title: New York Red Bulls

text: Petke showed a knack for making adjustments when he countered a slow 0–2–2 start by switching the formation from a 4–2–3–1 formation to a 4–4–2 – placing more emphasis on playing a strong defensive game, and playing up through the midfield. The rookie manager sought to turn the club around, and gain his first win by the end of the month. On March 30, 2013, he did just that against the Philadelphia Union, by the score of 2–1.


title: New York Red Bulls

text: Petke sought to instill a more aggressive mindset into the team to make up for the relative lack of time the team had spent playing together. Some have called the team "mentally weak" due to how the team has fluctuated between scrappy play and impressive displays of form and moments of "playing down to" inferior teams. However, after putting on impressive displays, the team went on a two-month undefeated streak and won the 2013 Supporters' Shield as the team with the best regular-season record.


title: New York Red Bulls

text: In the 2014 season, the Red Bulls qualified for the 2014 MLS playoffs, and eliminated Sporting Kansas City in the knockout round of the playoffs, advancing to face D.C. United. The Red Bulls made it to the Eastern Conference final to face the New England Revolution, but were defeated. The club lost two of their designated players when it announced that Thierry Henry would retire following the season, while Tim Cahill was released during the offseason.


title: New York Red Bulls

text: On December 23, 2014, former MLS player and league office executive Ali Curtis replaced the retiring Andy Roxburgh as Sporting Director. In a surprise announcement two weeks later on January 7, 2015, Petke was released as head coach and replaced with former Montreal Impact coach Jesse Marsch. Tension between the fans and the front office came to a head at a hectic town hall featuring Curtis, Marsch, goalkeeper Luis Robles and emcee and sportswriter Frank Isola.


title: New York Red Bulls

text: The target was to implement, on the pitch, a consequent pressing style implemented in many of then Red Bull footballs sporting director Ralf Rangnick teams, and, in apply this as well when transferring players, and in the academy. Marsch once said the team would play like "an energy drink," which was derided but "Energy Drink Soccer" became a way for the fanbase to describe the way in which they preferred the club play.


title: New York Red Bulls

text: In his first season with Red Bulls, Marsch implemented a high-pressure tactical system built around the talents of recently signed players such as Sacha Kljestan, Mike Grella and a returning Wright-Phillips, while academy product Matt Miazga emerged as a key defender, eventually being signed by English club Chelsea following the season. The Red Bulls won their second Supporter's Shield, qualifying for the 2015 MLS playoffs and reaching the Eastern Conference Final where they were ultimately defeated by the Columbus Crew.


title: New York Red Bulls

text: On May 21, 2016, the team tied an MLS record for largest victory margin, winning 7–0 at New York City FC. Marsch signed a multi-year extension in June 2016. At the end of July, Wright-Phillips became the club's all-time leading goal scorer, passing Henry on his way to a total he'd eventually double in New York. On September 27, 2016, the Red Bulls qualified for their first ever CONCACAF Champions League quarterfinal series with a 0–0 draw at Guatemalan club Antigua GFC.


title: New York Red Bulls

text: Prior to the 2017 season Ali Curtis left the club and was replaced by Denis Hamlett, who then sold captain and longest-tenured player Dax McCarty to the Chicago Fire for allocation money. Though highlighted by the emergence of homegrown talent Tyler Adams, the team went on to have a mixed campaign, with a sixth-place conference finish and quarterfinal playoff exit to Toronto FC while also reaching the final of the US Open Cup for the second time in their history, before losing a 2–1 result to Sporting Kansas City.


title: New York Red Bulls

text: New York made their best showing to date in continental competition the next year in the 2018 CONCACAF Champions League. In the quarterfinal against Club Tijuana, they became the first MLS club to win by multiple goals on Mexican soil, with a 2–0 defeat of Tijuana in the quarterfinals on a brace from Wright-Phillips and 13 saves by Robles.


title: New York Red Bulls

text: In the return leg, new designated player and record signing Kaku scored on his debut off the bench as the Red Bulls won 3-1 for a 5-1 victory in the tie in Harrison.


title: New York Red Bulls

text: In the semifinals, New York, despite outshooting Mexican giants Chivas 20-1 in the home second leg, were beaten by a goal in the first leg that resigned the Red Bulls to a 1-0 loss in the tie.


title: New York Red Bulls

text: Days before the third Hudson River Derby of the 2018 MLS season, it was announced that Jesse Marsch would leave his role as coach effective immediately, with assistant coach Chris Armas taking over the role, joining Ralf Rangnick in German Bundesliga RB Leipzig. Marsch, left the club, as most successful in franchise history, with one Supporters' Shield, topping the Eastern Conference twice, and runners up in the US Open Cup. He also left with most wins in the history of the franchise.


title: New York Red Bulls

text: Assistant coach Chris Armas replaced Jesse Marsch, who left the franchise after three and a half seasons. The Red Bulls won their third Supporters' Shield in the 2018 season after winning their last five games to overtake Atlanta United in a tight race on the season's final day, setting what was then a record for points in a season and securing qualification for the 2019 CONCACAF Champions League. Atlanta got revenge on New York in the Eastern Conference Finals, which they won 3-1 over two legs after a controversial offside call that denied Wright-Phillips an away goal in the first leg.


title: New York Red Bulls

text: Wright-Phillips became the fastest player to 100 MLS goals in the history of the league after scoring against DC United on July 25, 2018, all 100 scored with New York. The Englishman finished the season with 20 goals in the league, becoming the first player in MLS history to achieve the feat three times.


title: New York Red Bulls

text: Tyler Adams was sold to RB Leipzig in January 2019 for a sum of $3,000,000 and 33% of any future transfer earnings.


title: New York Red Bulls

text: New York stumbled through the 2019 season, with Wright-Phillips spending most of it injured, In his place, 20 other different Red Bulls registered at least a goal, a club record. After easing past Atlético Pantoja, their run in the 2019 CONCACAF Champions League was abruptly ended by Santos Laguna. New York finished 6th in the East and despite holding a 3–1 lead at halftime, fell in the first round of the 2019 MLS Cup Playoffs to Philadelphia Union in extra time 4–3.


title: New York Red Bulls

text: Luis Robles and Bradley Wright-Phillips, the player who'd played the most times for the club in their history and the player who'd scored the most goals in their history, departed in the offseason.


title: New York Red Bulls

text: Sean Davis was named the club's first homegrown captain ahead of the 2020 season, becoming the fifth native of New Jersey to wear the armband.


title: New York Red Bulls

text: Armas, having had a rough start to the COVID-19-impacted 2020 campaign (including a crashing out at the group stage of the MLS is Back Tournament) was formally released from his contract, along with assistant CJ Brown on September 4, 2020, via statement released from Kevin Thelwell, RBNY's Head of Sport who had come over in early 2020 from Wolverhampton Wanderers. Bradley Carnell was named as interim manager the day after.


title: New York Red Bulls

text: Kevin Thelwell hired former Barnsley F.C. manager (and former Red Bull Salzburg player and youth coach) Gerhard Struber as the club's new manager on October 6, 2020. Due to delays driven largely by the COVID-19 pandemic, Struber was unable to make his debut until the Red Bulls, under Carnell's direction, made the 2020 MLS Cup Playoffs. He oversaw a 3–2 away loss to Columbus.


title: New York Red Bulls

text: The second half of the 2020 season was notable for the emergence of teenage midfielder Caden Clark, who scored on his debut, second appearance and postseason debut. Clark was sold to RB Leipzig with the move scheduled coming after the 2021 season.


title: New York Red Bulls

text: Thelwell and Struber largely rebuilt the roster for the 2021 MLS season, signing 12 new players from a mix of European and South American clubs, as well as an academy product, Bento Estrela, who became the club's youngest-ever signing the day before his 15th birthday. New York also used two loan players from Red Bull Salzburg and signed former Celtic F.C. forward Patryk Klimala as a designated player.


title: New York Red Bulls

text: New York struggled for a good portion of the 2021 season with injuries including a ruptured achilles from US international Aaron Long, but put together a 7-1-4 finish to the season to qualify for their 12th consecutive playoffs. The Red Bulls were defeated in the opening round by the Philadelphia Union, 1-0 on a goal in the 123rd minute.


title: New York Red Bulls

text: In the offseason, former Salzburg loanee Carlos Miguel Coronel, considered by most to be the team's best player in 2021, was brought back on a permanent contract. The club also bought Lewis Morgan from Inter Miami CF for $1.2 million in targeted allocation money. Davis departed on a free agent contract to Nashville SC.


title: New York Red Bulls

text: On the day before the beginning of the 2022 season, Thelwell departed to take over as director of football at Everton. His final transfer window saw Brazilian Luquinhas brought in from Legia Warsaw and Englishman Ashley Fletcher on loan from Watford FC. Clark and defender Tom Edwards also returned on loan deals.


title: New York Red Bulls

text: With Long returning from injury and made captain following Davis' departure, New York began the 2022 season tying an MLS record set by the 1998 Los Angeles Galaxy, winning their first five league games on the road. In addition, Red Bulls went six matches undefeated away in the league and eight in all competitions to start 2022. Conversely, the club was winless in their first six home matches in 2022, before an Open Cup victory over Charlotte FC on May 25.


title: New York Red Bulls

text: New York reached the semifinals of the Open Cup in 2022, defeating Hartford Athletic, DC and New York City en route before crashing out with a 5-1 loss to Orlando City.


title: New York Red Bulls

text: Former VFB Stuttgart, Schalke 04, and Red Bull Global director Jochen Schneider replaced Thelwell as Head of Sport on June 11.


title: New York Red Bulls

text: New York qualified for the MLS Cup Playoffs for a 13th-consecutive season, equalling a league record set by Seattle and, with Seattle missing the playoffs in 2022, giving the Red Bulls the active league record. The New York Red Bulls lost, 1-2, against FC Cincinnati in the first round of the playoffs.


title: New York Red Bulls

text: During the team's first seasons, the MetroStars had solid black or solid white jerseys, before switching to a home jerseys featuring red and black vertical stripes (similar to those worn by A.C. Milan). Since the Red Bull takeover, the team has almost invariably worn white shirts with red shorts at home while using a combination of navy blue and yellow for road kits, each with a prominent Red Bull logo across the chest. Prior to the 2018 season, the club unveiled a new entirely red shirt, replacing the traditional blue-yellow secondary kit.


