title: I Am Love (film)

text: I Am Love () is a 2009 Italian romantic drama film directed by Luca Guadagnino, set in Milan around the year 2000. Tilda Swinton plays a rich industrialist's wife who has an affair with a chef. It is the first installment in Guadagnino's self-described "Desire" trilogy, preceding "A Bigger Splash" (2015) and "Call Me by Your Name" (2017). Producers Swinton and Guadagnino developed the film together over an 11-year period. The film's soundtrack uses pre-existing compositions by John Adams.


title: I Am Love (film)

text: The film premiered in September 2009 at the Venice Film Festival, followed by showings at various film festivals around the world. It first went on general release in Italy in March 2010, followed by the UK and Ireland in April 2010. In the United States it had only a limited release in June 2010, before being released on DVD in October 2010. The film received a nomination for an Academy Award for Best Costume Design at the 83rd Academy Awards.


title: I Am Love (film)

text: Aside from a few minor differences, the Recchi family are largely based on the aristocratic Castellini Baldissera family, whose properties and ancestral homes were used as the set for the film. Piero Castellini Baldissera appears in a cameo role multiple times throughout the film


title: I Am Love (film)

text: The wealthy Recchi family are first and second-generation textile manufacturers in Milan. Tancredi Recchi (Pippo Delbono) and his wife Emma (Swinton) are hosting a formal dinner party for Tancredi's ailing but still-formidable father, Edoardo Sr. (Gabriele Ferzetti), patriarch and founder of the family business, who is celebrating his birthday. As the many servants bustle about, the family note with disappointment the news that Edoardo Jr. (Flavio Parenti), Tancredi and Emma's eldest son, lost a competition the day of his grandfather's birthday. Edoardo Jr. arrives from that competition, having informed the family that he has invited a girlfriend. She is Eva, of the prominent Ugolini family, whom he plans to marry. Edoardo Jr.'s young adult siblings, Gianluca (Mattia Zaccaro) and Elisabetta (Alba Rohrwacher), complain of yet again being served "ukha", Edoardo Jr.'s favourite dish, a special soup his mother Emma, who is Russian by birth, has made for him since childhood. The grandfather announces he is passing the family business to his son, Tancredi, who has long worked with him, and also, unexpectedly, to Edoardo Jr.


title: I Am Love (film)

text: At the dinner, Elisabetta, who attends school in London, presents her grandfather with one of her artworks, a photograph, despite a tradition of presenting one another paintings. He is disappointed, but encouraged by his glamorous wife Allegra "Rori" Recchi (Marisa Berenson) to gloss over his disappointment.


title: I Am Love (film)

text: Later during the birthday celebration, Edoardo Jr. receives a surprise visit from Antonio (Edoardo Gabbriellini), the chef who defeated him in the competition earlier that day. Antonio brings a beautiful cake as a gift, and Edoardo, flattered by the gesture, introduces him to his mother.


title: I Am Love (film)

text: After the party, while Emma is running errands, she discovers a CD, with a note from Elisabetta to her brother Edoardo revealing that Elisabetta is a lesbian. She tells her brother of an encounter with a woman and that she is in love with another woman. Meanwhile, Edoardo Jr. visits Antonio in Antonio's father's restaurant. They later make plans to open a restaurant together on some property Antonio's father owns in San Remo.


title: I Am Love (film)

text: Months later, Emma is having lunch at Antonio's restaurant with Rori and Eva, and she is aroused while relishing a prawn dish he prepares for her. Elisabetta returns to Milan, with her hair cut short, and invites Emma to go with her to Nice to look for a venue for Elisabetta's art exhibition. While stopping in San Remo en route to Nice to surprise her daughter, Emma spots Antonio, follows him, and eventually speaks to him outside of a book shop. She goes with him to his house in the hills above the city, and they begin their affair.


title: I Am Love (film)

text: Meanwhile, Edoardo Sr. has died, and in London, Edoardo Jr. struggles as his father and other family members seek to sell the family business they inherited from Edoardo Sr. to foreign investors. Edoardo Jr. visits his sister and tells her of the future of the business and his opposition to the sale.


title: I Am Love (film)

text: On her second trip to San Remo, under the pretext of discussing a menu for the formal dinner she will host for the foreign investors who are buying the Recchi family business, Emma spends the day with Antonio, and the two enjoy passionate lovemaking. Emma tells Antonio how Tancredi met her during a trip to Russia hunting for art treasures. Antonio cuts Emma's blonde hair, a long lock of which falls unnoticed to the terrace, where Edoardo Jr. finds it during his own visit after the London meeting. They cook together, and Emma teaches him to make "ukha".


title: I Am Love (film)

text: On the night of the dinner at the Recchi villa for the investors, a conversation between Edoardo Jr. and Eva is overheard, revealing she is pregnant with his child. Antonio prepares "ukha". When Edoardo sees this dish served, he instantly realizes his mother is having an affair with Antonio. He leaves the dinner table in a fury. Emma follows him outside to the garden and alongside the pool she tries to talk to him. In pulling away from Emma's outstretched hand, Edoardo loses his balance, falls, strikes his head on the edge of the pool's stone trim, and falls into the pool. He sustains a cerebral haemorrhage and dies in hospital.


title: I Am Love (film)

text: At the cemetery following the funeral, Tancredi tries to console Emma. She tells him that she is in love with Antonio. He responds by telling her "You don't exist." Emma rushes home and changes her clothes while her housekeeper helps her pack her things to leave. Before she leaves, she exchanges a knowing glance with her daughter, who it appears understands her mother's desire to follow her heart. Eva, who has hardly been noticed by Edoardo's family since his death, clutches her abdomen as she calls out to Eduardo Jr.'s siblings and grandmother, revealing her pregnancy. When the family members look back into the foyer where Emma was standing, she is gone.


title: I Am Love (film)

text: Many of the scenes were shot in the , a 1930s mansion in the heart of Milan designed by architect Piero Portaluppi. and currently owned by Fondo Ambiente Italiano, following a 2001 donation by Gigina Necchi Campiglio and Nedda Necchi. While the plot and characters of the film are fictitious, the surname of the family portrayed (Recchi) clearly echoes that of the entrepreneurial family (Necchi) which owned the mansion, mixing it with the name of coastal town Recco (hinting to the role played by Liguria in the film). Tilda Swinton said the villa was perfect because they were looking for a house “that was part palace, part museum, and part prison.” The funeral and the subsequent scene were filmed in the Cimitero Monumentale di Milano and notably in its distinctive "Famedio" (Hall of Fame).


title: I Am Love (film)

text: The soundtrack is made up entirely of pre-existing pieces by the modern classical composer John Adams. Swinton explained that the film was actually created around the pieces of music, and that they went to Adams after finishing the film and asked to use his music, which he had not allowed before. They were relieved when he liked the film and said yes. The film's title is taken from a line from the aria "La mamma morta" (from the opera "Andrea Chénier" by Umberto Giordano), which is explored in the film "Philadelphia"—a scene from which Swinton's character watches in bed with her husband.


title: I Am Love (film)

text: The food and meals in the film were inspired by the cuisine of Carlo Cracco, the owner of the Cracco Peck restaurant in Milan.


title: I Am Love (film)

text: "I Am Love" was met with positive reviews. Review aggregator website Rotten Tomatoes gives the film an approval rating of 81% based on reviews from 133 critics, with an average score of 7.17/10. The website's critical consensus reads: "It stumbles into melodrama, but "I Am Love" backs up its flamboyance with tremendous visual style and a marvelous central performance from Tilda Swinton." Another review aggregator, Metacritic, which assigns a weighted average score out of 100 to reviews from mainstream critics, calculated a "generally favorable" score of 79 based on 32 reviews.


title: I Am Love (film)

text: Roger Ebert of "Chicago Sun-Times" gave the film four out of four stars, praising Swinton's performance and saying ""I Am Love" is an amazing film. It is deep, rich, human. It is not about rich and poor, but about old and new. It is about the ancient war between tradition and feeling." "The Washington Post"s Ann Hornaday said the film was "carefully composed and framed, gorgeously appointed, superbly choreographed and accompanied by a thrilling musical score, it would no doubt provide rewarding fodder for critics of art, design, fashion, dance and music." Peter Bradshaw of "The Guardian" gave the film three out of five stars, saying "It's a high-IQ picture – there are few enough of those – and it's fascinating, if a little bloodless. A gorgeously costumed and styled piece of work."


title: I Am Love (film)

text: Margaret Pomeranz of "At the Movies" gave the film four and a half out of five stars and said "This is a beautiful film, moving, stylish with a sensual romance at its heart." Betsy Sharkey of the "Los Angeles Times" praised Swinton's performance, saying "Swinton is one of the finest actresses working in contemporary cinema, but Guadagnino, who developed the project with her in mind, has created a film that literally luxuriates in her talents." "Empire"s Damon Wise gave the film four out of five stars and said "Though it drags a little, this stately film never descends into formula, using John Adams' score to great effect and boldly utilising the flourishes of '70s Italian genre cinema (zooms, handheld camera) to create something original, refreshing and really very moving."


title: I Am Love (film)

text: Lisa Schwarzbaum of "Entertainment Weekly" gave the film a grade of "C+", saying "O sexytime in the countryside! O many wardrobe changes! The film is almost deliriously stylish, which helps mask the silliness. But the bellowing music, by John Adams, is infuriatingly intrusive – which undoes the visual good." Mark Demetrius of "Filmink" gave the film a negative review, stating "Despite an elegant and impressive visual style, the narrative of this slow-paced film is uninteresting and full of cliché." New York Film Critics Online called the work the Best Foreign Film of 2010. Quentin Tarantino listed it as one of his favorite 20 films of 2010.


title: I Am Love (film)

text: The film was nominated at the 68th Golden Globe Awards for Best Foreign Film but lost out to Denmark's "In a Better World". Costume designer Antonella Cannarozzi was nominated for an Academy Award for Best Costume Design for her work in the film, but the award went to Colleen Atwood for "Alice in Wonderland". The film was also nominated for the BAFTA Award for Best Film Not in the English Language, but lost to Niels Arden Oplev's "The Girl with the Dragon Tattoo".


title: I Am Love (film)

text: By March 2011, the film had grossed a total of USD$11,568,202 in cinemas worldwide. Home entertainment and TV sales are not included in the totals.


