ If the ordinate is negative, then the hyperbola's major axis (through its vertices) is horizontal, while if the ordinate is positive then the hyperbola's major axis is vertical.

If $$a<0,$$ then the equation $$ y = \pm \sqrt{a x^2 + b x + c} $$ describes either a circle or other ellipse or nothing at all. If the ordinate of the maximum point of the corresponding parabola $$ y_p = a x^2 + b x + c$$ is positive, then its square root describes an ellipse, but if the ordinate is negative then it describes an empty locus of points.

Iteration
To iterate a function $$f(x)=ax^2+bx+c$$, one applies the function repeatedly, using the output from one iteration as the input to the next.

One cannot always deduce the analytic form of $$f^{(n)}(x)$$, which means the nth iteration of $$f(x)$$. (The superscript can be extended to negative numbers, referring to the iteration of the inverse of $$f(x)$$ if the inverse exists.) But there are some analytically tractable cases.

For example, for the iterative equation

 * $$f(x)=a(x-c)^2+c$$

one has
 * $$f(x)=a(x-c)^2+c=h^{(-1)}(g(h(x))),$$

where
 * $$g(x)=ax^2$$ and $$h(x)=x-c.$$

So by induction,
 * $$f^{(n)}(x)=h^{(-1)}(g^{(n)}(h(x)))$$

can be obtained, where $$g^{(n)}(x)$$ can be easily computed as
 * $$g^{(n)}(x)=a^{2^{n}-1}x^{2^{n}}.$$

Finally, we have
 * $$f^{(n)}(x)=a^{2^n-1}(x-c)^{2^n}+c$$

as the solution.

See Topological conjugacy for more detail about the relationship between f and g. And see Complex quadratic polynomial for the chaotic behavior in the general iteration.

The logistic map

 * $$ x_{n+1} = r x_n (1-x_n), \quad 0\leq x_0<1$$

with parameter 2<r<4 can be solved in certain cases, one of which is chaotic and one of which is not. In the chaotic case r=4 the solution is

 * $$x_{n}=\sin^{2}(2^{n} \theta \pi)$$

where the initial condition parameter $$\theta$$ is given by $$\theta = \tfrac{1}{\pi}\sin^{-1}(x_0^{1/2})$$. For rational $$\theta$$, after a finite number of iterations $$x_n$$ maps into a periodic sequence. But almost all $$\theta$$ are irrational, and, for irrational $$\theta$$, $$x_n$$ never repeats itself – it is non-periodic and exhibits sensitive dependence on initial conditions, so it is said to be chaotic.

The solution of the logistic map when r=2 is

$$x_n = \frac{1}{2} - \frac{1}{2}(1-2x_0)^{2^{n}}$$

for $$x_0 \in [0,1)$$. Since $$(1-2x_0)\in (-1,1)$$ for any value of $$x_0$$ other than the unstable fixed point 0, the term $$(1-2x_0)^{2^{n}}$$ goes to 0 as n goes to infinity, so $$x_n$$ goes to the stable fixed point $$\tfrac{1}{2}.$$

Bivariate (two variable) quadratic function
A bivariate quadratic function is a second-degree polynomial of the form
 * $$ f(x,y) = A x^2 + B y^2 + C x + D y + E x y + F,$$

where A, B, C, D, and E are fixed coefficients and F is the constant term. Such a function describes a quadratic surface. Setting $$f(x,y)$$ equal to zero describes the intersection of the surface with the plane $$z=0,$$ which is a locus of points equivalent to a conic section.

Minimum/maximum
If $$ 4AB-E^2 <0 ,$$ the function has no maximum or minimum; its graph forms a hyperbolic paraboloid.