title: New York Red Bulls

text: The team is headquartered and plays their home matches at Red Bull Arena in Harrison, New Jersey, which opened for the 2010 MLS season. The stadium has a seating capacity of 25,189. On March 20, 2010, the Red Bull team played an exhibition game against Santos FC in a 3–1 inaugural win. The first MLS league game took place in the new venue on March 27, 2010, with a 1–0 win over the Chicago Fire, the lone goal coming from Estonian international Joel Lindpere.


title: New York Red Bulls

text: The club in 2019 and 2022 used MSU Soccer Park, home of the reserve team, for US Open Cup matches when Red Bull Arena was unavailable.


title: New York Red Bulls

text: Previously the team played at Giants Stadium, where they had played their home matches from 1996 until the end of the 2009 season. The stadium was located in East Rutherford, New Jersey.


title: New York Red Bulls

text: The Red Bulls Training Facility is located in Hanover Township, New Jersey and opened in June 2013. The $6 million facility covers about 15 acres of the 73 acre property and includes four fields, three grass and one turf, each the size of the one at Red Bull Arena. The middle field, which has a grass surface, is heated, while one turf field has lights.


title: New York Red Bulls

text: The complex opened with four buildings, with the main one housing separate locker rooms for the senior team, academy teams and coaching staff, film analysis room, offices, a therapy room, a gym, a fitness/wellness area, a hot/cold tub room and a players' lounge, which includes a cafeteria that serves breakfast and lunch. In April 2015, the team opened a new training building, which includes two team locker rooms, a multipurpose weight and cardio area, a treatment room, exam room, coach and staff lockers, lavatories for both men and women and other miscellaneous areas. In 2017, the team opened a extension of the 2015 training building for the academy team and the third grass field.


title: New York Red Bulls

text: In 2021, the club announced plans to build a new, , privately funded training facility in nearby Morris Township. The facility is slated to open in 2024, which would coincide with the 30th anniversary of the club's founding and be usable in time for the 2026 World Cup.


title: New York Red Bulls

text: In the past, the Red Bulls led a nomadic existence, making use of several other training grounds before finishing construction of the Hanover facility:


title: New York Red Bulls

text: A variety of supporters clubs and groups have grown around the team since its inaugural year. The first of these was formed in 1995, prior to the inception of the team itself, as the Empire Supporters Club. 2005 saw the creation of the New Jersey-based Garden State Supporters, now the Garden State Ultras (GSU). The 2010 season's influx of personnel with a Scandinavian background led to the creation of the Viking Army Supporters Club. In 2021, the third supporters group named Torcida 96 was formed.


title: New York Red Bulls

text: The Red Bulls have designated some sections of Red Bull Arena as supporter specific. These included sections 101 for the Empire Supporters Club, 102 for the Viking Army, and 133 for Torcida 96. Sections 133, 101, and 102 are collectively known as the "South Ward".


title: New York Red Bulls

text: The Red Bulls' oldest rival is D.C. United, against whom they compete for the Atlantic Cup. The New England Revolution and the Philadelphia Union are also rivals of the Red Bulls. The Red Bulls had not defeated the Revolution at the latter's home venue Gillette Stadium for 12 years, until a 2–0 win on June 8, 2014, intensifying the rivalry. These rivalries arise out of geographic proximity and as a reflection of longstanding rivalries between New York-area teams and other teams in Washington, D.C., Boston, and Philadelphia.


title: New York Red Bulls

text: In 2015 the Hudson River Derby was born when the Red Bulls faced off against another team from the New York metropolitan area in MLS league play for the first time, when New York City FC entered MLS. Although initially regarded as a manufactured rivalry with little of the traditional banter apparent between long-time local rivals, the first meetings between the teams displayed an increasing level of animosity between the two sides. The Red Bulls won the first ever encounter between the two, a league game on May 10, 2015, at Red Bull Arena. Matches between the two teams were marred by a series of brawls between their supporters.


title: New York Red Bulls

text: Although the rivalry with NYCFC was built to be the major one for the Red Bulls, this was not the first time that they played against teams from the New York area, as they played matches in the U.S. Open Cup in both 2011 (against F.C. New York, who have since folded) and 2014 (against the New York Cosmos). The Red Bulls also played against the Cosmos in the 2015 U.S. Open Cup, to a 4–1 victory.


title: New York Red Bulls

text: Since its inception as the MetroStars in 1996, Red Bulls matches have been televised by MSG and MSG Plus. Joe Tolleson (play-by-play) and Tommy Smyth (analyst) were the original announcers. Derek Rae and JP Dellacamera followed as play-by-play announcers. As of 2012, Steve Cangialosi (play-by-play) and Shep Messing (analyst) are the MSG/MSG Plus announcers.


title: New York Red Bulls

text: In 2015, the Red Bulls launched streaming audio game broadcasts from the club's official site, with Matt Harmon and former MetroStar and Red Bull Steve Jolley on the English-language call, and Ernesto Motta in Spanish. Late in 2015, the club launched a streaming internet station with TuneIn, becoming the first MLS club to provide 24-hour streaming content to its fan base.


title: New York Red Bulls

text: New York Red Bulls II was established in 2015. It is a reserve team that competes in the USL Championship, the second tier of the American soccer pyramid. The team plays its home matches at MSU Soccer Park at Pittser Field in Montclair, New Jersey.


title: New York Red Bulls

text: The fully professional team completed its inaugural USL season with a 12–10–6 record in fourth place of the Eastern Conference. The team won its first playoff game against Pittsburgh Riverhounds and advanced as far as the Eastern Conference semifinals in the 2015 USL Playoffs.


title: New York Red Bulls

text: A New York Red Bulls team mostly composed of NYRB II players defeated Chelsea F.C. in a 2015 friendly.


title: New York Red Bulls

text: In 2016, New York Red Bulls II defeated the Swope Park Rangers 5–1 in the 2016 United Soccer League Final winning their first United Soccer League Championship and became the first Major League Soccer-owned team to win the United Soccer League title.


title: New York Red Bulls

text: The team was coached by former Red Bull and New York native John Wolyniec from its founding until the end of the 2021 season. He was replaced by former Seattle Sounders academy director Gary Lewis, with a plan to transition the reserve side into the newly-created MLS Next Pro in 2023.


title: New York Red Bulls

text: The New York Red Bulls Academy is the multi-layered youth system of the New York Red Bulls. It is the first cost-free program in MLS that provides a professional soccer training environment for youth players in the New York metropolitan area. The soccer programs are operated as part of a global approach to player development.


title: New York Red Bulls

text: This is a partial list of the last five seasons completed by the Red Bulls. For the full season-by-season history, see List of New York Red Bulls seasons.


title: Alain Prost

text: Alain Marie Pascal Prost (; born 24 February 1955) is a French retired racing driver and Formula One team owner. A four-time Formula One World Drivers' Champion, from 1987 until 2001 he held the record for most Grand Prix victories until Michael Schumacher surpassed Prost's total of 51 victories at the 2001 Belgian Grand Prix. In 1999, Prost received the World Sports Award of the Century in the motor sport category.


title: Alain Prost

text: Prost discovered karting at the age of 14 during a family holiday. He progressed through motor sport's junior ranks, winning the French and European Formula Three championships, before joining the McLaren Formula One team in 1980 at the age of 24. He finished in the points on his Formula One début – at the San Martín Autodrome in Buenos Aires, Argentina, where he took his first podium a year later – and took his first race victory a year later at his home Grand Prix in France, driving for the factory Renault team.


title: Alain Prost

text: During the 1980s and early 1990s Prost formed a fierce sporting rivalry, mainly with Ayrton Senna but also Nelson Piquet and Nigel Mansell. In 1986, at Adelaide in the last race of the season, he beat Mansell and Piquet of Williams to the title, after Mansell retired late in the race and Piquet was pulled in for a late precautionary pit stop. Senna joined Prost at McLaren in 1988 and the two had a series of controversial clashes, including a collision at the 1989 Japanese Grand Prix that gave Prost his third Drivers' Championship. A year later at the same venue they collided again, but this time Prost, driving for Ferrari, lost out. Before the end of a winless 1991 season Prost was fired by Ferrari for his public criticism of the team. After a sabbatical in 1992, he joined the Williams team, prompting Mansell, the reigning Drivers' Champion, to leave for CART. With a competitive car, Prost won the 1993 championship and retired from Formula One driving at the end of the year.


title: Alain Prost

text: In 1997, Prost took over the French Ligier team, running it as Prost Grand Prix until it went bankrupt in 2002. From 2003 to 2012 he competed in the Andros Trophy, which is an ice racing championship, taking 38 race victories and winning the championship 3 times.


title: Alain Prost

text: Prost employed a smooth, relaxed style behind the wheel, deliberately modelling himself on personal heroes like Jackie Stewart and Jim Clark. He was nicknamed "The Professor" for his intellectual approach to competition. Though it was not a name he particularly cared for, he would admit later that it was an appropriate summation of his approach to his racing. Skilled at setting up his car for race conditions, Prost would often conserve his brakes and tyres early in a race, leaving them fresher for a challenge at the end.


title: Alain Prost

text: Alain Prost was born in the commune of Lorette near the town of Saint-Chamond, in the département of Loire close to Saint-Étienne, France to André Prost and Marie-Rose Karatchian, born in France of Armenian descent. Prost had one younger brother called Daniel, who died of cancer in September 1986. Prost was an active and athletic child, who enthusiastically took part in diverse sports, including wrestling, roller skating and football. In doing so he broke his nose several times. He considered careers as a gym instructor or a professional footballer before he discovered kart racing at the age of 14 while on a family holiday. This new sport quickly became his career of choice.


title: Alain Prost

text: Prost was married to Anne-Marie (born 14 February 1955), but they divorced sometime later. They have two sons, Nicolas (born 18 August 1981) and Sacha Prost (born 30 May 1990). Prost also has a daughter, Victoria, born from his relationship with Bernadette Cottin. From 2014 to 2018, Nicolas raced in Formula E for e.dams Renault, a team partially run by his father. Prost lived in his hometown, Saint-Chamond, until he and his Renault team fell out in the early 1980s. In April 1983 the Prost family moved to Sainte-Croix, Switzerland, and shortly after to Yens, Switzerland. They moved to Switzerland after Renault workers went to Prost's house in France and burned his Mercedes-Benz and another one of his road cars. They lived there until November 1999, when they moved to Nyon in the same country. Through Nicolas, Prost has two grandsons named Kimi (born November 2015) and Mika (born December 2020). Through Sacha, he has another grandson named Liam (born June 2018).


