title: Knots Landing

text: While trying to find Valene, Gary sees the car she was in explode. Greg decides to retire from the Sumner Group, and he leaves one third of the company to Claudia, a third to Paige, and the other third to Mack and Karen in a trust for Meg. Anne reveals she is pregnant, leading to Greg marrying her, but she discovers she suffered a "hysterical pregnancy". Meanwhile, Anne's old beau Nick returns and the two rekindle their affair and their old conniving ways. Mack seeks $1 million to get Mary Robeson to stop the custody battle over Meg. Claudia gives Mack $500,000 from the Sumner Group, and gives the other half to Nick to start a restaurant. Paige demanded an audit, but Claudia cannot get the money from Nick back because he already spent it. Karen condemns Mack's handling of Mary Robeson's efforts to win custody of Meg. She leaves him and goes to New York to stay with her daughter Diana. A shady organization run by Daniel Treadwell (Daniel Gerroll) begins terrorizing everybody with its sights set on the Sumner Group. Gary starts a relationship with Kate. In the series finale, Karen returns to Mack, and the presumed dead Valene returns, revealing she had faked her death to hide from Treadwell's people, who had threatened to harm her for coming across secretive information. Treadwell's mysterious partner is revealed to be Abby, who has been orchestrating the takeover of the Sumner Group all along. However, Greg stops Abby by threatening to reveal her dirty dealings while she was in Japan. As Treadwell prepares to kill Nick, who was working for him, Treadwell himself was killed by Vanessa Hunt (Felicity Waterman). Anne offers to divorce Greg so he can resume his relationship with her daughter Paige, whom he loves. Claudia decides to leave Knots Landing for Monaco, and at the airport, she runs into Anne and Nick, who are also leaving town. In the final scenes, back at Seaview Circle, Karen, Mack, Valene, and Gary prepare a barbecue as a new couple begin moving into Frank Williams' old home. Meanwhile, Abby arrives at the gathering and reveals that she has just purchased her old house in Seaview Circle. Valene simply smiles and welcomes Abby back, before she and Gary go home. In the final shot, Abby is left face-to-face with Karen and comments "Just like old times, isn't it?"


title: Knots Landing

text: Throughout the show's fourteen seasons, there were a wide array of actors in supporting roles. The most notable of these include:


title: Knots Landing

text: Between seasons 1 and 4 of "Knots Landing", there were nine episodes where "Dallas" characters appeared, played by their respective actors.


title: Knots Landing

text: In addition to the above, the characters of Gary and Valene Ewing appeared in the following episodes of "Dallas", as listed below.


title: Knots Landing

text: On "Dallas", the character of Bobby Ewing (Patrick Duffy) was killed off in the final episode of the 1984–85 season. The following year, Duffy decided to return to "Dallas" and the character of Bobby was resurrected in the infamous "shower scene" at the end of the 1985–86 season. At the start of the 1986–87 season, it was revealed that Bobby's death and all but the final scene of the 1985–86 season had been a dream of Bobby's ex-wife, Pamela Barnes Ewing (Victoria Principal).


title: Knots Landing

text: On "Knots Landing" during the 1985–86 season, Bobby's death had an indelible impact on some of the characters (i.e. Gary struggling to deal with his brother's death and being comforted by his wife Abby, Abby and Greg then taking advantage of Gary's absence to control development of Empire Valley, and Valene naming her baby son after the late Bobby). When Bobby's death and the subsequent season were revealed to be a dream on "Dallas", this did not get applied to the continuity of "Knots Landing" and Bobby's return was simply never addressed or even mentioned. Following this, no further crossover storylines were featured on "Knots Landing".


title: Knots Landing

text: With the 2012 continuation of "Dallas", rumors began surfacing that both Joan Van Ark and Ted Shackelford would reprise their roles as Valene and Gary Ewing on the new series. Shackelford passed on the small role the producers offered him during the first season, but accepted a multi-episode role during the second. Shackelford returned to "Dallas" for three episodes and Van Ark returned for one. This was the first time the characters had been seen since the 1997 miniseries "". Although both Shackelford and Van Ark appeared in the 1991 series finale of "Dallas" playing "alternative" versions of Gary and Valene (the episode depicted an alternate reality in which J. R. Ewing had never been born), there have been no real crossovers of story or characters from "Knots Landing" to "Dallas" or vice versa since the 1985–86 season of each show (which, on "Dallas", turned out to be a dream had by Pam Ewing). In the 2013 "Dallas" storyline, it is made clear that Gary and Val had still been living together at their home in California, though had recently separated due to Gary's brief relapse into alcoholism due to financial worries. At the end of their appearances on the new series of "Dallas", Gary and Val return to California together.