title: 2015–16 Golden State Warriors season

text: The 2015–16 Golden State Warriors season was the 70th season of the franchise in the National Basketball Association (NBA), and its 54th in the San Francisco Bay Area. The Warriors entered the season as the defending NBA champions and they set the best ever regular-season record of, breaking the 1995–96 Chicago Bulls record of . Golden State broke over twenty-five NBA records and more than ten franchise records that season, including most wins ever recorded in a season (regular-season and postseason combined); with 88. However, they were defeated in the NBA Finals by the Cleveland Cavaliers in seven games, having lost the series after leading 3–1.


title: 2015–16 Golden State Warriors season

text: The Warriors began the 2015–16 season by winning their first 24 games, eclipsing the previous best start in NBA history, set by the 1993–94 Houston Rockets and the 1948–49 Washington Capitols at . Their record-setting start ended when they were defeated by the Milwaukee Bucks on December 12, 2015. The Warriors broke a 131-year-old record of set by the 1884 St. Louis Maroons baseball team, to claim the best start to a season in all of the major professional sports in America. They also won 28 consecutive regular-season games dating back to the 2014–15 season, eclipsing the 2012–13 Miami Heat for the second longest winning streak in NBA history. The team set an NBA record 54-straight regular-season home-game winning streak, which spanned from January 31, 2015, to March 29, 2016. The previous record of 44 was held by the 1995–96 Chicago Bulls. Golden State broke their franchise record of 28 road wins in a season which they set in 2014–15; they ended the season with 34, passing the same mid-1990s Chicago Bulls team led by Michael Jordan for the most road wins in NBA history. The team became the first in NBA history to go the entire regular season without back-to-back losses and without losing to the same team twice.


title: 2015–16 Golden State Warriors season

text: Steve Kerr was named Coach of the Year, the third coach in Warriors history to win the award. Stephen Curry was named Most Valuable Player for a second successive season and was the first unanimous winner in NBA history. Curry, Draymond Green and Klay Thompson were all named to the All-Star Game, the first time the Warriors have had three All-Stars since 1976. Along with the All-Star selection, Klay Thompson was also named to the All-NBA Third Team. Draymond Green was named to the All-NBA Second Team while also being selected as an All-Star. Green was named to the All-Defensive First Team and he finished in second place in DPOY voting with 44 first-place votes. Andre Iguodala finished in second place in Sixth Man of the Year voting with 33 first-place votes. Curry broke his own NBA record for made three-pointers in a season of 286, finishing with 402. Curry won the scoring title, averaging 30.1 points per game and led the league in steals and had the best free throw percentage. He became the seventh player to enter the 50–40–90 club (he shot 50% for field goals, 45% for three-pointers and 91% for free throws during the entire regular season).


title: 2015–16 Golden State Warriors season

text: The 2015 NBA draft took place on June 25 at Barclays Center in Brooklyn, New York. Golden State chose power forward Kevon Looney with the 30th pick of the first round. On July 27, the Warriors traded David Lee to the Boston Celtics for Gerald Wallace and Chris Babb. Four days later, Wallace was traded to the Philadelphia 76ers for Jason Thompson.


title: 2015–16 Golden State Warriors season

text: The Warriors opened the regular season on October 27 with assistant coach Luke Walton coaching for the team after it was confirmed that coach Steve Kerr's back would not heal in time for the beginning of the regular season. Before the opener, the Golden State Warriors revealed their first title banner in 40 years and received their championship rings during a ceremony acknowledging the 2014–15 champions. Every player on the roster, with the exception of traded player David Lee, was in attendance with also the full coaching staff to celebrate the winningest season for the franchise. Golden State opened the season with a 111–95 win over the visiting New Orleans Pelicans. In that game, Stephen Curry led the Warriors with 40 points. On their third game of the season, they were once again up against the Pelicans, this time, they were on the road. On their first meeting, Curry scored 40 points, this time, Curry scored a season-high 53 points to lead the Warriors towards their third straight win. The Warriors opened their season with four wins and a combined margin-of-victory of 100 points, surpassing the 1961–62 Boston Celtics (99 points) for the largest win-margin over the first four games. On November 4, the Warriors won their fifth straight win after handing their division rival, the LA Clippers, their first loss of the season. Curry led the Warriors with 31 points. Eight days later, the Warriors won their tenth straight game after beating the Timberwolves, recording their first ever 10–0 start in a season in franchise history. On November 17, the Warriors have won their 12th straight game to start a season with 115–110 win over the visiting Toronto Raptors. They became the first defending champions to have won their first 12 games of a season since the 1996-97 Chicago Bulls. Three days later, the Warriors opened up the season with a 14–0 record after beating the visiting Chicago Bulls, 106–94. They also became the first defending champions to start their season with a 14–0 record since the 1957-58 Boston Celtics. On November 24, the Warriors won at home, 111–77, against the visiting Lakers and became the first team in NBA History to start a season with a 16–0 record, besting the 15–0 record set by the 1947-48 Capitols and 1993-94 Rockets. On November 27, the Warriors set new franchise records for longest winning streak (17) and three-point field goals made (22) in a 135–116 victory over the Phoenix Suns. They also extended their streak of scoring at least 100 points in a game for 17 straight games, the first team to do since the 2009-10 Suns.


title: 2015–16 Golden State Warriors season

text: On December 5, the Warriors beat the Toronto Raptors 112–109 to improve to 21–0 and set a new record for the best start to a season in all major professional sports in America, eclipsing the 20–0 mark set by the 1884 St. Louis Maroons baseball team of the Union Association. Also, with this 11th straight road victory, the Warriors set a new franchise-record for the longest road winning streak in their history. Golden State's 131–123 win on December 8 over the Pacers in Indianapolis improved their road record to 13–0, the best such start to a season in NBA history. The win improved their overall record to 23–0. On December 11, Golden State defeated the Boston Celtics 124–119 (2OT) to improve to 24–0 and move into second place on the NBA's longest winning streaks list (28), five games behind the Los Angeles Lakers' 33-game win streak. During this game Draymond Green recorded a five-by-five game, with 24 points, 11 rebounds, 8 assists, 5 steals and 5 blocks. The feat of recording at least 20 points, 10 rebounds, five assists, five steals and five blocks has only been achieved seven times by three different players (including five times by Hakeem Olajuwon). Since the 1983–84 NBA season, only 16 players have recorded a 5x5 line. The winning streak to start the season ended at 24 games when they were beaten by the Milwaukee Bucks, 108–95. The loss also ended their 28-game winning streak (dating to the 2014–15 regular season), the second-longest in NBA history. The Warriors finished the 2015 calendar year with a 72–12 (.857) record between two seasons, the second-best winning percentage in NBA history. They went 88–17 (.838) including play-off games.


title: 2015–16 Golden State Warriors season

text: In a win against the New York Knicks on January 31, Green tied Hall of Famer Tom Gola's franchise record of nine triple-doubles in a season. Golden State reached the NBA All-Star break at 48–4, the best start to an NBA season at this juncture. On February 13, Klay Thompson won the Three-Point Contest at the All-Star weekend, beating Stephen Curry 27–23 in the final round. The 27 points tied Curry's record set the previous year for most points scored in a round. By defeating the Atlanta Hawks on February 22, the Warriors became the fastest team to reach 50 wins in a season, accomplishing this in just 55 games. Golden State also had 30 assists in a game for the 29th time this season, setting a new franchise record. On February 27, the Warriors defeated the Oklahoma City Thunder and won their 29th road game of the season, breaking the franchise record of 28 which they set last season. They also became the fastest team ever in NBA history to clinch a playoff berth, accomplishing it in just 58 games. They bettered the 1985–86 Boston Celtics by just one day. This was also the earliest a team had clinched a playoff spot in February since the 1987–88 Los Angeles Lakers (although the season started almost two weeks earlier than the season did within their respective calendar years). In this game Stephen Curry also broke the single season three-point record (286), a record that he himself held, by making his 287th and 288th three-pointers of the season as two of his 12 three-pointers of the game, tying the single game NBA three-point record (jointly holding it with Kobe Bryant and Donyell Marshall).


title: 2015–16 Golden State Warriors season

text: On March 3, the Warriors tied the 1995–1996 Chicago Bulls for the longest regular-season home-game winning streak in NBA history (44 games), with a 121–106 victory at home against the Oklahoma City Thunder. The Warriors' streak dated back to the previous year. Entering the game on March 6, the Los Angeles Lakers (.190) and Golden State (.917) had a .727 difference in win percentage, making the Lakers' blowout 112–95 win the biggest upset in NBA history. On March 7, the Warriors won their 45th-straight regular season home game over the Orlando Magic, eclipsing the 1995–96 Chicago Bulls 44 wins in a row, to claim the NBA record. Stephen Curry became the first player in NBA history to score 300 three-pointers in a single season. In a 128–112 win over the Portland Trail Blazers on March 11, both teams combined for 37 made three-pointers (18 by the Warriors, 19 by the Blazers), an all-time NBA record. With a Los Angeles Clippers' loss to the Cleveland Cavaliers on March 13, the Warriors officially clinched the Pacific Division title for second consecutive season and fourth time overall. By defeating the New Orleans Pelicans on March 14, the Warriors became the fastest team to reach 60 wins in a season, accomplishing this in just 66 games. With a road win over the Minnesota Timberwolves on March 21, Golden State became only the ninth team in NBA history to achieve 31 wins on the road in the regular season. The Warriors finished the Pacific Division with a 15–1 (.938) record, the best intradivisional record in franchise history.


title: 2015–16 Golden State Warriors season

text: In a 128–120 win over the Dallas Mavericks on March 25, both teams combined for 39 made three-pointers (21 by the Warriors, 18 by the Mavericks), an all-time NBA record, which beat the 37 set by the Warriors and Blazers two weeks earlier. Golden State also eclipsed the previous record for most three-pointers in a single season by a team in NBA history (933) that had been set by the Houston Rockets the previous year. The Warriors dished out 32 assists against the Philadelphia 76ers on March 27, the 39th time this season the team has had a 30-assist game; the most in the NBA since the 1991–92 Chicago Bulls finished with 40. With their 102–94 win against the Washington Wizards on March 29, the Warriors tied their franchise record of most wins in a single season (67) which had been set the previous year. The Warriors earned their franchise record 68th victory of the season with a 103–96 win in overtime against the Utah Jazz on March 30. They improved to 6–0 in overtime this season, extending a franchise record for OT wins in a single season. Draymond Green became the first player in NBA history with 1,000 points, 500 rebounds, 500 assists, 100 steals and 100 blocks in a season.