title: Alain Prost

text: Prost won several karting championships in his teens. In 1974, he left school to become a full-time racer, supporting himself by tuning engines and becoming a kart distributor. His prize for winning the 1975 French senior karting championship was a season in French Formula Renault, a category in which he won the title and all but one race in 1976.


title: Alain Prost

text: Prost went on to win the 1977 Formula Renault European championship before moving up to Formula Three (F3) in 1978. In 1979, he won both the French and European F3 championships, by which time he was on the shopping lists of several Formula One teams. After carefully considering his options, he chose to sign with McLaren for . He surprised the British team by declining their offer of a race drive in a third car at the final race of the 1979 season at Watkins Glen — reasoning that the token effort would benefit neither him nor the team. Prost felt that it would be a mistake to race in Formula One without being fully prepared: "..in the end I said, ‘No’ to Marlboro. I asked them to understand that I didn't want to make a mistake; I didn't know Watkins Glen and I didn't know the car. I said I thought it would be a better idea to organise a test."


title: Alain Prost

text: Prost began his career with McLaren (being run by Teddy Mayer) in 1980 alongside Ulsterman John Watson. On his debut in Buenos Aires, Argentina, he finished in sixth place, earning one point, something achieved by only a handful of drivers. Prost added four more points to his tally during the season, scoring points at Interlagos, Brands Hatch and Zandvoort. Prost finished the year 15th in the Drivers' Championship, equalling points with former world champion Emerson Fittipaldi. Despite the encouraging debut season, Prost had several accidents, breaking his wrist during practice at Kyalami and suffering a concussion during practice at Watkins Glen. He also retired from the previous round in Montreal a week earlier because of rear suspension failure. At the end of the season, despite having two years remaining on his contract, he left McLaren and signed with Renault. Prost has said that he left because of the large number of breakages on the car and because he felt the team blamed him for some of the accidents.


title: Alain Prost

text: Prost was partnered with fellow Frenchman René Arnoux for . Motor sports author Nigel Roebuck reports that there were problems between Prost and Arnoux from the start of the season, Prost being immediately quicker than his more experienced teammate. He did not finish the first two Grands Prix, due to collisions with Andrea de Cesaris in Long Beach and Didier Pironi at Jacarepaguá, but scored his first podium finish at Buenos Aires. He also did not finish in the next four races, and then won his first Formula One race at his home Grand Prix in France at the fast Dijon circuit, finishing two seconds ahead of his old teammate John Watson.


title: Alain Prost

text: Prost won the first two Grands Prix of the 1982 season in South Africa, where Prost recovered from losing a wheel, and Brazil, where he finished 3rd but was awarded the win after Piquet (1st) and Keke Rosberg (2nd) were disqualified. He finished in the points on four other occasions, but did not win again. Despite retiring from seven races, Prost improved on his Drivers' Championship position, finishing in fourth, but with nine fewer points than the previous year. His relationship with Arnoux deteriorated further after the French Grand Prix. Prost believes that Arnoux, who won the race, went back on a pre-race agreement to support Prost during the race. His relationship with the French media was also poor. He has since commented that "When I went to Renault the journalists wrote good things about me, but by 1982 I had become the bad guy. I think, to be honest, I had made the mistake of winning! The French don't really like winners."


title: Alain Prost

text: Arnoux left Renault in and American Eddie Cheever replaced him as Prost's partner, allegedly because of Renault's desire to sell more road cars in North America (three of the season's 15 races were on the North American continent). Prost earned a further four victories for Renault during the season and finished second in the Drivers' Championship, two points behind Nelson Piquet. Piquet and the Brabham team overhauled Prost and Renault in the last few races of the season. Prost, who felt the team had been too conservative in developing the car, found himself increasingly at odds with Renault's management, who made him the scapegoat for failing to win a championship. In addition to that, the French fans recalled the bitter fight that had caused their favourite, Arnoux, to leave the team. Prost said in an interview with ESPN during the final race that his car was "not competitive" and that he "didn't lose by my own fault" Renault fired Prost only two days after the South African race. He re-signed for McLaren for the 1984 season within days and moved his family home to Switzerland after Renault factory workers burned the second of 2 of Prost's cars, one of them being a Mercedes-Benz.


title: Alain Prost

text: Prost joined double world champion Niki Lauda at McLaren (now being run by Ron Dennis) in , driving the John Barnard designed McLaren MP4/2 which used a 1.5 litre TAG-Porsche V6 engine. He lost the world championship to Lauda in the final race of the season in Portugal by half a point, despite winning seven races to Lauda's five, including winning in Portugal. The half point came from the , where Prost had been leading, albeit with Ayrton Senna (Toleman) and Stefan Bellof (Tyrrell) closing on him rapidly, when Clerk of the Course Jacky Ickx stopped the race at half distance due to heavy rain, which was controversial, for Ickx displayed the red flag without consulting the race officials. Under Formula One regulations, Prost received only half of the nine points normally awarded for a victory.


title: Alain Prost

text: In Prost became the first French Formula One World Champion. He won five of the sixteen Grands Prix during the season. He had also won the San Marino Grand Prix, but was disqualified after his car was found to be 2 kg underweight in post-race scrutineering. Prost finished 20 points ahead of his closest rival, Michele Alboreto. Prost's performance in 1985 earned him the Légion d'honneur distinction in France.


title: Alain Prost

text: Niki Lauda retired for good at the end of 1985, and was replaced at McLaren by World Champion Keke Rosberg for . Prost successfully defended his title, despite his car struggling against the Honda-powered Williams cars driven by Nelson Piquet and Nigel Mansell. Until the latter stages of the final race of the 1986 season, the , Prost appeared set to finish second in the Championship, behind Mansell. Prost had the same number of wins as Piquet, but he had four second places to Piquet's three, thus placing him second before the final race. While running third behind Piquet, and directly behind Prost on the road (3rd was all he needed to win the title), Mansell suffered a rear tyre failure at and crashed out. The Williams team then pitted Piquet to change tyres as a safety precaution, while Prost had already pitted earlier due to a puncture and did not need to change his tyres again. He then held the lead ahead of a charging Piquet to the chequered flag and the Championship. Prost became the first driver to retain the title since Jack Brabham in 1960.


title: Alain Prost

text: With Rosberg retiring from Formula One at the end of 1986 season, underrated Swede Stefan Johansson filled the McLaren seat alongside Prost for the season. Even though McLaren had introduced the new Steve Nichols designed MP4/3 after three seasons with the MP4/2 model (Barnard had departed for Ferrari), the TAG engines were not the force they had been previously, lagging behind in power and with unreliability previously unseen. He never gave up though and challenged Piquet and Mansell almost until the end, winning three races and breaking Jackie Stewart's record for race victories by winning for the 28th time at the Portuguese Grand Prix. “People might not believe me,” said Stewart at the time. “But I’m glad to see Alain take my record. I am glad that he has done it because he’s the one that deserves it. There is no doubt in my mind that he is the best race driver of his generation.” Prost considers his win in the opening round in Brazil as his best and most rewarding race ever. The Williams-Hondas had been dominant during qualifying, and Prost started fifth on the grid with a time three seconds slower than Mansell's pole time. Knowing he didn't have the qualifying speed, he instead worked on his race set-up, and with everyone else going for a high-downforce set-up, he went the other way. The set-up meant less tyre wear, thanks to slower speeds in the corners while going fast down the straights. With his car having less tyre wear than his rivals, Prost was able to get through the 61 laps of the abrasive Jacarepaguá Circuit with only two stops compared to the three or more by his rivals (Piquet pitted for tyres 3 times within the first 40 laps). Prost finished 40 seconds in front of Piquet, with Johansson a further 16 seconds back in third.


title: Alain Prost

text: Despite Nelson Piquet winning the 1987 Drivers' Championship and Williams winning the Constructors' Championship, Honda decided not to supply the team with their engines, reportedly due to Williams's refusal to dump Nigel Mansell and hire Japanese driver and Honda test driver Satoru Nakajima (who debuted with Lotus in 1987), and instead supplied the McLaren team for . Prost had convinced Ron Dennis to sign Ayrton Senna to a three-year contract, which played a role in luring Honda (Senna's ability had been highly regarded by the Japanese giant when using their engines with Lotus in 1987 and both were keen to continue their association). However, this began the rivalry that pushed two of the sport's greatest drivers to unprecedented heights of success and controversy. McLaren-Honda dominated the season, winning 15 out of 16 races. Prost finished first or second in every race other than his two retirements at Silverstone and Monza. He won seven races and in total outscored his new teammate Senna by 11 points, despite Senna winning one more race than him. However, only the 11 best results from the season counted toward the championship total, and this gave Senna the title by three points. Prost went on to be a proponent of essentially the 1990s scoring system: all points counting toward the final results, with a race winner scoring 10 (rather than 9).


title: Alain Prost

text: McLaren's domination continued throughout , and the struggle between Prost and Senna for supremacy put them on a collision course. Mutual admiration turned to all-out hatred, with Prost accusing Senna of "dangerous driving" and of receiving more than a fair share of attention from both McLaren and Honda. For his part, Senna accused Prost of being in the pocket of FISA's French president Jean-Marie Balestre. The animosity between the two drivers came to a head at Round 2 in San Marino. The drivers made an agreement between them that whoever won the start would not be challenged by the other going into the first turn (in this case, the Tosa bend on the Imola circuit). Prost kept to the agreement after Senna won the first start. Prost however won the restart (caused by Gerhard Berger's fiery crash in his Ferrari), but was passed by Senna under brakes for Tosa. Prost went to a friend of his, a French journalist, and told him about the broken agreement between him and Senna. Against Prost's wishes, the journalist went public with the story. During testing at Pembrey in Wales, Senna denied in public any such agreement had ever existed between Prost and himself, but Prost's claim was backed up by Marlboro's John Hogan who had been present when the agreement was made.