title: Knots Landing

text: "Knots Landing" was created by David Jacobs, whose original concept was a show based on "family issues and examining relationships at the middle class level". CBS initially turned down this idea, as they wanted something more "glitzy" to put on the air, with wealthier characters, which would become "Dallas". Once that show became a success after the initial run as a five-episode miniseries, the producers decided to expand the roles of certain characters. They introduced Lucy Ewing’s (Charlene Tilton) parents, who had not been shown on-screen until that point, in the two-part episode "The Reunion". After the success of "Dallas", Jacobs presented his initial idea again and created "Knots Landing", with some alterations of his original script. In an interview, Jacobs explained: " Well, that's pretty good, but you know-and then he pulled out the pages that we'd left for them a few years ago on "Knots Landing", or a year before on "Knots", and he said, 'Is there any way we can make this a spin-off?' I just took one of the couples and made it, you know, Val and Gary who had already been created on the parent series and putting them into the mix, but when you have four couples and you change one, you sort of have to change the dynamic all the way around. However, once I wrote the script, remarkably little changed from the script and the pilot as you would see it."


title: Knots Landing

text: Gary Ewing was originally played by David Ackroyd on "Dallas", but Ackroyd was unable to sign on for "Knots Landing", and Ted Shackelford assumed the role. Joan Van Ark continued to play Val Ewing for the spin-off. Initially, it was presumed that Tilton would also be joining "Knots Landing" (and have Lucy move in with her parents to the Seaview Circle cul-de-sac), but the network decided to keep her on "Dallas" in order to keep the two shows separate. She did, however, make a guest appearance in the first-season episode "Home is for Healing".


title: Knots Landing

text: The actors on "Knots Landing" had more input than actors on other 1980s primetime soaps. In 1987, the writers wanted Mack (Kevin Dobson) to have an extramarital affair with Anne (Michelle Phillips). Michele Lee, who played Mack's wife Karen, protested this to Jacobs, saying, "There has to be one stable couple on the show." The extramarital affair storyline was nixed, and Michelle Phillips, who had been signed to a contract, was written out for a couple of seasons before returning in 1990. When she did return, Anne did not pursue Mack. William Devane, who played Greg Sumner, re-wrote most of his character's dialogue, to the point where, in co-star Michele Lee's words, "most people (on set) were (probably) frightened of him". The Gary/Val/Abby triangle that provided story throughout the mid-1980s was suggested by Ted Shackelford and Joan Van Ark in 1980, and the producers hesitated for a year and a half before going through with it in 1982. The famous 1984 storyline where Valene's babies got kidnapped was originally envisioned as one of scheming Abby's plots. Donna Mills, who played Abby, acknowledged that her character was evil but did not think she was "that" evil. Fearing the audience would never forgive her character for kidnapping another woman's babies, she asked the writers to make the kidnappings a result of Abby's actions, but only by accident, and the writers complied. Bruce Campbell, who appeared in a 1987 episode, would later marvel at "the "speed" and clinical precision" of the production as opposed to the low-budget films and television series he had acted in up until this point. In particular, he wrote that Michele Lee "ran the set like a drill seargent and laid out all the blocking."


title: Knots Landing

text: The writing team of Bernard Lechowick and Lynn Marie Latham (the head writers from 1986 to 1991) was controversial among both fans and actors. Their humor-imbued style of writing made them the favorites of Michele Lee, while John Pleshette felt they were "awful people." Pleshette, however, was not a regular cast member during their tenure (only making a guest appearance in 1987), and harbored resentment because the writing team, who had been represented by his wife, moved to a different agency. Joan van Ark, whose character was struck by a brain illness in season 12 and proceeded to thereafter go crazy, felt that Latham and Lechowick had turned her character into the "village idiot." Joan Van Ark's and Donna Mills' favorite "Knots Landing" writer was Peter Dunne, who was responsible for making "Knots Landing" a top ten show in 1984.