title: 2015–16 Golden State Warriors season

text: On April 1, Golden State lost at home for the first time since January 27, 2015. They fell to the Boston Celtics 109–106 and snapped a 54-game regular-season home winning streak. Their home record for this season dropped to 36–1 with the loss. Golden State became the first team in NBA history to score 1,000 three-pointers in a single season during their 136–111 win against the Portland Trail Blazers. The win was Golden State's 69th of the season, making them the fourth team in NBA history to record at least 69 wins in a season, along with the 1971–72 Los Angeles Lakers and 1995–96/1996–97 Chicago Bulls teams. The Warriors became the first team since the 1991–92 Chicago Bulls to record 40 games with at least 30 assists in a single season. By defeating the San Antonio Spurs on April 7, the Warriors became only the 2nd team in NBA history to reach 70 wins in a season, joining the 72-win 1995–96 Chicago Bulls. After defeating the Spurs again on April 10, the Warriors tied the NBA record for most regular-season wins with 72, previously set by the 1995–96 Chicago Bulls. Golden State snapped a 33-game regular season losing streak against the Spurs in San Antonio (lasting since February 14, 1997), the second longest such streak against one team in NBA history. The Warriors also ended the Spurs' NBA record 39 home wins to start the season (in total a 48-game home winning streak dating back to the previous season.) Golden State became the first team in NBA history to go the entire regular season without back-to-back losses and the first team in NBA history to go the entire regular season without losing to the same team twice.


title: 2015–16 Golden State Warriors season

text: The Warriors broke the 1995–96 Chicago Bulls' record for best regular season in NBA history after defeating the Memphis Grizzles 125–104 on April 13, finishing with a record of 73–9. With the win, Golden State tied their franchise record for home wins with 39, which they set last season. The Warriors finished the season at an NBA-record 64 games above .500. Curry made 10 three-pointers against Memphis, making him the first player in NBA history to hit 400 threes in a single season; he finished with 402. Curry finished the season averaging 30.1 points per game, making him the first Warriors NBA scoring champion since Rick Barry in the 1966–67 NBA season. Curry became the seventh player to enter the 50–40–90 club, where he shot 50% for field goals, 45% for three-pointers and 91% for free throws during an entire regular season. This feat has only been achieved eleven times by seven players (Steve Nash having done it four times).


title: 2015–16 Golden State Warriors season

text: Golden State beat the Houston Rockets 121–94 on April 24 to go up 3–1 in the first round series, in doing so they set the NBA record for threes made in a playoff game, hitting 21-of-40 (.525). Steve Kerr was named Coach of the Year on April 26, the third Warriors coach to win the award after Alex Hannum in 1963–64 and Don Nelson in 1991–92. Under Kerr's leadership the Warriors led the league in scoring (114.9 points), field goal percentage (.487), three-point percentage (.416), assists (28.9), point differential (+10.8) and offensive rating (112.5 points per 100 possessions), while becoming the first team in league history to hit 1,000 three-pointers in a single season with an NBA-record 1,077 triples. Kerr held an overall regular-season record of 140–24 (.854) in his first two seasons with the Warriors. The Warriors eliminated the Houston Rockets on April 27 with a blowout victory of 114–81, winning the series 4–1 and progressing to the Western Conference Semi-finals to face the Portland Trail Blazers. Klay Thompson became the first player in NBA history to make at least seven three-pointers in consecutive playoff games.


title: 2015–16 Golden State Warriors season

text: On May 9, a 132–125 OT win over the Portland Trail Blazers put Golden State up 3–1 in the series, Steph Curry scored 40 points in his first game back after being out injured for 15 days with an MCL sprain. He scored 17 of his points in overtime, which broke the NBA record of 16 held by Gilbert Arenas for most points scored in an overtime period (regular-season or postseason). Stephen Curry was named Most Valuable Player on May 10, making it the third time a Warrior had won the award after Wilt Chamberlain won in the 1959–60 NBA season and Curry in 2014–15. Curry is the 11th player to win back-to-back MVP honors and is the first unanimous winner in NBA history with all 131 first-place votes. On May 11, the Warriors beat the Trail Blazers 125–121 in Game 5 to clinch the series and advance to the Western Conference Finals for the second consecutive year, where they faced the Oklahoma City Thunder. In the game, Curry continued his streak of making a three-pointer in every playoff game he's ever played in and tied the NBA playoff record set by Reggie Miller of 44-straight.


title: 2015–16 Golden State Warriors season

text: In their 95th and 96th games of the season, Golden State lost back-to-back games for the first time all season (105–133 and 94–118 losses to the Thunder, putting them down 1–3 in the Western Conference Finals). On May 26, Stephen Curry, Draymond Green and Klay Thompson were named to the 2015–16 All-NBA Team, the first time three Warriors have earned the accolade since the 1955–56 season when Neil Johnston, Paul Arizin, and Jack George were selected. Curry was unanimously selected for first team honors, Green for the second team and Thompson got third team recognition. The Warriors tied the Western Conference Finals series at 3–3 on May 28, with a 108–101 road win over the Thunder. Klay Thompson made eleven three-pointers, breaking the NBA playoff record of nine. Golden State tied their franchise record for most three-pointers made in a playoff game with 21. Golden State also set a new franchise record for wins with their 84th of the season (regular-season and postseason combined), surpassing the 83 from the 2014–15 season. In Game 7, the Warriors defeated the Thunder 96–88, becoming only the 10th team (out of 233 teams) in NBA history to overcome a 3–1 series deficit. The win was their 85th of the year. It was the second time in NBA history that the defending champions came back from a 3–1 deficit in the conference finals, after the 1978–79 Washington Bullets. Golden State reached the NBA Finals for the second straight year, making this the franchise's first appearances in back-to-back NBA Finals since the 1946–47 season and 1947–48 season. The Warriors faced the Cleveland Cavaliers in a rematch of the 2015 NBA Finals.


title: 2015–16 Golden State Warriors season

text: In Game 1 on June 2, Golden State beat Cleveland 104–89. The Warriors were led by their bench, with Shaun Livingston scoring a team-high 20 points. The 35-point bench advantage (45–10) the Warriors had over the Cavs is the largest by any team in the Finals in the last 50 years. The Warriors won Game 2 by a blowout 110–77, to go up 2–0 in the series. Golden State won the first 2 games by a combined 48 points, the largest point-differential through first 2 games in NBA Finals history. After Golden State lost Game 3 by a blowout 120–90, they came back in Game 4 to win 108–97, to take a 3–1 series lead. The Warriors made 17 three-pointers, an NBA record for a single Finals game. The Warriors' win in Game 4 was their 88th of the season, which broke the 1995–96 Chicago Bulls record of 87 for most wins in an NBA season (regular-season and postseason combined). Late in the fourth quarter of Game 4, Draymond Green and LeBron James got into a scuffle. Green was retroactively charged with a Flagrant Foul 1 for swiping James in the groin and received a one-game suspension for Game 5, after accumulating his fourth flagrant foul point in the playoffs, and James was given a technical foul for taunting Green. The Cavaliers capitalized on Green's absence by beating the Warriors in Game 5 by a score of 112–97.


title: 2015–16 Golden State Warriors season

text: After serving his suspension, Green returned to play in Game 6. Game 6 was played on June 16, exactly one year after Golden State won Game 6 of the 2015 NBA Finals, which was also played in Cleveland. Unlike in the 2015 NBA Finals, however, the Warriors failed to clinch the title in Game 6. The Warriors were outscored 31–11 by the Cavaliers in the first quarter, and Cleveland never relinquished their lead as Golden State lost 115–101. This was only the second time in 105 games this season (regular-season and postseason) that the Warriors lost consecutive games. The loss evened the series at three games apiece, forcing a Game 7, the first Game 7 in an NBA Finals appearance in Golden State franchise history. During the fourth quarter of Game 6, Stephen Curry, who set the record for most three-pointers in an NBA Finals series during the game (28), fouled out with his sixth personal foul. Curry angrily responded by throwing his mouthguard into the stands and hit a fan, which resulted in a technical foul and the first ejection of his career. It was the first time in 20 years that a player had been ejected from an NBA Finals game. After the game, Curry received a $25,000 fine for his actions, but was not suspended for Game 7. Warriors head coach Steve Kerr also received a $25,000 fine for his criticism of the officiating, which he felt was biased against Curry, in the post-game press conference.


title: 2015–16 Golden State Warriors season

text: On June 19, 2016, Golden State lost Game 7, 93–89, becoming the first team in NBA history to squander a 3–1 lead in the NBA Finals. They also became the first team in NBA history to overcome a 1–3 deficit and lose a 3–1 lead in the same playoffs. The Warriors are the 11th team in NBA history to lose a 3–1 series lead and just the fourth team in NBA history to lose an NBA Finals' Game 7 on their home court. The loss marked the first time since Steve Kerr became head coach that the Warriors had lost three straight games. Golden State became the first team in NBA history to finish with the same number of regular-season and postseason losses (9). They also became the first team in NBA history with 69 or more regular season wins that failed to win the NBA Championship.


title: 2015–16 Golden State Warriors season

text: Golden State broke numerous regular-season, postseason, and franchise records this year, both as a team and individually.


title: Mimi Kennedy

text: Mary Claire "Mimi" Kennedy (born September 25, 1948) is an American actress, author, and activist. Best known for her roles in television sitcoms, Kennedy co-starred in numerous short-lived sitcoms before her role as Ruth Sloan on "Homefront" (1991–93). She received wider recognition with her roles in the Chuck Lorre created sitcoms; "Dharma & Greg" (1997–2002), and "Mom" (2013–2021). For her performance in the latter, Kennedy received a nomination for the Critics' Choice Television Award for Best Guest Performer in a Comedy Series. Kennedy has also appeared in various films, including; "Pump Up the Volume" (1990), "Erin Brockovich" (2000), "In the Loop" (2009), "Due Date" (2010), "Midnight in Paris" (2011), and "The Five-Year Engagement" (2012).