If $$ 4AB-E^2 >0 ,$$ the function has a minimum if both A > 0 and B > 0, and a maximum if both A < 0 and B < 0; its graph forms an elliptic paraboloid. In this case the minimum or maximum occurs at $$ (x_m, y_m) ,$$ where:

 * $$x_m = -\frac{2BC-DE}{4AB-E^2},$$

 * $$y_m = -\frac{2AD-CE}{4AB-E^2}.$$

If $$ 4AB- E^2 =0 $$ and $$ DE-2CB=2AD-CE \ne 0 ,$$ the function has no maximum or minimum; its graph forms a parabolic cylinder.

If $$ 4AB- E^2 =0 $$ and $$ DE-2CB=2AD-CE =0 ,$$ the function achieves the maximum/minimum at a line—a minimum if A>0 and a maximum if A<0; its graph forms a parabolic cylinder.

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

title: Quadratic function


text:
Sport Club Corinthians Paulista

Sport Club Corinthians Paulista is a Brazilian professional sports club based in São Paulo, in the district of Tatuapé. Although it competes in multiple sports modalities, it is best known for its professional men's football team, which plays in the Campeonato Brasileiro Série A, the top tier of Brazilian football, as well as in the Campeonato Paulista Série A1, the first division of the traditional in-state competition.

Founded in 1910 by five railway workers inspired by the London-based Corinthian Football Club, Corinthians traditionally plays in a white and black home kit. Their crest was first introduced in 1939 by modernist painter and former player Francisco Rebolo, featuring the São Paulo state flag in a shield, two oars, and an anchor, representing the club's early success in nautical sports. Corinthians has played their home matches at the Neo Química Arena since 2014, which served as one of the venues for the 2014 FIFA World Cup and also hosted the opening match. The club has longstanding rivalries with Palmeiras (known as Derby Paulista or simply The Derby), São Paulo (the Clássico Majestoso), and Santos (Clássico Alvinegro).

One of the most widely supported teams in the world and the second most in Brazil, with over 30 million fans, Corinthians is one of the most successful Brazilian clubs, having won seven national titles, three Copa do Brasil trophies, one Supercopa do Brasil title, and a record 30 São Paulo State championships. In international competitions, the club won the inaugural FIFA Club World Championship in 2000, repeated the feat in 2012 after being crowned Copa Libertadores de América champions for the first time that same year, and also won a Recopa Sudamericana title. In 2017, the club was listed by Forbes as the most valuable football club in the Americas, valued at $576.9 million.

History

In 1910, the top clubs were formed by people who were part of the upper classes. Among them were Club Athletico Paulistano, São Paulo Athletic Club, & Associação Atlética das Palmeiras. Lower-class society, excluded from larger clubs due to the socioeconomic division, founded their own minnow clubs and only played "floodplain" football.

Bucking the trend, a group of five workers of the São Paulo Railway, them being, Joaquim Ambrose and Anthony Pereira (wall painters), Rafael Perrone (shoemaker), Anselmo Correia (driver) and Carlos Silva (general laborer), residents of the neighborhood of Bom Retiro. It was 31 August 1910 when these workers were watching a match featuring a London-based club touring Brazil, Corinthian F.C. After the match, while the group returned home, the men talked about partnerships, business ideas, and general dreams of grandeur. They each surfaced one idea: the foundation of a club, after several exchanges in a lively argument, a common ground led those athletes the same dream. The arguments led to the conclusion that they would meet the next day to make their dream into reality.

On 1 September 1910, the group agreed to meet after sundown in public sight. That night at 8:30pm, on Rua José Paulino ("Rua dos Imigrantes" (Immigrants Street), the five workers reunited alongside their guest and neighbors from Bom Retiro. That night the club was founded, alongside its board of directors, who elected Miguel Battaglia as the first Club President.

Corinthians played their first match on 10 September 1910, away against União da Lapa, a respected amateur club in São Paulo, and they were defeated by 1–0.

On 14 September, Luis Fabi scored Corinthians' first goal against Estrela Polar, another amateur club in the city, and Corinthians won their first game (2–0).