title: Alain Prost

text: Prost signed to join Ferrari in 1990, becoming the first driver signed to the team after the death of team founder Enzo Ferrari in 1988. He replaced Gerhard Berger at Ferrari and was partnered with Britain's Nigel Mansell for (Berger took Prost's seat at McLaren). As reigning world champion, Prost took over as the team's lead driver and was said to have played on this status. Mansell recalls one incident where at the 1990 British Grand Prix, the car he drove didn't handle the same as in the previous race where he had taken pole position, and later found out from team mechanics that Prost saw Mansell as having a superior car and had them swapped without Mansell knowing. Prost won five races for Ferrari that year, in Brazil, Mexico, France, Britain and Spain. Notable among these was the Mexican Grand Prix, where he won after starting in 13th position. In both the Mexican and Spanish races, he led Mansell to Ferrari 1–2 finishes. The championship once again came to the penultimate round of the season in Japan with Prost trailing his McLaren adversary, Ayrton Senna, by nine points. As in 1989, a controversial collision between the two settled the race. At the first corner Senna, as admitted a year later, intentionally drove his race car into Prost's, taking them both out of the race and sealing the title in his favour. "What he did was disgusting," Prost said. "He is a man without value." Prost finished the season seven points behind Senna, and his Ferrari team were runners-up to McLaren.


title: Alain Prost

text: Mansell left the Scuderia due to his unstable relationship with Prost, to rejoin Williams for the 1991 Formula One season. Mansell's replacement was Frenchman Jean Alesi, who had been impressive during the previous two years at Tyrrell. Ferrari had entered a downturn, partially as their famous V12 engine was no longer competitive against the smaller, lighter and more fuel efficient V10s of their competitors. The Ferrari chassis, despite a major revision by the French Grand Prix (F-643) was also not up to the level of the McLaren and the Williams models. Prost won no races, only getting onto the podium five times. He took this out on the team, publicly criticising the team and the Ferrari 643, and subsequently had his contract terminated before the end of the season, immediately prior to the . He was replaced by Italian driver Gianni Morbidelli for the final race of the 1991 season and by another Italian, Ivan Capelli, for the following season. Despite being sacked, Prost received a significant payment from Ferrari to not drive for any other team.


title: Alain Prost

text: Prost went on a sabbatical year in , which was dominated by Nigel Mansell in a Williams-Renault. Prost performed pre-season testing for Ligier early in 1992 and later turned down an offer to drive for the team. After hearing that Prost would be his teammate again in 1993, Mansell left Williams to race in the CART series. Prost had a clause in his contract which prevented rival Ayrton Senna from joining the team that year. Prost was part of a new-look driver line-up at Williams, with test driver Damon Hill coming in to replace Riccardo Patrese, who had left to join Benetton.


title: Alain Prost

text: Prost won his fourth and final title in a year when he was regularly challenged by teammate Hill and by Ayrton Senna. Shortly before the Portuguese Grand Prix in October 1993, Prost announced he would not defend his world title, because the clause in his contract did not extend to 1994 and Senna would be able to join Williams for the upcoming season, and instead opted to retire. At the season's end Prost held the record for most Grand Prix victories, a record that stood for almost a decade. On the podium in Adelaide in 1993, Prost's last race, he and Senna embraced. Prost was surprised by the gesture, as Senna had declined a handshake at the previous race. Prost's performances earned him an OBE.


title: Alain Prost

text: German Michael Schumacher broke Prost's record of 51 Grand Prix wins during the 2001 season. He also shares the record for starting every race of a season from the front row (16, in ), with Ayrton Senna () and Damon Hill ().


title: Alain Prost

text: Prost's battles with Ayrton Senna were particularly notable. The rivalry originated in 1988, when Senna joined Prost at the McLaren team. The most notable event during the season between the two occurred during the Portuguese Grand Prix, where Senna tried to block Prost from taking the lead by forcing him to run close to the pit wall at around . Prost managed to edge Senna outwards, taking the lead as they went into the first corner, but remained angered by Senna's manoeuvre.


title: Alain Prost

text: The rivalry intensified after the 1989 San Marino Grand Prix, where the two drivers had an agreement that neither would get in each other's way to the first corner ("cf." 1982 San Marino Grand Prix). At the start, Senna got away in the lead and Prost followed him through the first corner without getting in his way. Gerhard Berger's crash on lap four stopped the race. At the restart, Prost got away the better of the two but Senna forced his way past him at the first corner, breaking the pair's agreement at the start of the race, leaving Prost furious. Senna argued that it was the restart. Prost himself was angered by McLaren apparently favouring Senna because of Senna's better relationship with engine supplier Honda, so he announced in mid-season that he had signed to race for Ferrari the following season. Prost mentioned many times during 1989 that he believed his car was not as competitive as Senna's, and even that this was confirmed to him by the CEO of Honda when Prost traveled to Japan. The information was actually confirmed during the French GP press conference when Ron Dennis said that Prost's car was consistently using more fuel, but not getting more power, than Senna's engine.


title: Alain Prost

text: The rivalry reached its peak at the end of 1989, when the title was to be decided between Senna and Prost at Suzuka. The two McLarens collided at the Casio Triangle chicane when Prost blocked an attempted pass by Senna. Prost walked away while Senna returned to the track. Senna went on to win the race, but was later disqualified in a highly controversial ruling over his path back to the track, as his car was pushed through the road around the chicane. After an unsuccessful appeal by McLaren, Senna received a further US$100,000 fine and a six-month suspension, leading him to accuse FIA president Jean-Marie Balestre of favouring his compatriot Prost.


title: Alain Prost

text: The following season saw the two drivers collide again. With Senna leading Prost, now in a Ferrari, in the world Drivers' Championship, Prost qualified second for the penultimate race of the season in Suzuka with Senna on pole. Senna was apparently told by a Steward that the pole position would be on one side of the track but discovered before the race that it would be actually be on the other side. Senna complained that no longer being on the racing line, his side of the grid was dirty, meaning he would get less grip (and therefore a slower start) than Prost who had been moved to the clean side of the grid. Senna's appeal was rejected. At the start of the race, Prost got the better start of the two, but while braking for the first corner Senna did not brake and collided with Prost at , clinching the title for himself. Prost almost retired from the sport, saying "What he did was disgusting. He is a man without value." A year later, Senna admitted that the move was premeditated, in retaliation for the collision at the chicane on the same course the previous year.


title: Alain Prost

text: There was another controversial incident in . Prost's inferior Ferrari was unable to put up a challenge regularly to Senna's front running McLaren. At the German Grand Prix at Hockenheim, Prost battled Senna for 4th place, but he felt Senna defended too aggressively and at the first chicane forced Prost to take avoiding action by using the escape road. Prost stalled his car rejoining the race. Coincidentally, Senna ran out of fuel on the last lap at the very same point. At the following race, in Hungary, the FIA ordered a sit-down meeting between the two men, not wanting any repeats of the incidents from the previous two years.


title: Alain Prost

text: Prost took a sabbatical in after being fired from Ferrari for publicly criticizing the car and the team, and Senna struggled, because McLaren was no longer competitive with Williams. Prost announced his signing with Williams for the upcoming 1993 season. Senna too had wanted to join Williams, as they were the most competitive, but Prost had a clause in his contract excluding Senna as a teammate. An infuriated Senna called the Frenchman a "coward" during a press conference at Estoril, and decried his unwillingness to compete for the Drivers' Championship on equal sporting terms:


title: Alain Prost

text: I think if Prost wants to be called the sole champion, three-times world champion, come back in a sportive way, maybe win another championship, he should be sportive. The way he's doing, he's behaving like a coward. And if he wants to be sportive, he must be prepared to race anybody, at any condition, at equal terms.


title: Alain Prost

text: During the 1993 season, Prost and Senna continued their on-track rivalry. Prost was escorted by police to the Interlagos circuit for the 1993 Brazilian Grand Prix due to the hostility of Brazilians towards him. The two continued their on-track battles at Silverstone where Senna aggressively defended his position against Prost. At Prost's last Grand Prix, the 1993 Australian Grand Prix, he was pulled up by Senna onto the top step of the podium for an embrace.


title: Alain Prost

text: On 1 May 1994, Ayrton Senna was killed during the . Prost was a pallbearer at his funeral. Speaking four years after Senna's death, Prost told Nigel Roebuck that he had "always refused to speak about him". Prost stated that when Senna died "a part of himself had died also", because their careers had been so bound together. Senna had also felt the same when Prost had retired at the end of 1993, when he admitted to a close friend that he had realised how much of his motivation had come from fighting with Prost. Only a couple of days before his death, when filming an in-car lap of Imola for French television channel TF1, he greeted Prost, by then a pundit on the channel: "A special hello to my...to our dear friend, Alain. We all miss you Alain." Prost said that he was amazed and very touched by the comment.


title: Alain Prost

text: Prost uses a helmet design based on the three colours of the French flag, blue, white and red, with his name along the side. During his early career Prost used a basic design of white all over with some blue detail around the visor (blue helmet with a white 180° flipped Y and red lines in the lower branch of the flipped Y and in the upper branch, surrounding the top). During Prost's time at Renault, he used more blue details, most notably around the rear of his helmet. Prost's helmet changed in 1985, as his helmet now had the blue detail around the front, surrounding the visor (with also a blue stripe on the side region, making the white area become a P) and a white ring with red lines surrounding the top (forming a white circle with a blue half in the rear of the top). Prost kept a similar design for his entry at Ferrari and Williams.


title: Alain Prost

text: Sometimes Prost used variants of his helmet design. In 2007 he used his original design, but with the circle top all red and a red line in the lower chin area. In 2010, he used a pearl white helmet with silver flames and a blue-white-red-white-blue stripe on the visor, designed by Kaos Design.


title: Alain Prost

text: During 1994 and 1995, Prost worked as TV pundit for the French TV channel TF1. He also worked for Renault as a PR man. Prost went back to his old team McLaren, working as a technical adviser; he also completed L'Étape du Tour, an annual mass-participation bike ride that takes place on a stage of the Tour de France. Although not an official race, riders fight hard for places; Prost finished 12th in his category, 42nd overall out of over 5000 riders.


title: Alain Prost

text: During 1989 Prost began to contemplate starting his own team, as his relationship with his McLaren teammate, Ayrton Senna, had turned sour. Prost and John Barnard, formerly chief designer at McLaren, came close to founding a team in 1990; but a lack of sponsorship meant that this was not possible, so Prost moved to Ferrari and Barnard left Ferrari to join Benetton. After falling out with the Italian team at the end of 1991, Prost found himself without a drive for 1992; after the failure of extensive negotiations with Guy Ligier about buying his Ligier team, Prost decided to join Williams for 1993. By 1995, when Prost was working for Renault, people had assumed that a Prost-Renault team would be formed. Renault refused Prost's request to supply engines for his team, ending the speculation.