title: Mimi Kennedy

text: Kennedy was born in Rochester, New York, the daughter of Nancy Helen (née Colgan) and Daniel Gerald Kennedy. She got her start in theater with the Rochester Community Players, appearing in Agatha Christie's "Spider Web" in October 1960 when she was 12 years old. She was raised in Rochester, where she graduated in 1966 from Our Lady of Mercy High School. In the 1970s, she was in the musical "Rhinegold", featuring songs by her friend Jim Steinman. She attended Smith College.


title: Mimi Kennedy

text: Kennedy was a member of the cast of "The National Lampoon Show", directed by John Belushi, who also starred in it. She auditioned for "Saturday Night Live", but lost to Jane Curtin.


title: Mimi Kennedy

text: She appeared in the Broadway musical "Grease", and in 1977 landed a part in the short-lived variety series "3 Girls 3", with Debbie Allen and Ellen Foley. She later played the role of Stockard Channing's sister in the short-lived "Stockard Channing in Just Friends" (1979), and she was a regular on "The Big Show" (1980). During the 1980s, she starred in a number of short-lived sitcoms, including "The Two of Us" (1981–82), "Spencer" (1984–85), and "Family Man" (1988). She also co-starred in the sitcom "Joe's Life" (1993).


title: Mimi Kennedy

text: Kennedy made her dramatic turn with a supporting role in the critically acclaimed "Homefront". The series ran from 1991 to 1993. She later was a regular on "Savannah" (1996–97), playing the rich socialite mother of Shannon Sturges' character. After the series was canceled, she was cast in "Pacific Palisades". This series also was canceled after a single season. In 1997, Kennedy returned to comedy roles playing Dharma's mother, Abby O'Neil, on the sitcom "Dharma & Greg" (1997-2002).


title: Mimi Kennedy

text: During the 2000s, Kennedy had many guest-starring roles on television, appearing on "Grey's Anatomy", "House", "ER", "Scandal", "In Plain Sight", "Drop Dead Diva", and "Veep". She also had a number of supporting film roles, appearing in "Man in the Chair", "In the Loop", "Due Date", "Midnight in Paris" and "The Five-Year Engagement". In 2013, Kennedy joined the cast of the sitcom "Mom" playing Marjorie, the twelve-step sponsor of the lead characters. She received a Critics' Choice Television Award nomination for her performance on the show. She became a series regular on the second season.


title: Mimi Kennedy

text: Early in 2022, Kennedy posted a video in which she and spouse Larry Dilg recall their friendships with Jim Steinman and, by extension, with Meatloaf. In the video, Kennedy shares details of her months touring with the National Lampoon Show.


title: Mimi Kennedy

text: Kennedy is involved in several progressive activist causes, including Progressive Democrats of America for which she serves as chairperson of the board. She is a regular contributor to the "LA Progressive". Her mid-life memoir "Taken to the Stage: The Education of an Actress" was published by Smith & Kraus in 1996,


title: Revenge (1990 film)

text: Revenge is a 1990 American romantic action thriller film directed by Tony Scott and starring Kevin Costner, Anthony Quinn, Madeleine Stowe, Miguel Ferrer and Sally Kirkland. Some scenes were filmed in Mexico. The film is a production of New World Pictures and Rastar Films and was released by Columbia Pictures. "Revenge" also features one of John Leguizamo's earliest film roles. The film is based on a novella written by Jim Harrison, published in "Esquire" magazine in 1979. Harrison co-wrote the script for the film.


title: Revenge (1990 film)

text: Michael J. "Jay" Cochran (Kevin Costner) is a U.S. Navy aviator, leaving the service after 12 years. He receives a matched pair of Beretta shotguns and an invitation from his wealthy friend, Tiburon "Tibey" Mendez (Anthony Quinn) to spend time at his hacienda in Mexico. Tibey is also a powerful crime boss, constantly surrounded by bodyguards.


title: Revenge (1990 film)

text: In Mexico, Cochran meets Tibey's beautiful young wife, Miryea (Madeleine Stowe) who lives in lavish surroundings, but is unhappy because her much-older husband does not want children, feeling pregnancy would spoil her looks.


title: Revenge (1990 film)

text: Jay presents Tibey with a Navy G-1 leather flight jacket. But he rubs Tibey's suspicious right-hand man, Cesar (Tomas Milian) the wrong way by behaving independently and not acting like an employee. After a dinner Tibey conducts a private meeting with business associates, killing one of them, while elsewhere Miryea and Jay get better acquainted, developing a romantic attraction for each other.


title: Revenge (1990 film)

text: During a party, with Tibey and his men nearby, Jay and Miryea secretly have sex in a closet. Jay tells her he intends to leave Mexico, worried that Tibey will become aware of the situation. Miryea begs him to stay and having fallen in love with her, he agrees and together, they arrange a secret rendezvous at a remote cabin in Mexico.


title: Revenge (1990 film)

text: Miryea tells Tibey that she will be visiting her sister in Miami, but Tibey overhears a telephone conversation in which Miryea asks her sister to lie for her. Tibey drives Miryea to the airport, giving her one last kiss. Jay is secretly waiting inside the airport and they drive off to the cabin.


title: Revenge (1990 film)

text: At their hideaway, they are surprised by Tibey and his men. Jay's beloved dog Rocky is shot dead. Calling Miryea a "faithless whore", Tibey strikes her and cuts her across the mouth with a knife (creating half a Glasgow smile) as Tibey's henchmen viciously beat Jay bloody. After setting fire to the cabin, they dump Jay in the desert, leaving him to die.


title: Revenge (1990 film)

text: Miryea is placed in a whorehouse with Tibby giving instructions for her to be “fucked 50 times a day”, where she is drugged, abused and relegated to "common use". The young man responsible for keeping her drugged has AIDS. As Miryea no longer wishes to live, she persuades him to share a needle with her, thus infecting her.


title: Revenge (1990 film)

text: An unconscious Jay is discovered by Mauro (Joaquín Martínez) a peasant farmer whose family slowly nurses Jay back to health. Jay returns to the burnt cabin and retrieves some money he had hidden. Mauro drives Jay to town and gives him a knife to "cut the balls off your enemy". Jay encounters a sickly Texan (James Gammon) transporting a horse, who offers Jay a ride to Durango. Inside a cantina, Jay notices one of the thugs who had thrashed him; he follows him into the men's room and cuts his throat.


title: Revenge (1990 film)

text: After a day on the road, the Texan delivers the horse to a wealthy man, who recognizes Jay from an afternoon at Tibey's estate. The friendly Texan later dies peacefully in his car, while Jay is driving.


title: Revenge (1990 film)

text: At a motel, Jay runs across Amador (Miguel Ferrer), Mauro's brother-in-law. Amador and his quiet friend, Ignacio (John Leguizamo) are willing to help Jay because Amador's sister was killed after getting mixed up in business that involved Tibey. They capture another of Tibey's henchmen, who tells them where Miryea can be found. Jay barges into the brothel, only to find that she has been moved. The madam taunts Jay that Miryea proved very popular with the clientele. No one but Tibey knows where she is.


title: Revenge (1990 film)

text: Jay, Amador and Ignacio ambush Tibey and his bodyguard during Tibey's morning horseback ride. Jay is there to ask Miryea's whereabouts, but first Tibey requests that Jay ask forgiveness for having stolen his wife. When Jay lowers his gun and asks Tibey's forgiveness, Tibey reveals that Miryea is in a convent.


title: Revenge (1990 film)

text: Miryea is in a convent hospice, dying of AIDS. Jay arrives in time to tell Miryea that he loves her. He carries her outside and Miryea tells Jay that she also loves him before she dies in his arms.


title: Revenge (1990 film)

text: The novella was published in 1979 along with two other novellas under the title "Legends of the Fall". "Esquire" magazine published the novella "Legends of the Fall" in January 1979 and public response was so enthusiastic that "Revenge" was published in May. Warner Bros promptly bought the screen rights and hired Harrison to do the screenplay.


title: Revenge (1990 film)

text: The project languished in development hell for eleven years. John Huston was to direct Jack Nicholson and then Orson Welles was attached to direct. Harrison later recalled he "wrote about 12 different endings to it". Walter Hill worked on the screenplay for a while.


title: Revenge (1990 film)

text: Costner had an interest in the novella from the mid-1980s. "It seemed to me something I wanted to do myself", he said. "I contemplated directing it because it seemed like a small movie. The story was manageable, but the themes were big and universal, and the writing was tough and it was honest and it was original. There was poignance in the story, and it read like an original movie to me."


title: Revenge (1990 film)

text: Producer Ray Stark eventually acquired the rights from Warner Bros in exchange for the film "Bird". Costner used his celebrity status to help get the film made.


title: Revenge (1990 film)

text: Costner would serve as executive producer and take a special interest in the script. The writer was Robert Garland who made "No Way Out" with Costner.


title: Revenge (1990 film)

text: For a time it seemed John Huston might direct Costner in the film and the two men met; Huston was not impressed by the actor. In 1987, New World Pictures teamed up with Rastar to co-own feature film rights to the "Revenge" project.


title: Revenge (1990 film)

text: Principal shooting took place in several Mexican cities, including Puerto Vallarta and Mexico City. Production completed on December 14, 1988. Some shooting took place in Sierra de Órganos National Park in the town of Sombrerete, Mexico. The closing scene was shot at the Iglesia de Nuestra Señora de los Remedios, one of several monasteries near the volcano Popocatapetl. Director Tony Scott would lend several assets from his prior making of Top Gun, including access to the Navy personnel to arrange footage of F-14s over rough desert terrain. Viewers would also recognize the familiar cockpit simulators in Revenge's opening sequence as those used in Top Gun.


title: Revenge (1990 film)

text: Columbia released "Revenge" on VHS in August 1990. The version included on the 2007 DVD and Blu-ray releases is Tony Scott's director's cut, shorter by 20 minutes, running 104 minutes, and including expanded scenes as well as some deletions and additional scoring by Harry Gregson-Williams.


title: Revenge (1990 film)

text: On Rotten Tomatoes the film has an approval rating of 32% based on reviews from 19 critics, with an average rating of 4.4/10. On Metacritic it has a score of 35 out of 100 based on reviews from 23 critics, indicating "generally unfavorable reviews". Audiences surveyed by CinemaScore gave the film a grade B− on scale of A to F.