With good results and an increasing number of supporters, Corinthians joined the Liga Paulista, after winning two qualifying games, and played in the São Paulo State Championship for the first time, in 1913. Just one year after joining the league, Corinthians was crowned champion for the first time (in 1914), and were again two years later. There were many fly-by-night teams popping up in São Paulo at the time, and during the first practice held by Corinthians a banner was placed by the side of the field stating "This One Will Last".

1922, the Centennial of Brazilian Independence, marks the start of Corinthians hegemony in the São Paulo State Championship. As football was almost exclusively played at Rio de Janeiro and São Paulo by that time, the two state champions were considered to be the two top clubs in Brazil. After defeating the Rio de Janeiro State Championship champion of that year, América, Corinthians joined the company of the great teams in Brazil.

The same year also marked the first of three State Championships in a row, something that happened again in 1928–30 and 1937–39.

Corinthians seemed destined to win State Championships in threes; after six years without being a champions, they came won three more from 1937 the 1939. The 1940s were a more difficult time; and the club would win a championship in 1941 and would only win their next in 1951.

At the beginning of the 1950s Corinthians made history in the São Paulo Championship. In 1951, the team composed of Carbone, Cláudio, Luisinho, Baltasar and Mário scored 103 goals in thirty matches of the São Paulo Championship, registering an average of 3.43 per game. Carbone was the top goal-scorer of the competition with 30 goals. The club would also win the São Paulo Championships of 1952 and 1954. In this same decade, Corinthians were champions three times of the Rio-São Paulo Championship (1950, 1953 and 1954), the tournament that was becoming most important in the country with the increased participation of the greatest clubs from the two most important footballing states in the country.

In 1953, in a championship in Venezuela, Corinthians won the Small Cup of the World, a championship that many consider as a precursor of the Worldwide Championship of Clubs. On the occasion, Corinthians, substituting for Vasco da Gama, went to Caracas, the Venezuelan capital and recorded six consecutive victories against Roma (1–0 and 3–1), Barcelona (3–2 and 1–0) and Selection of Caracas (2–1 and 2–0). The club would also win the Cup of the Centenary of São Paulo, in the same year (1954).

After the triumphs in the São Paulo Championship and the Rio-São Paulo of 1954, Corinthians had a lengthy title drought. The breakthrough finally came when they won the São Paulo state championship in 1977, breaking a string of 23 years without a major title.

Under the leadership of Sócrates, Wladimir and Casagrande, Corinthians were the first Brazilian club in which players decided about concentração, a common Brazilian practice where the football players were locked up in a hotel days before a game, and discussed politics. (In the early 1980s, military dictatorship, after two decades, ended in Brazil). In 1982, before the election of government of São Paulo State, the team wore a kit with the words: "DIA 15 VOTE" (Vote on 15th), trying to motivate the biggest number of fans to vote.

In 1990, Corinthians won their first Campeonato Brasileiro Série A, beating their rivals, São Paulo in the final at the opponents' own stadium, Estádio do Morumbi. In the following year, Corinthians beat Flamengo and won the Supercopa do Brasil. In the 1995, the club won the Copa do Brasil for the first time, beating Grêmio in the final at the Estádio Olímpico Monumental in Porto Alegre. In the same decade, the club won the state championship in 1995, 1997 and 1999, and won the national championship again in 1998 and in 1999. In 2000, the club won the first FIFA Club World Cup, eliminating Real Madrid in the semifinals and beating Vasco da Gama on penalties in the final.

In 2002 the club won the Rio-São Paulo Tournament, and the Copa do Brasil in 2002, beating Brasiliense in the final.

The club's situation in early 2004 was among the most difficult in their history. Bad administration, lack of money and terrible campaigns both in the 2003 Brazilian Championship and in the 2004 São Paulo State Championship caused their millions of supporters to worry. Fortunately, some young players and a new manager Tite helped the team to improve from their terrible start. At the end of the championship, Corinthians finished in 5th place and gained entry to the Copa Sudamericana (a minor continental championship, similar to Europa League).