title: Knots Landing

text: In 1987, CBS demanded that production costs be cut. This meant the firing of two regulars, Constance McCashin and Julie Harris. Season 13 saw a large ratings drop for the show after writer/producers Bernard Lechowick and Lynn Marie Latham left to create "Homefront" and creator David Jacobs had a health crisis and pulled back his involvement in production. Jacobs has publicly stated that the way he knew the show was in trouble was when waitresses at his favorite diner, whom he had heard gossiping about "Knots Landing" every Friday during past seasons, suddenly stopped discussing the show in late 1991. He attempted to save face by shutting down production on November 20, 1991, firing head writer John Romano, and replacing him with Ann Marcus. Cost cutting again plagued the series in its final season, when only 19 episodes were produced, and (with the exception of Michele Lee) regular cast members did not appear in every episode. Not wanting to compromise what he felt had been a good run, series creator David Jacobs described its end as a "mutual decision" between "Knots Landing" producers and the CBS Network, saying, "We don't know if they would have picked us up anyway...but even if they had, we would have had to pare away more to survive."


title: Knots Landing

text: The series' signature cul-de-sac, Seaview Circle, was actually Crystalaire Place in Granada Hills, California, a suburban street in Los Angeles' San Fernando Valley about 20 miles north of the Pacific Ocean. The opening credits during the first two seasons were edited in such a way to make it appear that the cul-de-sac was closer to the beach. The aerial shots as seen in the opening and end credits from 1981 to 1987, were filmed at Palos Verdes Estates, an affluent coastal area of Los Angeles.


title: Knots Landing

text: The theme song, which lasted all 14 seasons was composed by Jerrold Immel. Immel, along with Craig Huxley composed the background music for the pilot. The original background music cues by Immel and Huxley were never fully abandoned by the show, and were heard right through until the final season. The early Knots Landing background music cues heavily emphasized the brass section, and were often played with a very sparse bass line accompaniment. It was the only aspect of the series ever to win an Emmy award, for the music orchestration during its 1979–80 season.


title: Knots Landing

text: By the debut of the fourth season in 1982 the lushness of the 1980s was in full swing and background cues were changed to reflect that style. The new dramatic cues emphasized full orchestral arrangements as formerly middle-class Knots Landing became upwardly mobile. The background music of seasons 4–7 was frequently composed by either Lance Rubin or Ron Grant.


title: Knots Landing

text: Season 8 in 1986 introduced a completely new score for the show. New wave artists and bands had taken America by storm and the new style of music cues made good use of the synthesizer instead of a full orchestra. Bruce Miller was one of the main composers during this era. Updated orchestrations of the by-then familiar Lance Rubin cues were also re-arranged to be played by the synthesizer, and the Immel/Huxley cues were similarly utilized, albeit less commonly.


title: Knots Landing

text: In the early 1990s, soft contemporary acoustic music became popular and "Knots Landing" began incorporating this into its background music during season 12. Lance Rubin's music cues were mostly phased out at this point. Patrick Gleeson and Kennard Ramsey composed during this period.


title: Knots Landing

text: Though not as popular in the ratings as its parent series, "Knots Landing" eventually outlasted it and garnered much critical acclaim. The series peaked during the 1983–84 season with a 20.8 rating (when it finished in 11th place) and a 20.0 rating for the 1984–85 season (finishing 9th). This can be attributed, in part, to more dramatic storylines as the series became more soap opera-like, and the gradual inclusion of newer characters to interact with the original cast. By the 1988–89 season, "Knots Landing" was ahead of "Dallas" in the ratings, though audiences for both shows by this time were less than their earlier years. "Knots Landing" ended in 1993, two years after "Dallas" ended.


title: Knots Landing

text: Reruns of "Knots Landing" were first packaged into syndication for off-network broadcast in local markets by Lorimar in 1985. Before the show opening, each episode was preceded by a "Lorimar Presents" logo, followed by a narrated recap of the previous episode with the theme music played under. The first 190 episodes (the first eight seasons) were packaged in this manner, but only the first 160 episodes (the first seven seasons) were syndicated to local stations.