title: Revenge (1990 film)

text: "Variety" wrote, "This far-from-perfect rendering of Jim Harrison's shimmering novella has a romantic sweep and elemental power that ultimately transcend its flaws." Owen Gleiberman of "Entertainment Weekly" rated it D and called it a vanity project for Costner. Roger Ebert, writing for "The Chicago Sun-Times", rated it 2.5 out of 4 stars and wrote that the film "plays like a showdown between its style and its story." Vincent Canby of "The New York Times" described it as "soft and aimless ... the performances are without conviction." Hal Hinson of "The Washington Post" wrote that the story becomes so cynical that nothing has meaning.


title: Revenge (1990 film)

text: "They pretty much shot the novella", said Harrison. "I was so swept away by it that I cried – I really did. And I'm not known for crying".


title: The Runaways (2010 film)

text: The Runaways is a 2010 American biographical drama film about the 1970s rock band of the same name written and directed by Floria Sigismondi. It is based on the book "Neon Angel: A Memoir of a Runaway" by the band's lead vocalist Cherie Currie. The film stars Dakota Fanning as Currie, Kristen Stewart as rhythm guitarist and vocalist Joan Jett, and Michael Shannon as record producer Kim Fowley. "The Runaways" depicts the formation of the band in 1975 and focuses on the relationship between Currie and Jett until Currie's departure from the band. The film grossed around $4.6 million worldwide and received generally favorable reviews from critics.


title: The Runaways (2010 film)

text: Cherie Currie is a teenager in Los Angeles who desperately wants to be a rock star. She idolizes David Bowie and cuts her hair and dons make-up so she will resemble Bowie's character Aladdin Sane. At her high school talent show, she lip syncs to "Lady Grinning Soul" and wins, despite some hecklers in the audience.


title: The Runaways (2010 film)

text: Joan Jett is a teenager who also dreams of rock stardom. At a club one night, she meets record producer Kim Fowley and talks about starting an all-girl rock band. Kim is interested. He introduces Joan to Sandy West, a drummer. Joan and Sandy become friends and start jamming when Kim suggests that they recruit an attractive blonde in the vein of Brigitte Bardot.


title: The Runaways (2010 film)

text: Kim and Joan comb Los Angeles' clubs to look for attractive blondes and discover Cherie. They invite her to audition at a trailer park in the San Fernando Valley and to prepare a Suzi Quatro song to perform at her audition. Cherie learns Peggy Lee's "Fever" instead and goes to audition, but the band is disappointed at her choice. Kim and Joan then write "Cherry Bomb" on the spot for Cherie to audition with. Cherie sings the song and becomes part of the band, named the Runaways, joined by Lita Ford on lead guitar and Robin on bass. Joan and Cherie share a passionate kiss (but what follows between them is not explicit).


title: The Runaways (2010 film)

text: The Runaways are soon signed to Mercury Records and release an album. On account of the album's success, they travel to Japan to play a concert. Following their performance, Lita throws magazines at Cherie because they have pictures of Cherie only. Cherie is shocked because she thought the articles were to cover the whole band. As Lita, Cherie and Joan argue, overenthusiastic fans break through the window and chase the girls out of the building. Cherie's drug use worsens, until she overdoses in the hotel elevator and is sent to the hospital. Upon arriving back in the United States, Cherie begins to abuse her alcoholic father's painkiller medication.


title: The Runaways (2010 film)

text: At the studio recording their next album, Cherie has a mental breakdown and refuses to play after reading a cruel comment about her by Kim in a magazine article. Lita then rudely insults Cherie for being more popular than the rest of them; Cherie insists that she never asked for it. Kim orders Cherie to get in the booth and sing and Lita continues insulting her. Though Joan defends her, Cherie angrily quits the band and leaves the studio. Joan is outraged, and the Runaways are finished. Cherie returns home while Joan starts her own band, Joan Jett and the Blackhearts. Cherie collapses again in a phone booth in an abandoned parking lot after attempting to buy cheap liquor for herself. At the hospital, her twin sister Marie Currie visits her and orders her to straighten herself up.


title: The Runaways (2010 film)

text: A few years later, Cherie is working in a local bakery and hears Joan's cover of "I Love Rock 'n' Roll" on the radio and calls the station, where Joan is visiting for an interview. After an awkward conversation between Joan, Cherie, and radio host Rodney Bingenheimer, Cherie says her goodbyes and continues working, smiling when Joan's next song, "Crimson and Clover", comes on the radio.


title: The Runaways (2010 film)

text: Music video director Floria Sigismondi made her feature film directorial debut with "The Runaways". She said that she established early in development that she "wanted to make it a coming-of-age story and not a biopic": "What I loved about the Runaways was that they were doing things that girls weren't supposed to do, especially at 15. [...] I wanted to capture what it was like to be super-young and thrown in this rock 'n' roll world at a time when girls are just trying to figure out their bodies and create their identities." She also "made it a very early decision that the story was going to be about Cherie [Currie] and Joan [Jett]. [...] And so that was a conscious effort, you know, to kind of really focus it and make it more personal on the two of them and their relationship."


title: The Runaways (2010 film)

text: Producers Art and John Linson had wanted a female director at the helm, with Art saying, “We felt from the beginning that this is really a tale of two young girls…[Cherie and Joan] getting in way over their heads in a world they knew very little about, a man’s world, and there’s a price to pay for that. We thought: It’s got to come from the heart of another woman.”


title: The Runaways (2010 film)

text: Jett was involved in the production as an executive producer, along with her manager Kenny Laguna. She said that "[she] felt confident with the level of success—the people at River Road, the Linsons [producers of the film]" and "knew [she] was in good hands" with Sigismondi writing and directing.


title: The Runaways (2010 film)

text: Sigismondi watched films from and set in the 1970s in developing the visual style of the film. "I wanted to keep it very raw, so I shot on Super-16 and kept it kind of smoky. The color palette was designed to be a little more California Valley [bright colors] in the beginning and tougher and harder-looking near the end, sort of void of color. Japan's looking sort of trippy and metallic, and when they come back everything looks a little bit different."


title: The Runaways (2010 film)

text: Actors portraying the band, including Dakota Fanning and Kristen Stewart, took vocal lessons and learned to play the instruments of their character counterparts. Fanning got on stage with the band Living Things as part of research for her role, saying, “I had never sung with a band before and felt the power of something like that behind me.”


title: The Runaways (2010 film)

text: The film also includes "Lady Grinning Soul" by David Bowie, "Fujiyama Mama" by Wanda Jackson, "Do You Wanna Touch Me" by Gary Glitter, "Gimme Danger" by Iggy and the Stooges, "Vincent" by Don McLean, "I Love Rock 'n' Roll", "Bad Reputation", "Crimson and Clover", "I Want You" and "Love Is Pain" by Joan Jett and the Blackhearts. Kristen Stewart covers the Runaways' "I Love Playin' With Fire" in the film. The film included 34 credited songs, leaving 20 out of the official soundtrack, and it did not have an official composer.


title: The Runaways (2010 film)

text: Apparition acquired distribution rights to "The Runaways" in December 2009. It was slated to open nationwide March 19, 2010, in 1,400 theaters. The film's world premiere took place on January 24, 2010, at the Sundance Film Festival. Jett performed live in Park City the evening before the premiere and premiere night. Its Hollywood premiere took place March 11 at the ArcLight Hollywood.


title: The Runaways (2010 film)

text: Cherie Currie praised Fanning for her performance in the film, but noted that a number of events included in her book were not included in the film. She said "this is [the filmmakers'] movie. This is their portrayal. This is their version of the story. My book is a totally different story. My book is the real story. This is just a lighter kind of flash of what The Runaways were for a specific amount of time. How do you possibly take two and a half years and make it a film that's an hour and a half, and make it even closely touch what was truly going on? It’s an epic. The true story is an epic, and that’s just not anything that could have been done on film."


title: The Runaways (2010 film)

text: Joan Jett felt that the film captured 1970s Los Angeles, "that music, that sort of combination of glam and intensity" well, but said "initially it was mischaracterized, because at first it was called a 'biopic', which implies that it's going to be a literal reading of the action. But to me, it's more of a parallel narrative of The Runaways. It's based on Cherie's book, so it definitely comes from her perspective and focuses more on probably the two of us and Kim."


title: The Runaways (2010 film)

text: "The Runaways" received generally positive reviews from critics. On review aggregator Rotten Tomatoes, the film has a 69% rating based on 193 reviews, and an average rating of 6.20/10. The site's critical consensus reads, "Viewers expecting an in-depth biopic will be disappointed, but "The Runaways" is as electric as the band's music, largely thanks to strong performances by Michael Shannon, Dakota Fanning and Kristen Stewart". On Metacritic, the film received an average score of 65 based on 36 reviews, indicating "Generally favorable reviews". The performances by Fanning, Stewart and Shannon were highlighted as some of the film's strongest elements.


title: The Runaways (2010 film)

text: Mick LaSalle of the "San Francisco Chronicle" noted that the film "doesn't always tell the literal truth" about the band, but felt that "[m]ore crucially, it conveys precisely what it was like to be young in the mid-1970s [...] And in getting that one thing right—in capturing that strange combination of despair and frustrated energy—it gets everything right." Roger Ebert gave "The Runaways" 3 stars out of 4, praising the performances of Shannon, Stewart and Fanning, while writing that the film's visuals and music "[helped] cover an underwritten script and many questions about the characters" which he found slimly developed. Dennis Harvey of "Variety" gave the film a positive review, commenting that it "proves [to be a] conventionally enjoyable making-and-breaking-of-the-band saga" and goes on to compliment the cinematography and soundtrack. A. O. Scott of "The New York Times" felt that Sigismondi "infuses crucial scenes with a rough, energetic spirit, and shows a willingness to accept the contradictions inherent in the material without prurience, moralism or too much sentimentality." Even if "The Runaways" "hits a few too many standard music biography beats" and "may be a little too tame in the end", he added, "at its best it is just wild enough."