This situation was one of the factors which enabled Corinthians' president, Alberto Dualib, to convince the club's advisors to sign a controversial deal with an international fund of investors called Media Sports Investment. The deal granted the company a large degree of control over the club for 10 years in exchange for large financial investments in return. This has brought many quality players to the team, such as Carlos Tevez, Roger, Javier Mascherano and Carlos Alberto.

Despite the MSI investments, Corinthians experienced a slow start in the 2005 state championship, but managed to improve as it progressed, eventually managing to finish second. Their start to the Brazilian championship during 2005 was difficult, too, but after Daniel Passarella's dismissal (due to an unexpected 5–1 loss to Corinthians' rivals, São Paulo), the club finished the championship round well, and were eventually crowned Brazilian Champions for the fourth time, after a controversial annulment of eleven games due to a betting scandal. Tevez went on to win the Brazilian League Best Player award.

The relationship between Corinthians' managers and the MSI president, Kia Joorabchian was not good, and after being eliminated in the Copa Libertadores, the club experienced a crisis which was responsible for the bad performances for the rest of 2006. Eventually, the partnership came to an end.

On 2 December 2007, following a 1–1 draw away to Grêmio, Corinthians were relegated to the second division for the first time in the club history.

Corinthians, who won promotion to the top division of Brazilian football for 2009 by winning the Serie B tournament in 2008, with the best campaign in the history of the tournament, signed with three-time FIFA Player of the Year, Ronaldo. In 2009, led by Ronaldo, Corinthians won their 26th Campeonato Paulista and their third Brazilian Cup. Confirming the club's good moment, and the 100 years of the club, Corinthians announced the construction of their new stadium, Arena Corinthians, they finished the Campeonato Brasileiro 2010 in 3rd place, granting their place on the subsequent Copa Libertadores. After being eliminated from the South American tournament by the country rivals, Flamengo, though, Corinthians saw Ronaldo retire from football. To replace him, the club signed the with Inter Milan legend, Adriano. In 2011, Corinthians once again were eliminated in the Copa Libertadores, but this time in the playoff round by Deportes Tolima. After that, the team went on to win their fifth national title.

On 4 July, after reaching the final of the 2012 Copa Libertadores undefeated, Corinthians won its first title after a two-match final against 6-time champions Boca Juniors by drawing 1–1 in Argentina and winning 2–0 at the Estádio do Pacaembu in São Paulo, becoming the ninth Brazilian side to win the Copa Libertadores. The club won the 2012 FIFA Club World Cup after defeating English club Chelsea 1–0 on 16 December 2012.

In 2015, the team started the year by being eliminated in the Campeonato Paulista semifinal, and then being eliminated in Libertadores and Brazilian Cup last 16, but went on to win their sixth league title. In 2017 the team started the year winning the Campeonato Paulista for the 28th time, and ending the year winning the league title for the second time in three years, and doing a historic campaign by not losing in the first 20 games of the season. In 2018, the team won the Campeonato Paulista for the 29th time, this time against their biggest rivals, Palmeiras. In 2019, Corinthians won the Campeonato Paulista for the 30th time.

In 2020, Corinthians lost the Campeonato Paulista final to arch rivals Palmeiras on penalties. In the league they finished only 10 points ahead of the first team in the relegation zone, that was the first season since 2007 that Corinthians fought against relegation. In 2021 the new president of the club brought back Willian who had left the club in 2007, helping Corinthians to finish in 5th, granting the club to the Copa Libertadores playoffs. In 2022 Corinthians had their best league season since 2017, finishing in 4th place, granting their place on the subsequent Copa Libertadores. In the Libertadores, the team finished in 2nd in the group stage, then went on to eliminate Boca Juniors in La Bombonera on penalties, reaching the quarter finals for the first time since 2012, but were eliminated to Flamengo. In the Brazilian Cup, they lost once again to Flamengo, but this time at the final, on a penalty shoot out. After all, it was considered the club's best season since 2017.