title: Alain Prost

text: On 13 February 1997, Prost bought the Ligier team from Flavio Briatore and renamed it "Prost Grand Prix". The day after he bought the team, Prost signed a three-year deal with French car manufacturer Peugeot, who would supply the team with engines from until . For the team's first season, Prost kept one of Ligier's 1996 drivers, Olivier Panis, who had won the Monaco Grand Prix the previous year; Japanese driver Shinji Nakano was signed to partner Panis. The team raced with the Mugen-Honda engines used by Ligier the previous season, while the car was actually the originally intended Ligier JS45, but was renamed the Prost JS45. Things looked promising at the start of the season, as the team picked up two points on its Grand Prix debut in Australia when Olivier Panis finished fifth. The team scored a further 13 points before Panis broke his leg in an accident during the Canadian Grand Prix. He was replaced by Minardi's Jarno Trulli. From there, things started to go downhill slightly, the team scored only five points during Panis's recovery. He came back at the end of the season to race in the last three Grands Prix. Prost GP finished sixth in the Constructors' Championship in its first season, with 21 points.


title: Alain Prost

text: Prost became the president of Prost Grand Prix at the start of 1998. With Peugeot supplying the engines for Prost GP, Mugen-Honda decided to supply the Jordan team. Prost GP scored a single point during the season when Jarno Trulli finished sixth in Belgium.


title: Alain Prost

text: Peugeot's final year as Prost's engine supplier in 2000 saw some optimism. Prost hired his 1991 Ferrari teammate Jean Alesi to drive the lead car and German Nick Heidfeld, who had won the 1999 Formula 3000 championship, to partner him. The season proved to be yet another disastrous one: the AP03 proved to be unreliable and ill handling. Things weren't helped when the drivers collided with each other in the Austrian Grand Prix. Newly hired technical director Alan Jenkins was fired midway through the year. Prost restructured the team, hiring Joan Villadelprat as the managing director and replacing Jenkins with Henri Durand as the team's new technical director.


title: Alain Prost

text: In Ferrari agreed to supply engines for the season. The money ran out at the start of the season and Prost was out of business, leaving debts of around $30 million.


title: Alain Prost

text: During 2002, Prost spent time with his family and competed in eight bicycle races, finishing third in the "Granite – Mont Lozère". The Frenchman raced in the Andros ice race series in 2003, finishing second in the championship behind Yvan Muller. In 2003 and 2004, Prost took part in the Étape du Tour.


title: Alain Prost

text: Prost continued to compete in the Andros Trophy, winning the title with Toyota in 2006/07, 2007/08 and with Dacia in 2011/2012.


title: Alain Prost

text: For the 2010 Formula One season, the Sporting Regulations were changed so that a former driver sits on the stewards' panel. Prost was the first such driver to take on this role, at the 2010 Bahrain Grand Prix. Prost also took part in the Race of Champions in 2010, a race organised for legends of motor sport to compete in equal machinery.


title: Alain Prost

text: In February 2012, Prost was named as Renault's new international ambassador, representing the company in sports demonstrations and at events organized or attended by Renault.


title: Alain Prost

text: Prost has finished the Absa Cape Epic, an eight-day 700 km mountain bike race in South Africa, twice. He first completed the race in 2012 with partner Sebastien di Pasqua and then again in 2013, and started but did not finish the race in 2014.


title: Alain Prost

text: In October 2013, it was announced that Prost would join forces with Jean-Paul Driot's DAMS racing team to form e.dams, a team which would compete in the FIA Formula E Championship for electric racing cars from its commencement in September 2014. In June 2014, the team announced that its initial driver line-up would consist of Nicolas Prost and Sébastien Buemi. The team went on to win the inaugural Formula E teams championship. In 2017, he was employed as a special adviser for the Renault Formula One Team. Since July 2019, he took up a non-executive director role with Renault Sport. During the 1000th Formula One race, the 2019 Chinese Grand Prix, Prost had the honor of waving the chequered flag as Mercedes driver Lewis Hamilton crossed the line to take his 75th career victory. Prost continued in his role within Renault Formula One Team, renamed "Alpine F1 Team" in 2021, until January 2022, when his departure from the team was announced.


title: Alain Prost

text: Prost is widely regarded as one of the greatest ever Formula One drivers, and is considered by some to be the greatest Formula One driver of all time. In 2009, an "Autosport" survey taken by 217 Formula One drivers saw Prost voted as the fourth greatest Formula One driver of all time. In October 2020, "The Economist" ranked champion drivers by the relative importance of car quality to driver skill. According to this ranking, Prost is Formula One's third best driver of all time. In November 2020, Carteret Analytics used quantitative analysis methods to rank Formula One drivers. According to this ranking, Prost is Formula One's eighth best driver of all time. A 2022 mathematical analysis of all F1 drivers by f1-analysis.com put Prost as the 4th greatest driver of all time, and the second greatest once differences between different eras had been corrected for.


title: Pascal's triangle

text: In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy.


title: Pascal's triangle

text: The rows of Pascal's triangle are conventionally enumerated starting with row formula_1 at the top (the 0th row). The entries in each row are numbered from the left beginning with formula_2 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number of row 1 (or any other row) is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in row 3 are added to produce the number 4 in row 4.


title: Pascal's triangle

text: The entry in the formula_3th row and formula_4th column of Pascal's triangle is denoted formula_5. For example, the unique nonzero entry in the topmost row is formula_6. With this notation, the construction of the previous paragraph may be written as follows:


title: Pascal's triangle

text: for any non-negative integer formula_3 and any integer formula_9. This recurrence for the binomial coefficients is known as Pascal's rule.


title: Pascal's triangle

text: The pattern of numbers that forms Pascal's triangle was known well before Pascal's time. Pascal innovated many previously unattested uses of the triangle's numbers, uses he described comprehensively in the earliest known mathematical treatise to be specially devoted to the triangle, his "Traité du triangle arithmétique" (1654; published 1665).


title: Pascal's triangle

text: Centuries previously, discussion of the numbers had arisen in the context of Indian studies of combinatorics and binomial numbers. It seems from later commentaries that the binomial coefficients and the additive formula for generating them, formula_10, were known to Pingala during or before the 2nd century BC. While Pingala's work only survives in fragments, the commentator Varāhamihira, around 505, gave a clear description of the additive formula, and a more detailed explanation of the same rule was given by Halayudha, around 975. Halayudha also explained obscure references to "Meru-prastaara", the "Staircase of Mount Meru", giving the first surviving description of the arrangement of these numbers into a triangle. In approximately 850, the Jain mathematician Mahāvīra gave a different formula for the binomial coefficients, using multiplication, equivalent to the modern formula formula_11. In 1068, four columns of the first sixteen rows were given by the mathematician Bhattotpala, who was the first recorded mathematician to equate the additive and multiplicative formulas for these numbers.


title: Pascal's triangle

text: At about the same time, the Persian mathematician Al-Karaji (953–1029) wrote a now-lost book which contained the first description of Pascal's triangle. It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048–1131); thus the triangle is also referred to as the Khayyam triangle in Iran. Several theorems related to the triangle were known, including the binomial theorem. Khayyam used a method of finding "n"th roots based on the binomial expansion, and therefore on the binomial coefficients.


title: Pascal's triangle

text: Pascal's triangle was known in China during the early 11th century as a result of the work of the Chinese mathematician Jia Xian (1010–1070). During the 13th century, Yang Hui (1238–1298) presented the triangle and hence it is still known as Yang Hui's triangle () in China.


title: Pascal's triangle

text: In Europe, Pascal's triangle appeared for the first time in the "Arithmetic" of Jordanus de Nemore (13th century).


title: Pascal's triangle

text: The binomial coefficients were calculated by Gersonides during the early 14th century, using the multiplicative formula for them. Petrus Apianus (1495–1552) published the full triangle on the frontispiece of his book on business calculations in 1527. Michael Stifel published a portion of the triangle (from the second to the middle column in each row) in 1544, describing it as a table of figurate numbers. In Italy, Pascal's triangle is referred to as Tartaglia's triangle, named for the Italian algebraist Niccolò Fontana Tartaglia (1500–1577), who published six rows of the triangle in 1556. Gerolamo Cardano, also, published the triangle as well as the additive and multiplicative rules for constructing it in 1570.


title: Pascal's triangle

text: Pascal's "Traité du triangle arithmétique" ("Treatise on Arithmetical Triangle") was published in 1655. In this, Pascal collected several results then known about the triangle, and employed them to solve problems in probability theory. The triangle was later named for Pascal by Pierre Raymond de Montmort (1708) who called it "Table de M. Pascal pour les combinaisons" (French: Table of Mr. Pascal for combinations) and Abraham de Moivre (1730) who called it "Triangulum Arithmeticum PASCALIANUM" (Latin: Pascal's Arithmetic Triangle), which became the basis of the modern Western name.


title: Pascal's triangle

text: Pascal's triangle determines the coefficients which arise in binomial expansions. For example, consider the expansion


title: Pascal's triangle

text: The coefficients are the numbers in the second row of Pascal's triangle: formula_13, formula_14, formula_15.


title: Pascal's triangle

text: In general, when a binomial like formula_16 is raised to a positive integer power of formula_3, we have:


title: Pascal's triangle

text: where the coefficients formula_19 in this expansion are precisely the numbers on row formula_20 of Pascal's triangle. In other words,


title: Pascal's triangle

text: The entire right diagonal of Pascal's triangle corresponds to the coefficient of formula_22 in these binomial expansions, while the next diagonal corresponds to the coefficient of formula_23 and so on.


title: Pascal's triangle

text: To see how the binomial theorem relates to the simple construction of Pascal's triangle, consider the problem of calculating the coefficients of the expansion of formula_24 in terms of the corresponding coefficients of formula_25 (setting formula_26 for simplicity). Suppose then that


title: Pascal's triangle

text: We now have an expression for the polynomial formula_31 in terms of the coefficients of formula_25 (these are the formula_19s), which is what we need if we want to express a line in terms of the line above it. Recall that all the terms in a diagonal going from the upper-left to the lower-right correspond to the same power of formula_34, and that the formula_35-terms are the coefficients of the polynomial formula_25, and we are determining the coefficients of formula_31. Now, for any given formula_38, the coefficient of the formula_39 term in the polynomial formula_31 is equal to formula_41. This is indeed the simple rule for constructing Pascal's triangle row-by-row.