title: The Runaways (2010 film)

text: Owen Gleiberman of "Entertainment Weekly" gave the film a B− and wrote that Sigismondi's "sixth sense for how the Runaways were bad-angel icons first and a rock 'n' roll band second" was the "most entertaining thing about" the film, which he described as a "highly watchable if mostly run-of-the-mill group biopic". Betsy Sharkey of the "Los Angeles Times" felt that the film, which she described as "a street-level snapshot" of the titular band's creation, should have featured Jett's story instead of staying "too narrowly focused" on that of Currie. David Edelstein of "New York" magazine gave the film a less positive review, commenting that "since the music itself is secondary, there's not a lot to this story," and adding "It’s Fanning's movie: You can taste the ex–child actor's relish for playing jailbait." "Time" praised the acting in the film, stating that Fanning "turns in a performance of startling maturity", "seduces us utterly" and is "like a mini-Meryl Streep". Nathan Rabin of "The A.V. Club" gave "The Runaways" a C, writing that the film is "numbingly familiar" and filled with "rock-movie clichés". He concluded, "The Runaways were the first major all-girl punk band. In honor of this distinction, they’re now the first major all-girl punk band to inspire a bleary, excessive, and altogether mediocre big-screen biography."


title: The Runaways (2010 film)

text: The film's opening weekend gross was $805,115—placing it at #18 at the box office—averaging $3,300 per theater, and most of its audience that weekend were 25 or older. Apparition changed their marketing strategy due to the company's sudden shut down and reduced their planned wide release of 1,400 theaters to less than 300. It left theaters June 3 with a domestic gross of $3,573,673. "Variety" reported that the film's underperformance at the box office could have been due to underfunded marketing and a failure to find an audience with either an age demographic that would remember the band or with fans of Stewart for her performance in "Twilight" (2008).


title: The Runaways (2010 film)

text: The DVD for Region 1 and Blu-ray for Region A was released by Sony Pictures Home Entertainment on July 20, 2010.


title: Animal Crossing (video game)

text: Animal Crossing, known in Japan as is a 2001 social simulation game developed and published by Nintendo for the GameCube. It is an enhanced version of the Nintendo 64 game which was only released in Japan earlier the same year, and was followed by another edition, in 2003.


title: Animal Crossing (video game)

text: "Animal Crossing" is an endless and non-linear game in which a human takes up residence in a village inhabited by anthropomorphic animals. The main goal of the game is to save money in order to pay off the mortgage on the human's house. This requires collecting natural materials and selling them. The human can engage in everyday life in the village, interact with the animals, attend events, and contribute to the village's development. The game's western localization differs significantly from the original release in that Japanese holidays and cultural references are replaced with Western ones.


title: Animal Crossing (video game)

text: The game was originally conceived as a role-playing adventure, with the main action taking place in dungeons. However, development was stalled by the failure of the 64DD peripheral. Reviewing the existing developments, designer Katsuya Eguchi decided to create a non-linear life simulator, which would carry the themes of family, friendship, and community as well as allow several players to develop a virtual town at different times. Eguchi also wanted to create a game that catered to a wider audience inclusive of those unfamiliar with video games.


title: Animal Crossing (video game)

text: "Animal Crossing" was a critical and commercial success domestically and internationally, attracting many non-traditional gaming audiences. Critics praised the game's unusual but immersive and addictive gameplay, which was devoid of purpose and stressful elements. Criticisms centered on its outdated graphics and simple art style. The game is considered one of the earliest examples of the casual game genre, and marked the beginning of a franchise of the same name, which saw further success in its sequels.


title: Animal Crossing (video game)

text: "Animal Crossing" is a social simulation game, dubbed a "communication game" by Nintendo. It is open-ended, and the player's character can live a separate life with very little set plot or mandatory tasks. Players assume the role of a new resident to the town. The gender and looks of the character depend on answers given to a cat named Rover, whom the player meets on the train the character takes to the town. There are also tasks that players can complete and goals they can achieve. The game is played in real-time, observing days, weeks, months and years using the GameCube's internal clock. Many real-life events and holidays span the year, including Independence Day, Halloween, the Harvest Festival (Thanksgiving), and Toy Day (Christmas). Other activities, such as fishing tournaments and early-morning fitness classes, occur on a regular schedule. When players stop playing, they can talk to their Gyroid, a creature next to their house, to save their progress. If the player turns off the game or resets the GameCube without saving first, a mole named Mr. Resetti appears in front of the player's house the next time they play to scold them for resetting; what they achieved during the previous unsaved game is lost, but everything else is kept.


title: Animal Crossing (video game)

text: One of the main goals of the game, given to the player during the game's opening cut scenes, is to increase the size of the player's character's house. This house is the repository for furniture and other items acquired during the course of the game. It can be customized in several ways, such as roof colour, furniture, music, wallpaper and flooring. These customisations are judged by the Happy Room Academy (HRA).


title: Animal Crossing (video game)

text: Tom Nook, a tanuki (raccoon dog) in the Japanese versions and a raccoon in the American and European versions, runs the local store. At the beginning of the game, he gives the player their first house with a mortgage of 19,800 Bells (the in-game currency). After paying the debt, part of which is done through a part-time job with Nook, the house is expanded, prompting another debt from Nook. The house is expanded several times during the course of the game. Players can sell virtually anything to Nook in exchange for Bells. As the player buys and sells items at Nook's store, it will gradually expand, offering a wider selection of products for purchase. Players can also visit locations such as the Able Sisters' clothing shop, where they can purchase or design new clothes; the Police Station, where they can obtain additional items from the Lost and Found; and the Museum, where they can donate fossils, paintings, fish and insects to put on display.


title: Animal Crossing (video game)

text: The village initially contains six villagers, and more villagers move in or out depending on the player's actions. There is a maximum of fifteen villagers living there at a time. All villagers are animals and each has a home that the player can visit. There are many possible interactions between the player and the villagers, including talking, trading items, completing tasks, writing letters, and, in "e+", buying medicine for when they get sick. Villagers interact with each other independent of player control.


title: Animal Crossing (video game)

text: Up to four players can take turns creating their own houses in a single village. They can each affect the village in their own ways, communicate with each other via the town board and mail, and share in the experiences of the village. Multiple players can take turns shipping items to each other via Tom Nook, using a system of codes. Multiplayer NES games are available.


title: Animal Crossing (video game)

text: The traveling system allows each player to visit other players' villages. This system requires an additional memory card with the game's data, and three blocks of memory to save travel data. Players can meet new villagers, shop at stores, drop items, and do almost anything else that they can do in their own town. Visitors have reduced privileges and do not receive the same services that they would in their own town. For example, another town's Tom Nook will not travel to paint a roof, which means players cannot buy paint in another town. After visiting another town, one of the villagers may move to the visited town. If the visited town has a full fifteen villagers, this will prompt someone from the visited town to move away. Depending upon how many memory cards a player or their friends own, there can be many other villages to see and different items to find. If a player interacts with a villager who has moved away from their village to the visited village, the villager will remember the player.


title: Animal Crossing (video game)

text: Game Boy Advance connectivity plays a role in "Animal Crossing", using a Nintendo GameCube – Game Boy Advance link cable. Each town has an island that can be accessed by plugging in a Game Boy Advance with a GameCube link cable. A character called Kapp'n ferries the player to the island for free. An exclusive animal roams the island, with whom the player can become friends. The island has an exclusive type of fruit: coconuts. The player can also decorate a small communal beach house and fish at the shores. On leaving, the player can download the island to a GBA and give fruit to the villager, who drops Bells; if the player returns to the island, they can pick up the money that has been dropped. Players can leave the islander tools to use, such as the shovel or net. Downloaded islands can be traded between GBAs, using a Game Boy Advance Link Cable.


title: Animal Crossing (video game)

text: The Game Boy Advance can be used when shopping at the Able Sisters. The pattern design tool can be downloaded to a Game Boy Advance, and the player can then upload designs made on a Game Boy Advance to the GameCube. This feature can be accessed by plugging in a Game Boy Advance with a GameCube Game Boy Advance Cable and talking to Mabel in the Able Sisters shop. The game is also compatible with the e-Reader; by visiting the Post Office while connected to the accessory via the Game Boy Advance link cable, players can scan "Animal Crossing" themed cards to receive new items, town tunes, or pattern designs.


title: Animal Crossing (video game)

text: Players can collect various Nintendo Entertainment System games in "Animal Crossing", which are playable via emulation. North American releases were packaged with a memory card that automatically gave the player two games upon creating a game file. Others are acquired in various ways, such as gifts from villagers, hidden on the island, or via special giveaways from Nintendo's website. The available NES games differ slightly between each release.


title: Animal Crossing (video game)

text: Four additional NES games are not obtainable in-game through normal means. In North America, two of these games, "Ice Climber" and "Mario Bros.", were released through the use of two e-Reader cards, which were not distributed in Europe or Japan. Japanese players received "Ice Climber" as a gift if they used a special service provided by Nintendo to transfer their save data from "Dōbutsu no Mori" to "Dōbutsu no Mori+"; this service has since been discontinued. "Super Mario Bros." was distributed in Japan as a "Famitsu" prize to "Dōbutsu no Mori+" players. "The Legend of Zelda" exists in the game's code, but is not accessible in-game. These four bonus games can be obtained using a cheat device in earlier GameCube releases, but were removed in "Dōbutsu no Mori e+".


title: Animal Crossing (video game)

text: The Advance Play feature allows players to link a Game Boy Advance to the GameCube and temporarily transfer the NES game to the handheld. This is not compatible with games that were originally produced for the Famicom Disk System, such as "Clu Clu Land D" and "The Legend of Zelda", or are larger than 192 KB, such as "Punch-Out!!" and "Wario's Woods", as they cannot fit into the GBA's RAM. All other games can be played via Advance Play, but multiplayer functionality is not supported and their graphics appear slightly squashed on the GBA's display due to its smaller vertical resolution.


title: Animal Crossing (video game)

text: An additional NES furniture item was intended to allow players to emulate other NES titles not included with the game by reading NES ROMs stored on the player's memory card. While the emulator remains accessible in the final game, no additional ROMs were ever distributed, leaving the feature ultimately unused. In 2018, an independent software developer managed to reverse engineer the emulation software and convert ROMs into a compatible format, allowing new NES games to be imported into the "Animal Crossing" emulator.