In 2023, despite being eliminated from Libertadores, the club reached the Copa Sulamericana semifinals, where they were eliminated by Fortaleza. In the league once again fought against relegation.

Colours

Even though the club has been recognized by the colors black and white for most of their history, the first Corinthians' kit originally consisted of cream shirts and black shorts. Back then, the choice of colors proved wrong, as the cream color would gradually fade white when the shirts were washed, representing a cost a recently created club could not afford. Thus, early after the foundation, the official shirt colors were changed to white. In 1954 the traditional black with thin white stripes uniform was introduced, and became the alternative uniform since then.

Badge
The Corinthians shirt had no badge or crest until 1913, when the club joined the Liga Paulista, that mandated that every club in the competition should have one in their uniforms. A simple composition of the letters C (Corinthians) and P (Paulista) was hastily created and embroidered on the players uniforms for the upcoming matches, thus being considered the club's first de facto badge.

Unlike the kit, the badge went through several changes over the years. In 1914, lithographer Hermogenes Barbuy, brother of then-player Amilcar Barbuy designed the club's first official badge, which premiered at a friendly against Torino (Italy), in São Paulo. In 1919, the round shield with the São Paulo state flag was introduced, and modified in 1939 by modernist painter Francisco Rebolo, a former reserve player of the club in the 1920s, to include a string, an anchor and two oars, representing the early success the club achieved in nautical sports. Thereafter, the badge passed through small changes over time, specifically in the flag and in the frame.

In 1990, a yellow star was added above the badge to celebrate Corinthians' first national title. The same would occur when achieving the national titles in 1998, 1999 and 2005, and a larger star was introduced in 2000 after winning the inaugural FIFA Club World Cup. The stars remained as part of the badge until 2011, when the board decided the badge would not present any stars in the future.

Badge evolution

Kit suppliers and sponsors
Nike is the manufacturer of the club's kit since 2003. Previous manufacturers have been: Topper (1980–1989, 1999–2002), Finta (1990–1994) and Penalty (1995–1998).

In 2017, Corinthians and Nike have reached a 12-year U$115 million deal to renew their partnership until 2029.

Previous main sponsors have been: Bombril (1982), Cofap (1983), Citizen (1984), Bic (1984), Corona (1984), Kalunga (1985–1994), Suvinil (1995–1996), Banco Excel (1996–1998), Embratel (1998), Batavo (1999–2000; 2009), Pepsi (2000–2004), Samsung (2005–2007), Medial Saúde (2008), Hypermarcas (2009–2012), Iveco (2012), Caixa (2012–2017), Banco BMG (2019–2021), Neo Química (2021–2024) and Vaidebet.com (2024)

Early grounds
The first playing ground Corinthians used was located in the neighborhood of Bom Retiro (where the club was founded in 1910), in a vacant lot owned by a firewood seller, from which it got its nickname: Campo do Lenheiro ("Lumberjack's field"). It was the time of the floodplain and the players themselves had to clean and flatten the lawn.

In January 1918, Corinthians inaugurated its first official football field, Ponte Grande, on the banks of Tiete River. The land was leased from the municipality under the influence of the intellectual Antonio de Alcantara Machado, one of the first to approach the club workers. It was built by the players and fans in a community helping system. The Corinthians played their games there until 1927, upon the completion of their first stadium. It was then donated to São Bento.

Parque São Jorge
In 1926, the club purchased Parque São Jorge ("Saint George's Park"), located within the Tatuapé district of the city, belonging to then rivals Esporte Clube Sírio, After purchasing, President Ernesto Cassano decided to reform the stage, with financial support from the members.

The renovated Parque São Jorge, still without floodlights, was inaugurated on 22 July, in a friendly game against América-RJ that ended in a 2-2 draw. The land purchased included a Syrian farm - hence the nickname Fazendinha ("Little Farm"), still used today. It was from here that the Corinthians began to develop and could build up its headquarters.