title: Knots Landing

text: "Knots Landing" later appeared on the cable channel TNT in September 1992 and ran through May 1993; as with the syndicated run, only the first 160 episodes (the first seven seasons) were broadcast. TNT would later become the first network to broadcast all 344 episodes of "Knots Landing" during its second syndication run of the series beginning in 1995.


title: Knots Landing

text: SOAPnet later acquired the rights to the series when it first went on the air in January 2000. "Knots Landing" has not been seen in United States syndication since SOAPnet quit broadcasting it in 2005.


title: Knots Landing

text: The UK satellite channel CBS Drama began airing the series in its entirety starting from April 1, 2013. This was the first time the show had been rerun in the UK since the early 2000s when it was shown on UK Gold. Once CBS Drama completed the series in July 2014, the channel immediately began a second round of reruns, followed by a third in 2015.


title: Knots Landing

text: RTÉ television in Ireland broadcast the first seven seasons in an early morning weekend slot in 2011.


title: Knots Landing

text: The first season of "Knots Landing" was released on DVD on March 28, 2006, in Region 1. Fans of the series lobbied Warner Home Video via an online petition at www.knotslanding.net for further releases, and Warner Home Video released season two on April 14, 2009. No further seasons have yet been announced for release.


title: Knots Landing

text: In the 2005 , the cast along with creator David Jacobs, said that the lasting legacy of the show was their dealings with many of the issues real middle-class people were having. While its parent show "Dallas" was a show about the rich upper class, "Knots Landing" had this aspect as well but was much more about the struggles of parenting, drug addictions, spousal issues and many of the evolving problems in the 1980s and early '90s. The reunion special showed such subjects as: women's power in the workforce, the HIV/AIDS crisis and the matter of safe sex, the cocaine epidemic in the 1980s, and the ever-growing spread of crime in America (Michele Lee's character Karen alluded to this in a famous speech about not feeling safe and being happy being a Pollyanna).


title: Knots Landing

text: Screenwriter Alan Ball declared the show had been an inspiration to him when he created the hit series "Six Feet Under," describing his show as ""Knots Landing" set in a funeral home".


title: Knots Landing

text: Screenwriter Marc Cherry also confirmed the show was an inspiration to him when he created the hit series "Desperate Housewives", describing it as a cross between "Knots Landing", "American Beauty" and "Twin Peaks".


title: Knots Landing

text: When asked which character from film and TV history he wished he had created, Mike Kelley, the creator of ABC's popular prime time soap opera "Revenge", said: "Abby Ewing. Donna Mills, you rocked my world."


title: Wake Me Up When September Ends

text: "Wake Me Up When September Ends" is a song by American rock band Green Day, released on June 13, 2005, as the fourth single from the group's seventh studio album, "American Idiot" (2004). The acoustic ballad was written by frontman Billie Joe Armstrong about the death of his father when he was 10 years old.


title: Wake Me Up When September Ends

text: The song became a hit single, peaking at number six on the US "Billboard" Hot 100. It was also a top-10 single in the United Kingdom, Belgium, and New Zealand and was a number-one single in the Czech Republic. In the United States, the song became symbolic after Hurricane Katrina, where it was dedicated to victims of the disaster, and also regarded as a dedication to the victims of the September 11 attacks that occurred in 2001. The song was certified platinum by the Recording Industry Association of America.


title: Wake Me Up When September Ends

text: The song's music video depicts a couple broken apart by the Iraq War, which was intended to convey the song's central theme of loss.


title: Wake Me Up When September Ends

text: "Wake Me Up When September Ends" was written by frontman Billie Joe Armstrong about his father, who died from esophageal cancer when Armstrong was 10 years old. Armstrong at one point dubbed the song the most autobiographical he had written to that point, considering it "therapeutic" but also difficult to perform.


title: Wake Me Up When September Ends

text: The song is notable in that it is largely unrelated to the storyline that runs throughout the rest of the album.