title: Pascal's triangle

text: It is not difficult to turn this argument into a proof (by mathematical induction) of the binomial theorem.


title: Pascal's triangle

text: An interesting consequence of the binomial theorem is obtained by setting both variables formula_34 and formula_44 equal to one. In this case, we know that formula_45, and so


title: Pascal's triangle

text: In other words, the sum of the entries in the formula_3th row of Pascal's triangle is the formula_3th power of 2. This is equivalent to the statement that the number of subsets (the cardinality of the power set) of an formula_3-element set is formula_50, as can be seen by observing that the number of subsets is the sum of the number of combinations of each of the possible lengths, which range from zero through to formula_3.


title: Pascal's triangle

text: A second useful application of Pascal's triangle is in the calculation of combinations. For example, the number of combinations of formula_3 items taken formula_4 at a time (pronounced "n choose k") can be found by the equation


title: Pascal's triangle

text: But this is also the formula for a cell of Pascal's triangle. Rather than performing the calculation, one can simply look up the appropriate entry in the triangle. Provided we have the first row and the first entry in a row numbered 0, the answer will be located at entry formula_55 in row formula_56. For example, suppose 8 jobs need to be filled but there are 10 candidates; the selection committee wants to know how many ways there are of selecting 8 from the 10. The answer is entry 8 in row 10, which is 45; that is, 10 choose 8 is 45.


title: Pascal's triangle

text: When divided by formula_57, the formula_56th row of Pascal's triangle becomes the binomial distribution in the symmetric case where formula_59. By the central limit theorem, this distribution approaches the normal distribution as formula_56 increases. This can also be seen by applying Stirling's formula to the factorials involved in the formula for combinations.


title: Pascal's triangle

text: This is related to the operation of discrete convolution in two ways. First, polynomial multiplication corresponds exactly to discrete convolution, so that repeatedly convolving the sequence formula_61 with itself corresponds to taking powers of formula_62, and hence to generating the rows of the triangle. Second, repeatedly convolving the distribution function for a random variable with itself corresponds to calculating the distribution function for a sum of "n" independent copies of that variable; this is exactly the situation to which the central limit theorem applies, and hence results in the normal distribution in the limit.


title: Pascal's triangle

text: The symmetry of the triangle implies that the "n" d-dimensional number is equal to the "d" "n"-dimensional number.


title: Pascal's triangle

text: The geometric meaning of a function P is: P(1) = 1 for all "d". Construct a "d"-dimensional triangle (a 3-dimensional triangle is a tetrahedron) by placing additional dots below an initial dot, corresponding to P(1) = 1. Place these dots in a manner analogous to the placement of numbers in Pascal's triangle. To find P("x"), have a total of "x" dots composing the target shape. P("x") then equals the total number of dots in the shape. A 0-dimensional triangle is a point and a 1-dimensional triangle is simply a line, and therefore P("x") = "1" and P("x") = "x", which is the sequence of natural numbers. The number of dots in each layer corresponds to P("x").


title: Pascal's triangle

text: There are simple algorithms to compute all the elements in a row or diagonal without computing other elements or factorials.


title: Pascal's triangle

text: To compute row formula_3 with the elements formula_82, formula_83, ..., formula_84, begin with formula_85. For each subsequent element, the value is determined by multiplying the previous value by a fraction with slowly changing numerator and denominator:


title: Pascal's triangle

text: For example, to calculate row 5, the fractions are  formula_87,  formula_88,  formula_89,  formula_90 and formula_91, and hence the elements are  formula_92,   formula_93,   formula_94, etc. (The remaining elements are most easily obtained by symmetry.)


title: Pascal's triangle

text: To compute the diagonal containing the elements formula_82, formula_96, formula_97, ..., we again begin with formula_85 and obtain subsequent elements by multiplication by certain fractions:


title: Pascal's triangle

text: By symmetry, this same process can be used to compute the diagonal formula_84, formula_101, formula_102... .


title: Pascal's triangle

text: For example, to calculate the diagonal beginning at formula_103, the fractions are  formula_104,  formula_105,  formula_106, ..., and the elements are formula_92,   formula_108,   formula_109, etc. By symmetry, these elements are equal to formula_110, formula_111, formula_112, etc.


title: Pascal's triangle

text: Due to its simple construction by factorials, a very basic representation of Pascal's triangle in terms of the matrix exponential can be given: Pascal's triangle is the exponential of the matrix which has the sequence 1, 2, 3, 4, ... on its subdiagonal and zero everywhere else.


title: Pascal's triangle

text: Pascal's triangle can be used as a lookup table for the number of elements (such as edges and corners) within a polytope (such as a triangle, a tetrahedron, a square, or a cube).


title: Pascal's triangle

text: Let's begin by considering the 3rd line of Pascal's triangle, with values 1, 3, 3, 1. A 2-dimensional triangle has one 2-dimensional element (itself), three 1-dimensional elements (lines, or edges), and three 0-dimensional elements (vertices, or corners). The meaning of the final number (1) is more difficult to explain (but see below). Continuing with our example, a tetrahedron has one 3-dimensional element (itself), four 2-dimensional elements (faces), six 1-dimensional elements (edges), and four 0-dimensional elements (vertices). Adding the final 1 again, these values correspond to the 4th row of the triangle (1, 4, 6, 4, 1). Line 1 corresponds to a point, and Line 2 corresponds to a line segment (dyad). This pattern continues to arbitrarily high-dimensioned hyper-tetrahedrons (known as simplices).


title: Pascal's triangle

text: To understand why this pattern exists, one must first understand that the process of building an "n"-simplex from an -simplex consists of simply adding a new vertex to the latter, positioned such that this new vertex lies outside of the space of the original simplex, and connecting it to all original vertices. As an example, consider the case of building a tetrahedron from a triangle, the latter of whose elements are enumerated by row 3 of Pascal's triangle: 1 face, 3 edges, and 3 vertices. To build a tetrahedron from a triangle, we position a new vertex above the plane of the triangle and connect this vertex to all three vertices of the original triangle.


title: Pascal's triangle

text: The number of a given dimensional element in the tetrahedron is now the sum of two numbers: first the number of that element found in the original triangle, plus the number of new elements, "each of which is built upon elements of one fewer dimension from the original triangle". Thus, in the tetrahedron, the number of cells (polyhedral elements) is ; the number of faces is the number of edges is the number of new vertices is . This process of summing the number of elements of a given dimension to those of one fewer dimension to arrive at the number of the former found in the next higher simplex is equivalent to the process of summing two adjacent numbers in a row of Pascal's triangle to yield the number below. Thus, the meaning of the final number (1) in a row of Pascal's triangle becomes understood as representing the new vertex that is to be added to the simplex represented by that row to yield the next higher simplex represented by the next row. This new vertex is joined to every element in the original simplex to yield a new element of one higher dimension in the new simplex, and this is the origin of the pattern found to be identical to that seen in Pascal's triangle.


title: Pascal's triangle

text: A similar pattern is observed relating to squares, as opposed to triangles. To find the pattern, one must construct an analog to Pascal's triangle, whose entries are the coefficients of , instead of . There are a couple ways to do this. The simpler is to begin with Row 0 = 1 and Row 1 = 1, 2. Proceed to construct the analog triangles according to the following rule:


title: Pascal's triangle

text: That is, choose a pair of numbers according to the rules of Pascal's triangle, but double the one on the left before adding. This results in:


title: Pascal's triangle

text: The other way of producing this triangle is to start with Pascal's triangle and multiply each entry by 2, where k is the position in the row of the given number. For example, the 2nd value in row 4 of Pascal's triangle is 6 (the slope of 1s corresponds to the zeroth entry in each row). To get the value that resides in the corresponding position in the analog triangle, multiply 6 by . Now that the analog triangle has been constructed, the number of elements of any dimension that compose an arbitrarily dimensioned cube (called a hypercube) can be read from the table in a way analogous to Pascal's triangle. For example, the number of 2-dimensional elements in a 2-dimensional cube (a square) is one, the number of 1-dimensional elements (sides, or lines) is 4, and the number of 0-dimensional elements (points, or vertices) is 4. This matches the 2nd row of the table (1, 4, 4). A cube has 1 cube, 6 faces, 12 edges, and 8 vertices, which corresponds to the next line of the analog triangle (1, 6, 12, 8). This pattern continues indefinitely.


title: Pascal's triangle

text: To understand why this pattern exists, first recognize that the construction of an "n"-cube from an -cube is done by simply duplicating the original figure and displacing it some distance (for a regular "n"-cube, the edge length) orthogonal to the space of the original figure, then connecting each vertex of the new figure to its corresponding vertex of the original. This initial duplication process is the reason why, to enumerate the dimensional elements of an "n"-cube, one must double the first of a pair of numbers in a row of this analog of Pascal's triangle before summing to yield the number below. The initial doubling thus yields the number of "original" elements to be found in the next higher "n"-cube and, as before, new elements are built upon those of one fewer dimension (edges upon vertices, faces upon edges, etc.). Again, the last number of a row represents the number of new vertices to be added to generate the next higher "n"-cube.


title: Pascal's triangle

text: In this triangle, the sum of the elements of row "m" is equal to 3. Again, to use the elements of row 4 as an example: , which is equal to formula_115.


title: Pascal's triangle

text: Each row of Pascal's triangle gives the number of vertices at each distance from a fixed vertex in an "n"-dimensional cube. For example, in three dimensions, the third row (1 3 3 1) corresponds to the usual three-dimensional cube: fixing a vertex "V", there is one vertex at distance 0 from "V" (that is, "V" itself), three vertices at distance 1, three vertices at distance and one vertex at distance (the vertex opposite "V"). The second row corresponds to a square, while larger-numbered rows correspond to hypercubes in each dimension.