Due to their growing number of fans, Estádio Alfredo Schürig (the official name of "Fazendinha") and the commissioning of city-owned Pacaembu in the 1940s, from the 1950s the stadium was mostly used for Academy level competitions and friendly matches. The last first team match played there was a friendly against Brasiliense on 3 August 2002. Since 1997, it is also the home ground of the professional women's football team.

Pacaembu
The club has established a relationship with Paulo Machado de Carvalho Stadium, which belongs to the municipality of São Paulo and is best known as Pacaembu Stadium, inaugurated in 1940 as the largest stadium in Latin America with a capacity of more than 70,000 people, in a double-fixture that pitted rivals Palestra Italia against Coritiba in the preliminary match and then current three-time state champion Corinthians against Atlético Mineiro, in a match Corinthians won by 4–2. Currently, the Pacaembu has capacity for up to 40,000 spectators.

Arena Corinthians
In 2009 there were some conjectures that the government of São Paulo could make a deal for a 30-year allotment of Pacaembu, but it never materialized, even though it was the club's directors preference, with projects designed to that matter.

After the Estádio do Morumbi, then named as the city's host in the World Cup, failed to comply to FIFA's standards, a new project to create a home for Corinthians emerged as a possibility. In August 2010 the president of the CBF, Ricardo Teixeira, along with Governor of São Paulo state, Alberto Goldman, and the mayor of São Paulo, Gilberto Kassab announced that the opening ceremony of the World Cup of Brazil would be held in the new Corinthians Stadium to be built in the district of Itaquera, in the eastern part of São Paulo city.

On 1 September 2020 (Corinthians' 110th anniversary) a special event live from the stadium was held to announce the Arena's new name. It was officially renamed Neo Química Arena, part of a 20-year partnership with Hypera Pharma, Brazil's largest pharmaceutical company. Neo Química is Hypera's generic drugs division, which already served as Corinthians' main sponsor during the 2010 and 2011 seasons. The full contract is expected to be around R$300–320 million.

CT Joaquim Grava
Corinthians inaugurated their state-of-the-art training facilities in September, 2010 during the celebrations of the club's 100th anniversary. The training facilities were named after long-time associate and consulting medical doctor, Joaquim Grava, that oversaw the medical department construction.

The training facilities feature a 32 bedroom hotel for the players, a bio-mechanics complex (Lab Corinthians-R9. named after Brazilian legend Ronaldo), a center for player rehabilitation and therapy (CePROO, named after fan and journalist Osmar de Oliveira), basketball and volleyball courts (approved by FIBA and FIVB for official matches), as well as other amenities.

An extension to be used by the Academy teams is currently under construction.

Supporters
The Corinthians fan base is fondly called Fiel ("The Faithful"), starring memorable moments like the "Corinthian Invasion" (pt / Invasão Corinthiana) in 1976, when more than 70,000 Corinthians Fans traveled from São Paulo to Rio de Janeiro to watch the match against Fluminense at Maracanã Stadium, in that year's national championship semifinals, as well as having one of the biggest average attendances in the country. Fans being famous for being passionate about the team and loyal supporters motivated the club to make a tribute documentary to their fans, named "Faithful" (pt / Fiel), highlighting the fans' support in one of the most difficult moments in the club's history: the relegation to national second division in 2007. Similar initiatives would be made in the next years, reflecting other moments in the club's history in that the fanbase was essential.

Integral to the club culture are the fan organizations ("torcidas organizadas") such as Gaviões da Fiel ("The Hawks of the Faithful"), founded in 1969 by fans attempting to recover political and administrative control of the club and now the largest of such organizations in Brazil with almost 100,000 associates. Camisa 12 ("The 12th Shirt", founded in 1971), Estopim da Fiel ("Faithful's Fuse", 1979), Coringão Chopp ("Corinthians Draught Beer", 1989), Pavilhão Nove ("Pavillion Nine", 1990), and Fiel Macabra ("Macabre Faithful", 1993) are other important fan organizations that have been actively supporting social and cultural activities representing the club.