title: Wake Me Up When September Ends

text: The single peaked at number six in the United States, becoming Green Day's second top-10 single. It also peaked at number eight in Canada and the UK, while reaching number 13 in Australia. The song was certified Gold in the United Kingdom for sales of 400,000. The song ended the streak of Green Day's three consecutive number-one hits on the Modern Rock Tracks chart ("American Idiot", "Boulevard of Broken Dreams", and "Holiday"), but it peaked at number two on the chart, kept from number one by Gorillaz' "Feel Good Inc." The song also made it to number two on the Adult Top 40 chart and the Mainstream Top 40 chart. This was the band's most successful song in the adult contemporary market, hitting number three on the Adult Contemporary Chart and their only song to appear on that specific chart other than "Boulevard of Broken Dreams".


title: Wake Me Up When September Ends

text: Rob Sheffield of "Rolling Stone" deemed the song a sequel to the group's 1997 single "Good Riddance (Time of Your Life)".


title: Wake Me Up When September Ends

text: The song's music video was directed by Samuel Bayer, best known for his work with Nirvana and Metallica. Bayer wrote the treatment for the video, which he envisioned as a mini-movie. Bayer brought the idea of an Iraq War-themed video to the trio after interviewing soldiers who had signed up to fight after being persuaded by a television advertisement. The song's music video thus attempts to "turn the machine on itself" by acting as a commercial for "free thought or peace." Although it was far from the song's literal meaning, Armstrong felt it appropriate considering the song's theme of loss. Bayer noted that he felt bored with predictable music videos, and wanted to produce a video that felt like a film. Consequently, he and a crew spent a month casting actors for the roles and conducted rehearsals, uncommon for music videos. The clip was filmed in Los Angeles in late March 2005.


title: Wake Me Up When September Ends

text: The video focuses on a couple in love (played by Jamie Bell and Evan Rachel Wood). The boyfriend promises never to leave his girlfriend but they later argue when the boyfriend enlists in the United States Marine Corps. The boyfriend interprets his actions as a way to show her that he loves her so much that he would put his life on the line to keep her safe. However, the girlfriend is heartbroken, as he broke his vow to never leave her. The video then shows the boyfriend in battle in Iraq being ambushed by insurgents. Despite the Marines fighting back, the boyfriend watches as several of his comrades fall to the ground wounded. Their fate—and his—is left unknown. This scene is intercut with scenes of the girlfriend tearfully mourning in a quiet field. The video ends on this juxtaposition, emphasizing the pain and heartache of losing loved ones due to the war.


title: Wake Me Up When September Ends

text: The clip prompted criticism from conservative media pundits. On the subject of the clip being seen as exploitive of the war for entertainment purposes, Green Day's Mike Dirnt rejected this notion: "Rock & roll "should" be dangerous. […] It should be striking and stir questions, and I think that that video, at the end of the day, comes down to that core emotion of loss." Bayer considered it his best production to that point, remarking, "'September' is hands down the greatest thing I've ever done."


title: Wake Me Up When September Ends

text: The video reached number one on "Total Request Live", and came in second for best video of the year in a 2005 Reader's Poll by "Rolling Stone".


title: Wake Me Up When September Ends

text: "Wake Me Up When September Ends" became closely associated with Hurricane Katrina, which struck the Gulf Coast of the United States on August 29, 2005, three days before the start of September. "Wake Me Up When September Ends" became symbolic in the aftermath; one blogger paired the song with television coverage of the disaster, creating a viral video. Green Day performed the song days after the disaster on "", a benefit concert broadcast on MTV and its associated properties.


title: Wake Me Up When September Ends

text: A live version of the song, recorded on September 3, 2005, at Gillette Stadium in Foxborough, Massachusetts, was released soon after and dedicated to the hurricane's victims.


title: Wake Me Up When September Ends

text: The song was performed live with U2 guitarist The Edge in the pregame show of the Monday Night Football game between the New Orleans Saints and the Atlanta Falcons; it was the first game played in the Superdome in New Orleans after the hurricane.


title: Wake Me Up When September Ends

text: Internet memes have circulated on social media between the dates of September 30 and October 1, featuring captions ordering Armstrong to wake up because September has ended, a literal interpretation of the song's title. Armstrong has expressed his displeasure with the memes and has joked about wanting to write a sequel song in response called "Shut the Fuck Up When October Begins".