title: Pascal's triangle

text: As stated previously, the coefficients of ("x" + 1) are the nth row of the triangle. Now the coefficients of ("x" − 1) are the same, except that the sign alternates from +1 to −1 and back again. After suitable normalization, the same pattern of numbers occurs in the Fourier transform of sin("x")/"x". More precisely: if "n" is even, take the real part of the transform, and if "n" is odd, take the imaginary part. Then the result is a step function, whose values (suitably normalized) are given by the "n"th row of the triangle with alternating signs. For example, the values of the step function that results from:


title: Pascal's triangle

text: compose the 4th row of the triangle, with alternating signs. This is a generalization of the following basic result (often used in electrical engineering):


title: Pascal's triangle

text: is the boxcar function. The corresponding row of the triangle is row 0, which consists of just the number 1.


title: Pascal's triangle

text: If n is congruent to 2 or to 3 mod 4, then the signs start with −1. In fact, the sequence of the (normalized) first terms corresponds to the powers of i, which cycle around the intersection of the axes with the unit circle in the complex plane: formula_118


title: Pascal's triangle

text: Pascal's triangle has higher dimensional generalizations. The three-dimensional version is known as "Pascal's pyramid" or "Pascal's tetrahedron", while the general versions are known as "Pascal's simplices".


title: Pascal's triangle

text: This extension preserves the property that the values in the "m"th column viewed as a function of "n" are fit by an order "m" polynomial, namely


title: Pascal's triangle

text: This extension also preserves the property that the values in the "n"th row correspond to the coefficients of (1 + "x"):


title: Pascal's triangle

text: When viewed as a series, the rows of negative "n" diverge. However, they are still Abel summable, which summation gives the standard values of 2. (In fact, the "n" = -1 row results in Grandi's series which "sums" to 1/2, and the "n" = -2 row results in another well-known series which has an Abel sum of 1/4.)


title: Pascal's triangle

text: Another option for extending Pascal's triangle to negative rows comes from extending the "other" line of 1s:


title: Pascal's triangle

text: Also, just as summing along the lower-left to upper-right diagonals of the Pascal matrix yields the Fibonacci numbers, this second type of extension still sums to the Fibonacci numbers for negative index.


title: Vengeance (2022 film)

text: Vengeance is a 2022 American black comedy film written and directed by B. J. Novak, in his directorial debut. It stars Novak, Boyd Holbrook, Dove Cameron, Issa Rae, and Ashton Kutcher. Jason Blum is a producer under his Blumhouse Productions banner, and Greg Gilreath and Adam Hendricks are producers under their Divide/Conquer banner.


title: Vengeance (2022 film)

text: "Vengeance" had its world premiere at the Tribeca Festival on June 12, 2022, and was theatrically released in the United States on July 29, 2022, by Focus Features. It received generally favorable reviews from critics.


title: Vengeance (2022 film)

text: New York journalist Ben Manalowitz unexpectedly receives a phone call from Ty Shaw informing him that his "girlfriend" Abby Shaw (in actuality just someone Ben hooked up with), has died of an apparent drug overdose. On Ty's request, Ben flies to Texas to attend the funeral and meets Abby's family: brother Ty, mother Sharon, sisters Paris and Kansas City, younger brother known as "El Stupido", and Granny Carole. Ty informs Ben that he suspects Abby was actually murdered, adamantly maintaining that she never took drugs, and asks Ben to accompany him to find the truth and avenge her. After conferring with his podcast producer Eloise, Ben elects to aid them as part of a story about grief and denial.


title: Vengeance (2022 film)

text: Ben and Ty travel to the oil pumps to meet Ty's friend Crawl, who explains that parties often occur at the oil fields, that there is a spot just outside where the parties are normally held that is dubbed "the Afterparty", where dead bodies have been reported over time, and that there is a particular drug dealer named Sancholo who Ty suspects may have killed Abby. Ben later meets Quentin Sellers, an eccentric record producer who, like Ben, is an outsider and college-educated but has come to adopt Texas as his home. Quentin gives Ben a memory stick that has video and audio of Abby performing. Ben gets to know Abby more through these videos, learning about her family and her. He learns that "El Stupido's" real name is Mason, and about how much the family loved each other. Ben confronts Sancholo outside of a bar to discuss Abby's death, and Sancholo reveals he was in Tulsa on the night of Abby's death and reiterates Ty's belief that Abby was not a drug abuser. Ben later joins the Shaw family at a rodeo, where he accidentally draws the crowd's ire by expressing support for the Texas Longhorns, when the crowd is overwhelmingly in favor of the Texas Tech Red Raiders.


title: Vengeance (2022 film)

text: Ben speaks to law enforcement agencies in the area and learns that they each tend to shift responsibility of "the Afterparty" to another agency because it is in a spot where the jurisdictions overlap. While speaking with Eloise about the updated status of the show, Eloise informs Ben that the show will be previewed on NPR; his car then explodes. To his surprise, the whole Shaw family comes to see him and takes him to Whataburger for the first time. During dinner, Eloise tells Ben that the story is finished and to come home, much to Ben's dismay. When back inside, Granny lets slip that Abby was in fact a drug user, and that Ty had lied to Ben to try and get closer to her supposed boyfriend. Leaving the restaurant, Ben reveals that he was not close with Abby and Ty punches him in the stomach, and they leave separately.


title: Vengeance (2022 film)

text: While in bed, Mason mentions how Abby would speak in code with him, saying "1435" ("I love you mucho"). Enlightened, he uses that number to unlock Abby's phone. He sees someone else labeled "Ben" in her phone, and sees texts indicating that she was abandoned by this person. Armed with one of Ty's pistols, Ben rides with Mason to a party at the oil pumps. After learning that his car was blown up by Texas Tech fans from the rodeo, Ben meets with Ty and Quentin. When Quentin and Ben start speaking, they go back to Quentin’s tent. Ben notices numerous packaged drugs that match the description given by one of the law enforcement officers, and sees an unconscious woman being dragged out of the tent. After turning off his main recorder, Ben elicits a confession from Quentin that he caused Abby to overdose and then dragged her to the Afterparty, where she later died. Ben pulls out his phone, which recorded the entire confession, and Quentin expands upon how there is more story that will be told, about how attention will be shifted to Ben, then to Abby's family. Ben executes Quentin on the spot. Upon returning to the Shaw house, Ben reconciles with Ty and deletes his recordings, electing to keep the story between the Shaws and himself.


title: Vengeance (2022 film)

text: Between 2015 and 2018, B. J. Novak, who lives in Los Angeles, California, took several trips to Texas to do research for a film he wanted to write about a blue state podcaster who travels to a red state. In March 2020, it was announced Novak would direct and star in the film, with Issa Rae, Ashton Kutcher, and Boyd Holbrook joining the cast.


title: Vengeance (2022 film)

text: Principal photography began in Albuquerque, New Mexico in March 2020, but was halted due to the COVID-19 pandemic. In January 2021, Isabella Amara joined the cast and production resumed that month. In March 2021, J. Smith-Cameron and Lio Tipton joined the cast, with Focus Features set to distribute.


title: Vengeance (2022 film)

text: "Vengeance" premiered on June 12, 2022, at the Tribeca Festival and was theatrically released in the United States on July 29, 2022. On September 16, 2022, it was released on Peacock to stream exclusively on the platform. The film was released on Blu-ray and DVD 4 days later on September 20, 2022.


title: Vengeance (2022 film)

text: In the United States and Canada, "Vengeance" was released alongside "DC League of Super-Pets", and was projected to gross around $2 million from 998 theaters on its opening weekend. The film made $650,000 on its first day and a total of $1.8 million over the weekend, finishing 10th. "Deadline Hollywood" noted that while the amount was "not super," being a low-budget film that received a theatrical release would make it "more attractive and stand-out in a streaming and PVOD menu." The film fell 60% to $720,000 in its second weekend.


title: Vengeance (2022 film)

text: On the review aggregator website Rotten Tomatoes, 81% of 156 critics' reviews are positive, with an average rating of 6.9/10. The website's critical consensus reads, "Writer-director-star B.J. Novak could have taken a sharper approach to this dark comedy's deeper themes, but if you're in the mood for a slyly smart mystery, "Vengeance" is yours." Metacritic, which uses a weighted average, assigned the film a score of 65 out of 100, based on 39 critics, indicating "generally favorable reviews". Audiences polled by CinemaScore gave the film an average grade of "B+" on an A+ to F scale, while PostTrak gave the film a 76% overall positive score, with 57% saying they would definitely recommend it.


title: Possession (1981 film)

text: Possession is a 1981 psychological horror drama film directed by Andrzej Żuławski, and written by Żuławski and Frederic Tuten. The plot obliquely follows the relationship between an international spy (Sam Neill) and his wife (Isabelle Adjani), who begins exhibiting increasingly disturbing behavior after asking for a divorce.


title: Possession (1981 film)

text: "Possession", an international co-production between France and West Germany, was filmed in West Berlin in 1980. Żuławski's only English-language film, it premiered at the 34th Cannes Film Festival, where Adjani won the Best Actress award for her performance. The screenplay was written during the painful divorce of Żuławski with actress Malgorzata Braunek. While not commercially successful either in Europe or in the United States, with the latter only receiving a heavily edited cut on its initial release, the film eventually acquired cult status and has been more positively appraised in later years.


title: Possession (1981 film)

text: Mark is a spy who returns home to West Berlin from a mysterious espionage mission to find that his wife, Anna, wants a divorce. She will not say why but insists it is not because she found someone else. Mark reluctantly turns the apartment and custody of their young son, Bob, over to her. After recovering from a destructive drinking spree, he visits the apartment to find Bob alone, unkempt, and neglected. When Anna returns, he stays with Bob, refusing to leave her alone with the child, but attempts to make amends. Anna leaves in the middle of the night.


title: Possession (1981 film)

text: Mark receives a phone call from Anna's lover, Heinrich, telling him that Anna is with him. The next day, Mark meets Bob's teacher, Helen; she inexplicably looks identical to Anna but with green eyes. Mark visits and fights Heinrich, who beats him. Mark then beats Anna at home, after which she flees. The next morning, they have another hysterical argument during which they both cut themselves with an electric knife, Anna on the throat and Mark on the arm.


title: Possession (1981 film)

text: Mark hires a private investigator to follow Anna and discovers that she has been keeping a second flat in a derelict apartment building. When the investigator discovers a bizarre tentacled creature in the bedroom, Anna kills him with a broken bottle. The lover of the now-dead detective, Zimmerman, goes to the flat himself, where he finds the creature and his lover's dead body. Anna beats Zimmerman in a rage before stealing his gun and then shooting him to death.