Many of the groups above have established branches for fans living outside of São Paulo city, out-state and even internationally. Most are also involved in the Brazilian Carnival festivities, most famously Gaviões da Fiel, one of the most important Carnival of São Paulo samba schools, having won the contest 4 times, the most among groups of football supporters.

Derby Paulista
Derby Paulista is a crosstown fixture between Corinthians and Palmeiras, consistently cited as one of the greatest rivalries worldwide by sources including FIFA and CNN. Palmeiras was founded by a group of Italians who were formerly members of Corinthians. Since 1914, when that treasonous act was taken upon these former supporters, a deep-seated hatred was born. The Derby atmosphere is fierce on and off the pitch, as violence is common between the clubs.

Clássico Majestoso
Clássico Majestoso is a crosstown fixture between Corinthians and São Paulo. The Derby dates back to 1935, at the final re-founding São Paulo after being thrice defunct. Corinthians possesses the largest number of supporters in the state (25 million), whereas São Paulo's lies in second place (16 Million). The Clássico's most memorable match for Corinthians is the 1990 Campenato Brasileiro finals, which led to Corinthians first national title.

Clássico Alvinegro
Clássico Alvinegro is a regional fixture between Corinthians and Santos. 'Alvinegro' is given after the colors worn by both teams, black and white (Alvi, from Latin albus, white, and negro, black). The Classico reached one of its highest stages for Corinthians supporters when Corinthians met Santos in the Semi-Finals of Libertadores 2012. Corinthians won 2-1 on aggregate.

Other rivalries
Derby dos Invictos (Derby of the Undefeated), Corinthians and Portuguesa is a crosstown rivalry. Corinthians vs Ponte Preta is an in-state rivalry that peaked in the 1977 Campeonato Paulista final, which led to Ponte Preta's greatest Paulista Finish (runner-up). Classico das Multidões (Classic of The Masses) is an inter-state rivalry pegging the two most supported teams in Brazil: Corinthians and Flamengo. Corinthians and Vasco led to great match ups and some rivalry recently, mostly after Vasco winning the Brasileirão in 1997 and 2000, and Corinthians in 1998 and 1999. Their greatest match coincided with the first FIFA Club World Cup in 2000, with a Corinthians victory in the penalty shootout. Corinthians also won the 2011 Brasileirão in the last round of the season, two points over the runners-up Vasco. Corinthians saved Vasco from their usual runner-up fate by defeating the cariocas in 2012 Libertadores Quarter-finals.

Musketeer
Corinthians' official mascot is the Musketeer, a symbol of bravery, audacity and fighting spirit. The adoption of that character recalls the first years of the club.

In 1913 most of the leading football clubs in São Paulo State founded the APEA (Paulista Athletic Sports Association). The depleted Paulista League was left with only Americano, Germania and Internacional, known as the "three musketeers" of São Paulo football. Corinthians joined the three as D'Artagnan, being the fourth and most adored musketeer, just like in Alexandre Dumas, père's novel The Three Musketeers. To be accepted in that "musketeers universe", Corinthians had to show their bravery. As there was many other teams who coveted the spot in the Liga Paulista, Corinthians participated in a selective tournament against Minas Gerais and São Paulo, two other great teams of Paulista amateur football at that time. The Corinthian team beat Minas 1–0 and São Paulo 4–0, earning acceptance into the group and acquiring the right to participate in the Special Division of the Paulista League in the following year.

Saint George
An important symbol for Corinthians is Saint George/(Ogum). Saint George is one of the most revered Catholic Saints in Brazil, a nation with a blend of cultures. The collusion between African & European cultures is seen in Brazil's definition of São Jorge as a mash between Catholicism & Western African Mythology. The comparison may be drawn the entities similar characteristics; St George, the soldier who protects those who pray to him; Ogum God of War who serves the communities who believe in him. it is this warrior demeanor that made Corinthians fans indebted to São Jorge.