title: Animal Crossing (video game)

text: The game was developed by Nintendo EAD with an inexperienced team led by Katsuya Eguchi, Hisashi Nogami, and Super Mario co-creator Takashi Tezuka, most of whom had regrouped after the release of Yoshi’s Story in 1997. The 64DD peripheral served as an enabling technology platform for the conception and development of the game, with its real-time clock and floppy disk for writable mass storage. Due to 64DD's extended delays and cancellation, the game's development was moved to the Game Pak cartridge mediumthe only Game Pak containing a real-time clockplus a Controller Pak for saving progress. Kazumi Totaka served as the game's sound director. Kenta Nagata composed background music for the fields, Toru Minegishi for the indoor areas and Shinobu Tanaka for the events. The game was originally released as "Dōbutsu no Mori" (lit. "Animal Forest") on the Nintendo 64 in Japan in April 2001. It is the last game Nintendo released for the Nintendo 64, and third to last game released for the system in Japan.


title: Animal Crossing (video game)

text: The game was ported to the GameCube as "Dōbutsu no Mori+", released on December 14, 2001, in Japan, eight months after the original game. This version contains extra features that were originally left out of the Nintendo 64 version, and uses the GameCube's built-in clock. This led to the game's slogan, "the real life game that's playing, even when you're not". "Dōbutsu no Mori+" cost with 92,568 copies sold during its first week in Japan.


title: Animal Crossing (video game)

text: When Nintendo began localizing "Dōbutsu no Mori+" for release in North America as "Animal Crossing", the game underwent an immense translation project, which resulted in much more text than the Japanese version. Not only did thousands of lines of text have to be translated, but translators Nate Bihldorff and Rich Amtower had to create new holidays and items to be relatable outside of Japan. The translation process took six months total, which at the time was Nintendo of America's largest translation project to date. Nintendo's Japanese leadership was so impressed with the work done by Nintendo of America's Treehouse division that they added the American content back into the Japanese version and released it as "Dōbutsu no Mori e+" along with more new content. It was released in Japan on June 27, 2003, with 91,658 copies sold during its first week.


title: Animal Crossing (video game)

text: Upon its release, "Animal Crossing" was subject to critical acclaim. It was named the seventh best game of all time on the GameCube by the television show "X-Play" on the G4 network. On IGN, the game holds an "outstanding" 9.1 rating.


title: Animal Crossing (video game)

text: Some critics praised the game's use of the GameCube's internal clock and calendar and its inclusion of hidden NES games. However, others, such as IGN's Peer Schneider, criticized its audio and visuals, for being below-standard quality for a GameCube game. According to the review aggregator site Metacritic, the game received a score of 87 out of 100, indicating "generally favorable reviews" based on 42 critics. According to GameRankings, the game received a score of 86% based on 72 reviews. The game was a commercial success, at more than 2 million copies sold worldwide. By July 2006, 1.3 million copies had been sold, totaling $43 million in the United States. "Next Generation" ranked it as the 37th highest-selling game launched for the PlayStation 2, Xbox, or GameCube between January 2000 and July 2006 in that country. It is one of the best-selling Nintendo GameCube games. ScrewAttack rated it the fifth-best GameCube game on its "Farewell to the GameCube, ten GameCube games" list, saying, "It's a game that plays even when you're not and can last up to 30 years!" The popularity of the series inspired the creation of an animated film based on the game's sequel "Animal Crossing: Wild World", titled "Dōbutsu no Mori", which was released exclusively in Japan.


title: Animal Crossing (video game)

text: The Academy of Interactive Arts & Sciences awarded it the Innovation in Console Gaming, Outstanding Achievement in Game Design, Console Role-Playing Game of the Year and nominated it for Console Game of the Year, Console Role-Playing Game of the Year, Game of the Year, Innovation in Console Gaming, Outstanding Achievement in Game Design, and Outstanding Achievement in Gameplay Engineering. "GameSpot" named it the best GameCube game of September 2002, and gave the game its annual "Best Role-Playing Game on GameCube" award. It was a runner-up for "GameSpot"s 2002 "Game of the Year on GameCube" prize, but lost to "Metroid Prime". The game was ranked 126th in Electronic Gaming Monthly’s “The Greatest 200 Video Games of Their Time” in 2006. In 2021, The Strong National Museum of Play inducted "Animal Crossing" to its World Video Game Hall of Fame.


title: Euclidean vector

text: In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a "directed line segment", or graphically as an arrow connecting an "initial point" "A" with a "terminal point" "B", and denoted by formula_1 .


title: Euclidean vector

text: A vector is what is needed to "carry" the point "A" to the point "B"; the Latin word "vector" means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from "A" to "B". Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.


title: Euclidean vector

text: Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.


title: Euclidean vector

text: The vector concept, as we know it today, is the result of a gradual development over a period of more than 200 years. About a dozen people contributed significantly to its development. In 1835, Giusto Bellavitis abstracted the basic idea when he established the concept of equipollence. Working in a Euclidean plane, he made equipollent any pair of parallel line segments of the same length and orientation. Essentially, he realized an equivalence relation on the pairs of points (bipoints) in the plane, and thus erected the first space of vectors in the plane. The term "vector" was introduced by William Rowan Hamilton as part of a quaternion, which is a sum of a Real number (also called "scalar") and a 3-dimensional "vector". Like Bellavitis, Hamilton viewed vectors as representative of classes of equipollent directed segments. As complex numbers use an imaginary unit to complement the real line, Hamilton considered the vector to be the "imaginary part" of a quaternion:


title: Euclidean vector

text: Several other mathematicians developed vector-like systems in the middle of the nineteenth century, including Augustin Cauchy, Hermann Grassmann, August Möbius, Comte de Saint-Venant, and Matthew O'Brien. Grassmann's 1840 work "Theorie der Ebbe und Flut" (Theory of the Ebb and Flow) was the first system of spatial analysis that is similar to today's system, and had ideas corresponding to the cross product, scalar product and vector differentiation. Grassmann's work was largely neglected until the 1870s. Peter Guthrie Tait carried the quaternion standard after Hamilton. His 1867 "Elementary Treatise of Quaternions" included extensive treatment of the nabla or del operator ∇. In 1878, "Elements of Dynamic" was published by William Kingdon Clifford. Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product. This approach made vector calculations available to engineers—and others working in three dimensions and skeptical of the fourth.


title: Euclidean vector

text: Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwell's "Treatise on Electricity and Magnetism", separated off their vector part for independent treatment. The first half of Gibbs's "Elements of Vector Analysis", published in 1881, presents what is essentially the modern system of vector analysis. In 1901, Edwin Bidwell Wilson published "Vector Analysis", adapted from Gibb's lectures, which banished any mention of quaternions in the development of vector calculus.


title: Euclidean vector

text: In physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. It is formally defined as a directed line segment, or arrow, in a Euclidean space. In pure mathematics, a vector is defined more generally as any element of a vector space. In this context, vectors are abstract entities which may or may not be characterized by a magnitude and a direction. This generalized definition implies that the above-mentioned geometric entities are a special kind of vectors, as they are elements of a special kind of vector space called Euclidean space. This particular article is about vectors strictly defined as arrows in Euclidean space. When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.


title: Euclidean vector

text: Being an arrow, a Euclidean vector possesses a definite "initial point" and "terminal point". A vector with fixed initial and terminal point is called a bound vector. When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector. Thus two arrows formula_2 and formula_3 in space represent the same free vector if they have the same magnitude and direction: that is, they are equipollent if the quadrilateral "ABB′A′" is a parallelogram. If the Euclidean space is equipped with a choice of origin, then a free vector is equivalent to the bound vector of the same magnitude and direction whose initial point is the origin. The term "vector" also has generalizations to higher dimensions, and to more formal approaches with much wider applications.


title: Euclidean vector

text: In classical Euclidean geometry (i.e., synthetic geometry), vectors were introduced (during the 19th century) as equivalence classes under equipollence, of ordered pairs of points; two pairs and being equipollent if the points , in this order, form a parallelogram. Such an equivalence class is called a "vector", more precisely, a Euclidean vector. The equivalence class of is often denoted formula_4


title: Euclidean vector

text: A Euclidean vector is thus an equivalence class of directed segments with the same magnitude (e.g., the length of the line segment ) and same direction (e.g., the direction from to ). In physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are not located at a specific place, in contrast to scalars, which have no direction. For example, velocity, forces and acceleration are represented by vectors.


title: Euclidean vector

text: In modern geometry, Euclidean spaces are often defined from linear algebra. More precisely, a Euclidean space is defined as a set to which is associated an inner product space of finite dimension over the reals formula_5 and a group action of the additive group of formula_5 which is free and transitive (See Affine space for details of this construction). The elements of formula_7 are called translations. It has been proven that the two definitions of Euclidean spaces are equivalent, and that the equivalence classes under equipollence may be identified with translations.


title: Euclidean vector

text: Sometimes, Euclidean vectors are considered without reference to a Euclidean space. In this case, a Euclidean vector is an element of a normed vector space of finite dimension over the reals, or, typically, an element of formula_8 equipped with the dot product. This makes sense, as the addition in such a vector space acts freely and transitively on the vector space itself. That is, formula_8 is a Euclidean space, with itself as an associated vector space, and the dot product as an inner product.


title: Euclidean vector

text: The Euclidean space formula_8 is often presented as "the" Euclidean space of dimension . This is motivated by the fact that every Euclidean space of dimension is isomorphic to the Euclidean space formula_11 More precisely, given such a Euclidean space, one may choose any point as an origin. By Gram–Schmidt process, one may also find an orthonormal basis of the associated vector space (a basis such that the inner product of two basis vectors is 0 if they are different and 1 if they are equal). This defines Cartesian coordinates of any point of the space, as the coordinates on this basis of the vector formula_12 These choices define an isomorphism of the given Euclidean space onto formula_13 by mapping any point to the -tuple of its Cartesian coordinates, and every vector to its coordinate vector.


title: Euclidean vector

text: Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector. As an example, consider a rightward force "F" of 15 newtons. If the positive axis is also directed rightward, then "F" is represented by the vector 15 N, and if positive points leftward, then the vector for "F" is −15 N. In either case, the magnitude of the vector is 15 N. Likewise, the vector representation of a displacement Δ"s" of 4 meters would be 4 m or −4 m, depending on its direction, and its magnitude would be 4 m regardless.