title: Possession (1981 film)

text: Anna continues her erratic behavior and recounts to Mark a violent miscarriage she suffered in the subway while he was gone. She claims it resulted in a nervous breakdown; during the miscarriage, she oozed blood and fluids from her orifices. Heinrich visits Anna at the second apartment and is shocked to discover the creature in the bedroom, as well as a collection of dismembered body parts in her refrigerator. She attacks him and Heinrich flees, bleeding.


title: Possession (1981 film)

text: Heinrich calls Mark and begs him to pick him up. Mark stops by Anna's apartment first and discovers the body parts; the creature, however, is gone. Mark meets Heinrich at the bar where he murders him, but stages it as an accidental death in the bathroom stall. He then sets Anna's apartment on fire before fleeing on Heinrich's motorcycle. At home, he finds Anna's friend Margie on the point of death as she emerges from the lift, bleeding from knife wounds. She dies; he drags the body inside where Anna greets him, and the two have sex in the kitchen. Afterward, he makes plans to cover up Margie's death. He then discovers Anna having sex with the creature. Heinrich's mother phones Mark asking about her son. When he goes to meet with her, she commits suicide by taking several pills.


title: Possession (1981 film)

text: The next day, as Mark wanders the street, his former business associates pressure him to rejoin them. He is evasive and returns to Margie's apartment to find it surrounded by police and his former employers. He stages a distraction, allowing someone to sneak away in his car, but he is wounded in the ensuing shootout. Fleeing on the motorbike, he has a horrific accident and races into a building where he is pursued by Anna, the police, and his business associates. Anna reveals the creature, now fully formed as Mark's doppelgänger. Mark raises his gun to shoot it but he and Anna are gunned down by a hail of bullets from the police below. Bloodied and dying, Anna lies atop Mark and uses his gun to shoot herself. She dies in his arms and he jumps to his death through the stairwell. The doppelgänger flees through the roof.


title: Possession (1981 film)

text: Later, Helen is at the flat babysitting Bob when the doorbell rings. Bob implores her not to open the door, but Helen ignores him. From outside, the sound of sirens, planes, and explosions fill the air. Bob races through the flat into the bathroom, where he floats in the bathtub face-down. The silhouette of Mark's doppelgänger is seen from the frosted glass door. Helen stares, her eyes shining.


title: Possession (1981 film)

text: Trying to classify "Possession", critics drew parallels with Roman Polanski's "Repulsion" and David Cronenberg's "The Brood". The genre of the film is still a matter of controversy. As J. Hoberman notes:


title: Possession (1981 film)

text: A number of critics deny the creature with tentacles exists within physical reality: it may be a reflection of Anna's psychosis; the product of Mark's inflamed consciousness, unable to accept his wife's betrayal; or a kind of revenge of the director traumatized by his own divorce from his ex-wife.


title: Possession (1981 film)

text: Many writers about "Possession" have paid attention to the motif of doppelgänger throughout the film. Both spouses die, but they are replaced by doubles, ideal models of husband and wife. Anna "grows" a double of Mark from the creature, an indefatigable lover who is always by her side. The real Mark finds a copy of Anna in the person of the school teacher Helen – she is a gentle character, and does not demand anything from Mark, being an "ideal housewife".


title: Possession (1981 film)

text: As in the case of "The Devil", the director placed political subtext under the layer of expressive horror after deliberately choosing Berlin as it was the least remote point from Poland and other countries of the European socialist bloc. The plot of "Possession" is not limited to an autobiographical description of a difficult breakup, separation and marital disintegration in family relations – at that time Żuławski also experienced a final separation from Poland. Two houses in the film – the modern one, which is Mark and Anna's apartment, and the old abandoned house in Kreuzberg, where Anna hides the squid-like creature – are located next to the Wall. The film contains elements of a spy thriller. Mark, an intelligence agent, leaves his job for his family. Anna leaves her family to become an "agent of the dark forces". The confrontation ends with death for both, and in the last frames of the film, there is a direct allusion (the sounds of sirens and the rumble of explosions) on the armed conflict that began in the city divided in two, which could end in a nuclear apocalypse.


title: Possession (1981 film)

text: Scholar Bartłomiej Paszylk writes that the metaphors present in the film also represent "a disintegrating country. The very fact that the film takes place in Cold War-era West Berlin is quite significant for the metaphor of divorce—the wall that separates it from East Berlin being a symbol of disconnection of what was once united—but [Żuławski's] additional intention might have been for the Berlin wall to symbolize the Iron Curtain, and for Germany to symbolize Poland, a country he had to leave in order to keep making movies."


title: Possession (1981 film)

text: Żuławski approached Danièle Thompson and asked if she would work on a film. After receiving a script about 20 pages long, Thompson suggested Frederic Tuten, thus Żuławski went to New York to meet him. They worked on the script for the film in New York and Paris while Żuławski was in a state of deep depression. In 1976, he divorced the actress Malgorzata Braunek. Żuławski recalled how he once returned home late in the evening and found his five-year-old son Xavier alone in the apartment, smeared with jam, after his wife left him alone for several hours – this scene was directly reflected in "Possession". A year and a half later, following the authorities' halting of work on the film "On the Silver Globe" in 1978, the director faced a "de facto" ban and was forced to leave Poland. While emigrating, he did not give up on suicidal thoughts, which he had initially been able to get rid of by starting to work on a new film.


title: Possession (1981 film)

text: Żuławski and the film's producer, Marie-Laure Reyre, immediately chose Isabelle Adjani as Anna. By this time, Adjani had already become a celebrity, but the producers had reasons to expect that she would accept the offer. After an unsuccessful attempt to start a career in Hollywood (released in 1978, Walter Hill's "The Driver" failed at the box office), Adjani decided to return to European cinema. She starred in "Nosferatu the Vampyre" (1979), but it had not yet been possible to repeat her success in being nominated for the Academy Award for her role in "The Story of Adele H." (1975). However, Adjani's management company turned down the offer, and the filmmakers chose the next candidate Judy Davis, whose work in the film "My Brilliant Career" (1979) impressed Żuławski. Sam Neill, a less well-known actor who appeared with Davis in the same film, was chosen for the role of Mark. Davis was hesitating over whether to take the role, so Adjani eventually accepted the offer.


title: Possession (1981 film)

text: The role was emotionally exhausting for Adjani. In one of the interviews, she stated that it took her several years to recover from her performance, which J. Hoberman called "a veritable aria of hysteria". It was rumored that she attempted suicide after filming completed, which was confirmed by Żuławski. "Time Out" magazine compared the behavior of her character to the actions of "a dervish of unrestrained emotion and pure sexual terror".


title: Possession (1981 film)

text: Sam Neill has also commented on the rigours of filming: "I call it the most extreme film I've ever made, in every possible respect, and he asked of us things I wouldn't and couldn't go to now. And I think I only just escaped that film with my sanity barely intact."


title: Possession (1981 film)

text: The budget for "Possession" was $2.4 million, and a 12-week shoot was scheduled. The director chose Berlin as the setting for the story because of its proximity to the Communist world. Principal photography began on 7 July 1980 in West Berlin, and most of the film was shot next to the Wall, in the Kreuzberg section of West Berlin. The "surrealist, clean quality" Żuławski wanted for the film was aided by the Steadicam work of camera operator Andrzej J. Jaroszewicz and Bruno Nuytten's cinematography and lighting. Carlo Rambaldi, the famous Italian special effects artist and the creator of the "Alien" animatronic head, assisted in creating the tentacle creature featured in the film.


title: Possession (1981 film)

text: After an initial limited theatre release in the United Kingdom, the film was banned as one of the notorious "video nasties". On American screens, it came out in a heavily edited 81-minute cut version from Limelight International Films on the eve of Halloween 1983, having lost more than a third of its runtime; the distributor turned "Possession" into an eccentric body horror, almost completely eliminating the main theme of the painful breakdown of marriage. This version was ridiculed by the American press as an example of "a cheap Grand Guignol" and had no public success.


title: Possession (1981 film)

text: A new 4K restoration of the film by Metrograph premiered in United States at Fantastic Fest in September 2021 and expanded nationwide on October 15.


title: Possession (1981 film)

text: "Possession" had a modest total of 541,120 admissions in France. In the United States, it was released on 28 October 1983 and grossed $1.1 million at the box office.


title: Possession (1981 film)

text: Although the film was banned from distribution in the United Kingdom, it was later released uncut on VHS and DVD in 2000 by Anchor Bay Entertainment. In 2014, Mondo Vision released a region-free Blu-ray of the film featuring the uncut version. This release was available in a standard special edition, as well as a limited edition numbered to 2,000 units.


title: Possession (1981 film)

text: "Possession" received lukewarm critical response when it was initially released in the summer of 1981. Derek Malcolm of "The Guardian" stated that, while Żuławski displayed talent and the special effects were unforgettable, the film itself was far too serious for its own good. Dennis Schwartz from "Ozus' World Movie Reviews" gave the film a grade of "C+", calling it "[an] uncompromising demented cult oddity." Leonard Maltin wrote of the film: "Adjani 'creates' a monster, to the consternation of husband Neill, lover Bennent—and the viewer", ultimately deeming the film a "confusing drama of murder, horror, intrigue, though it's all attractively directed." Vincent Canby of "The New York Times" wrote, "At times, the living-color "Possession" recalls Roman Polanski's black-and-white "Repulsion", though only because Miss Adjani is required to slice up as many male victims as Catherine Deneuve did in the earlier, far better film."


title: Possession (1981 film)

text: "Variety" gave the film a positive review, praising Żuławski's direction, symbolism, and pacing, writing "mass of symbols and unbridled, brilliant directing meld this disparate tale into a film that could get cult following on its many levels of symbolism and exploitation."


title: Possession (1981 film)

text: Harry Haun of the "New York Daily News" alternately panned the film, awarding it one-and-a-half out of four stars and writing that Adjani's "prize-winning mad-act is impossible to appraise because the film it's in is outlandishly unhinged as well... Just about any dialogue accompanying this mess would seem ludicrous." The "Philadelphia Daily News"s Joe Baltake deemed the film a "boringly camp-elegante attempt by a group of reputable French, German and Polish filmmakers," and assessed Adjani's performance as "babbling, incoherent yet arresting." In his review, however, Baltake conceded that the truncated version of the film he had seen—cut by approximately 50 minutes—may have contributed to the film's incoherency.