Corinthians began as a small team for the lower classes of São Paulo, even though they obtained initial success. Lack of respect for the working class forced Corinthians to leave their São Paulo State Football League in protest. after multiple championships Timão made its largest leap in prestige in the founding of a Corinthians' Headquarters, 1926. The creation of said headquarters became the first fusion of Timão & São Jorge. The land purchased for the headquarters was formerly Parque São Jorge (St. George Park) at 777 Rua São Jorge, Tatuapé, São Paulo, SP.

Corinthians support for São Jorge became fanatical during the decade of the 60's, Between 1954 and 1977, Corinthians failed to add to its gallery of conquests and the Corinthian Nation lived the hardest moments of its history. While the stream struggled in the 60's, fan recanted that they were blessed by a "Santo Guerreiro" (Warrior Saint). In the early 60's the lack of success lingered in the minds of fans & gave birth to a utilization of the blessings of São Jorge. this caused Corinthians to erect a chapel in honor of the saint, in order to strengthen the clubs resolve via mysticism. 1969, after the death of two players Lidu & Eduardo, the funeral was held in Capela São Jorge, & strengthened the clubs identity at a time when championships were non-existent. 1974 Paulista Final, after a heart-wrenching loss to arch-rival Palmeiras, composer Paulinho Nogueira recorded "Oh Corinthians", a song that had popular commercial success at the time. In the verses of the composition dedicated to the suffering Corinthians could not miss the quote to the patron Saint George:

"...Oh, são 20 anos de espera. Mas meu São Jorge me dê forças, para poder um dia enfim, descontar meu sofrimento em quem riu de mim". ("... Oh, It's been 20 years of waiting, but my St. George gives me strength to be able to one day finally cashing in my suffering upon those who laughed at me.)"

Corinthians' 2011 third kit was burgundy colored & featured São Jorge slaughtering a dragon in a dark watermark across the right side of the chest. The utilization of São Jorge's image on the shirt is the practice of São Jorge's Prayer.

title: Sport Club Corinthians Paulista


text:
List of heads of government of Liechtenstein

The head of government of Liechtenstein (Regierungschef), known informally as the Prime Minister, is the chief executive of the Government of Liechtenstein and chairs the Cabinet of Liechtenstein. They are appointed by the sovereign prince of Liechtenstein in conjunction with the Landtag of Liechtenstein and are expected to command the confidence of both the prince and Landtag. The appointed head of government is typically the leader of the political party with the most seats in the Landtag or a coalition of parties but is not required to be a member of the Landtag themselves, although they should meet the eligibility requirements for that office.

The role originated from Landesverweser, which was created upon the ratification of the 1862 Constitution of Liechtenstein. In 1921, a new constitution was ratified in which the office was replaced by that of Prime Minister.

The incumbent Prime Minister is Daniel Risch since 25 March 2021.

State administrator (1861–1921)
The Landesverweser, also known as simply 'Governor', was the title of the head of government from 1848 to 1921. The role originated from Michael Menzinger by him applying for the creation of the role in 1833, also serving as the first. The role was renamed to Governor as a concession following the Revolution of 1848 in Liechtenstein, and was formalized upon the ratification of the 1862 constitution of Liechtenstein on 26 September.

Prime Minister (1921–present)
The Regierungschef (lit. 'head of government') is the current title for the head of government. The office replaced State Administrator upon the ratification of the constitution of Liechtenstein on 5 October 1921. Under this constitution, the eligibility for becoming head of government was changed to require residency in Liechtenstein.

Deputy head of government
The deputy head of government is the secondary chief executive in Liechtenstein. The role is appointed by the prince of Liechtenstein from one of the cabinet ministers upon the proposal of the Landtag of Liechtenstein.