title: Euclidean vector

text: Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. An example is velocity, the magnitude of which is speed. For instance, the velocity "5 meters per second upward" could be represented by the vector (0, 5) (in 2 dimensions with the positive "y"-axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction and follows the rules of vector addition. Vectors also describe many other physical quantities, such as linear displacement, displacement, linear acceleration, angular acceleration, linear momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field. Examples of quantities that have magnitude and direction, but fail to follow the rules of vector addition, are angular displacement and electric current. Consequently, these are not vectors.


title: Euclidean vector

text: In the Cartesian coordinate system, a bound vector can be represented by identifying the coordinates of its initial and terminal point. For instance, the points and in space determine the bound vector formula_1 pointing from the point on the "x"-axis to the point on the "y"-axis.


title: Euclidean vector

text: In Cartesian coordinates, a free vector may be thought of in terms of a corresponding bound vector, in this sense, whose initial point has the coordinates of the origin . It is then determined by the coordinates of that bound vector's terminal point. Thus the free vector represented by (1, 0, 0) is a vector of unit length—pointing along the direction of the positive "x"-axis.


title: Euclidean vector

text: This coordinate representation of free vectors allows their algebraic features to be expressed in a convenient numerical fashion. For example, the sum of the two (free) vectors (1, 2, 3) and (−2, 0, 4) is the (free) vector


title: Euclidean vector

text: In the geometrical and physical settings, it is sometimes possible to associate, in a natural way, a "length" or magnitude and a direction to vectors. In addition, the notion of direction is strictly associated with the notion of an "angle" between two vectors. If the dot product of two vectors is defined—a scalar-valued product of two vectors—then it is also possible to define a length; the dot product gives a convenient algebraic characterization of both angle (a function of the dot product between any two non-zero vectors) and length (the square root of the dot product of a vector by itself). In three dimensions, it is further possible to define the cross product, which supplies an algebraic characterization of the area and orientation in space of the parallelogram defined by two vectors (used as sides of the parallelogram). In any dimension (and, in particular, higher dimensions), it's possible to define the exterior product, which (among other things) supplies an algebraic characterization of the area and orientation in space of the "n"-dimensional parallelotope defined by "n" vectors.


title: Euclidean vector

text: In a pseudo-Euclidean space, a vector's squared length can be positive, negative, or zero. An important example is Minkowski space (which is important to our understanding of special relativity).


title: Euclidean vector

text: However, it is not always possible or desirable to define the length of a vector. This more general type of spatial vector is the subject of vector spaces (for free vectors) and affine spaces (for bound vectors, as each represented by an ordered pair of "points"). One physical example comes from thermodynamics, where many quantities of interest can be considered vectors in a space with no notion of length or angle.


title: Euclidean vector

text: In physics, as well as mathematics, a vector is often identified with a tuple of components, or list of numbers, that act as scalar coefficients for a set of basis vectors. When the basis is transformed, for example by rotation or stretching, then the components of any vector in terms of that basis also transform in an opposite sense. The vector itself has not changed, but the basis has, so the components of the vector must change to compensate. The vector is called "covariant" or "contravariant", depending on how the transformation of the vector's components is related to the transformation of the basis. In general, contravariant vectors are "regular vectors" with units of distance (such as a displacement), or distance times some other unit (such as velocity or acceleration); covariant vectors, on the other hand, have units of one-over-distance such as gradient. If you change units (a special case of a change of basis) from meters to millimeters, a scale factor of 1/1000, a displacement of 1 m becomes 1000 mm—a contravariant change in numerical value. In contrast, a gradient of 1 K/m becomes 0.001 K/mm—a covariant change in value (for more, see covariance and contravariance of vectors). Tensors are another type of quantity that behave in this way; a vector is one type of tensor.


title: Euclidean vector

text: In pure mathematics, a vector is any element of a vector space over some field and is often represented as a coordinate vector. The vectors described in this article are a very special case of this general definition, because they are contravariant with respect to the ambient space. Contravariance captures the physical intuition behind the idea that a vector has "magnitude and direction".


title: Euclidean vector

text: Vectors are usually denoted in lowercase boldface, as in formula_16, formula_17 and formula_18, or in lowercase italic boldface, as in a. (Uppercase letters are typically used to represent matrices.) Other conventions include formula_19 or "a", especially in handwriting. Alternatively, some use a tilde (~) or a wavy underline drawn beneath the symbol, e.g. formula_20, which is a convention for indicating boldface type. If the vector represents a directed distance or displacement from a point "A" to a point "B" (see figure), it can also be denoted as formula_21 or "AB". In German literature, it was especially common to represent vectors with small fraktur letters such as formula_22.


title: Euclidean vector

text: Vectors are usually shown in graphs or other diagrams as arrows (directed line segments), as illustrated in the figure. Here, the point "A" is called the "origin", "tail", "base", or "initial point", and the point "B" is called the "head", "tip", "endpoint", "terminal point" or "final point". The length of the arrow is proportional to the vector's magnitude, while the direction in which the arrow points indicates the vector's direction.


title: Euclidean vector

text: On a two-dimensional diagram, a vector perpendicular to the plane of the diagram is sometimes desired. These vectors are commonly shown as small circles. A circle with a dot at its centre (Unicode U+2299 ⊙) indicates a vector pointing out of the front of the diagram, toward the viewer. A circle with a cross inscribed in it (Unicode U+2297 ⊗) indicates a vector pointing into and behind the diagram. These can be thought of as viewing the tip of an arrow head on and viewing the flights of an arrow from the back.


title: Euclidean vector

text: In order to calculate with vectors, the graphical representation may be too cumbersome. Vectors in an "n"-dimensional Euclidean space can be represented as coordinate vectors in a Cartesian coordinate system. The endpoint of a vector can be identified with an ordered list of "n" real numbers ("n"-tuple). These numbers are the coordinates of the endpoint of the vector, with respect to a given Cartesian coordinate system, and are typically called the scalar components (or scalar projections) of the vector on the axes of the coordinate system.


title: Euclidean vector

text: As an example in two dimensions (see figure), the vector from the origin "O" = (0, 0) to the point "A" = (2, 3) is simply written as


title: Euclidean vector

text: The notion that the tail of the vector coincides with the origin is implicit and easily understood. Thus, the more explicit notation formula_24 is usually deemed not necessary (and is indeed rarely used).


title: Euclidean vector

text: In "three dimensional" Euclidean space (or ), vectors are identified with triples of scalar components:


title: Euclidean vector

text: These numbers are often arranged into a column vector or row vector, particularly when dealing with matrices, as follows:


title: Euclidean vector

text: Another way to represent a vector in "n"-dimensions is to introduce the standard basis vectors. For instance, in three dimensions, there are three of them:


title: Euclidean vector

text: These have the intuitive interpretation as vectors of unit length pointing up the "x"-, "y"-, and "z"-axis of a Cartesian coordinate system, respectively. In terms of these, any vector a in can be expressed in the form:


title: Euclidean vector

text: where a, a, a are called the vector components (or vector projections) of a on the basis vectors or, equivalently, on the corresponding Cartesian axes "x", "y", and "z" (see figure), while "a", "a", "a" are the respective scalar components (or scalar projections).


title: Euclidean vector

text: In introductory physics textbooks, the standard basis vectors are often denoted formula_32 instead (or formula_33, in which the hat symbol ^ typically denotes unit vectors). In this case, the scalar and vector components are denoted respectively "a", "a", "a", and a, a, a (note the difference in boldface). Thus,


title: Euclidean vector

text: The notation e is compatible with the index notation and the summation convention commonly used in higher level mathematics, physics, and engineering.


title: Euclidean vector

text: As explained above, a vector is often described by a set of vector components that add up to form the given vector. Typically, these components are the projections of the vector on a set of mutually perpendicular reference axes (basis vectors). The vector is said to be "decomposed" or "resolved with respect to" that set.


title: Euclidean vector

text: The decomposition or resolution of a vector into components is not unique, because it depends on the choice of the axes on which the vector is projected.


title: Euclidean vector

text: Moreover, the use of Cartesian unit vectors such as formula_33 as a basis in which to represent a vector is not mandated. Vectors can also be expressed in terms of an arbitrary basis, including the unit vectors of a cylindrical coordinate system (formula_36) or spherical coordinate system (formula_37). The latter two choices are more convenient for solving problems which possess cylindrical or spherical symmetry, respectively.


title: Euclidean vector

text: The choice of a basis does not affect the properties of a vector or its behaviour under transformations.


title: Euclidean vector

text: A vector can also be broken up with respect to "non-fixed" basis vectors that change their orientation as a function of time or space. For example, a vector in three-dimensional space can be decomposed with respect to two axes, respectively "normal", and "tangent" to a surface (see figure). Moreover, the "radial" and "tangential components" of a vector relate to the "radius of rotation" of an object. The former is parallel to the radius and the latter is orthogonal to it.


title: Euclidean vector

text: In these cases, each of the components may be in turn decomposed with respect to a fixed coordinate system or basis set (e.g., a "global" coordinate system, or inertial reference frame).


title: Euclidean vector

text: Two vectors are said to be equal if they have the same magnitude and direction. Equivalently they will be equal if their coordinates are equal. So two vectors


title: Euclidean vector

text: Two vectors are parallel if they have the same direction but not necessarily the same magnitude, or antiparallel if they have opposite direction but not necessarily the same magnitude.


title: Euclidean vector

text: The addition may be represented graphically by placing the tail of the arrow b at the head of the arrow a, and then drawing an arrow from the tail of a to the head of b. The new arrow drawn represents the vector a + b, as illustrated below:


title: Euclidean vector

text: This addition method is sometimes called the "parallelogram rule" because a and b form the sides of a parallelogram and a + b is one of the diagonals. If a and b are bound vectors that have the same base point, this point will also be the base point of a + b. One can check geometrically that a + b = b + a and (a + b) + c = a + (b + c).


title: Euclidean vector

text: Subtraction of two vectors can be geometrically illustrated as follows: to subtract b from a, place the tails of a and b at the same point, and then draw an arrow from the head of b to the head of a. This new arrow represents the vector (-b) + a, with (-b) being the opposite of b, see drawing. And (-b) + a = a − b.