title: Latrell Sprewell

text: Latrell Fontaine Sprewell (born September 8, 1970) is an American former professional basketball player who played for the Golden State Warriors, the New York Knicks, and the Minnesota Timberwolves in the National Basketball Association (NBA). During his career, Sprewell received four NBA All-Star selections and an All-NBA First Team selection; he also helped the Knicks reach the 1999 NBA Finals and the Timberwolves to the 2004 Western Conference finals. Despite Sprewell's accomplishments, his career was overshadowed by a 1997 incident in which he choked and punched then-Warriors coach P. J. Carlesimo during practice, which resulted in a 68-game suspension.


title: Latrell Sprewell

text: Sprewell played competitively with the Three Rivers Community College Raiders Basketball Team in Poplar Bluff, Missouri, from 1988 to 1990, and from 1990 to 1992 with the University of Alabama, where he was a teammate of future NBA players Robert Horry, Jason Caffey, James Robinson, and Marcus Webb.


title: Latrell Sprewell

text: Sprewell was selected 24th overall in the 1992 NBA draft by the Golden State Warriors. Sprewell, nicknamed "Spree", made an immediate impact, starting 69 of the 77 games he played in during his rookie season and averaging 15.4 points per game. His performance improved over the next few years; he led the team in scoring and played on the Western Conference All-Star team in 1994, 1995, and 1997, scoring 24.2 ppg in 1996–97, fifth in the league. In 1993–1994 he led the league in games played and minutes per game as the Warriors, led by Sprewell and NBA Rookie of the year power forward Chris Webber, made it back to the playoffs. They lost in the first round to the Phoenix Suns in three games.


title: Latrell Sprewell

text: A significant blemish on Sprewell's career occurred on December 1, 1997, when he attacked head coach P. J. Carlesimo during a Warriors practice in Oakland. When Carlesimo yelled at Sprewell to make crisper passes (specifically asking him to "put a little mustard" on a pass), Sprewell responded that he was not in the mood for criticism and told the coach to keep his distance. When Carlesimo approached, Sprewell threatened to kill him and dragged him backward by his throat, choking him for 7–10 seconds before his teammates and assistant coaches pulled him off Carlesimo. Sprewell returned about 20 minutes later after showering and changing and again accosted Carlesimo. He landed a glancing blow at Carlesimo's right cheek before being dragged away again by the assistant coaches. This was not Sprewell's first violent incident with the Warriors; in 1995, he fought with teammate Jerome Kersey, returned to practice carrying a two-by-four, and reportedly threatened to return with a gun. In a 1993 practice, Sprewell fought with Byron Houston, who was 50 pounds heavier than Sprewell and had what many teammates described as a Mike Tyson-like demeanor and physique.


title: Latrell Sprewell

text: Sprewell was suspended for 10 games without pay. The next day, in the wake of a public uproar, the Warriors voided the remainder of his contract, which included $23.7 million over three years, and the NBA suspended him for a year. Sprewell took the case to arbitration and the contract voiding was overturned, but the league did suspend him for the rest of the season without pay, which amounted to 68 games. He sought to vacate the arbitration contract under the terms of the collective bargaining agreement. His case went through all appeals, and was remanded. During the time he was serving his suspension from the NBA, Sprewell was charged with reckless driving for his role in a 90-mile-per-hour accident that injured two people. He spent three months under house arrest as part of a no-contest plea.


title: Latrell Sprewell

text: Sprewell's 68-game suspension was the longest suspension given by the NBA until Ron Artest was suspended for the remainder of the 2004–05 season (including the playoffs), totaling to 86 games, due to his involvement in a brawl in Detroit.


title: Latrell Sprewell

text: Due to the NBA lockout, Sprewell did not play again until February 1999, after the Warriors traded him to the New York Knicks for John Starks, Chris Mills, and Terry Cummings. Sprewell played 37 games for the Knicks that season, playing off the bench in all but four games.


title: Latrell Sprewell

text: Many pundits felt that trading for the alleged volatile Sprewell was too big a gamble for the Knicks, but Sprewell vowed he was a changed man. The Knicks, who at the time still revolved around veteran All-Star center Patrick Ewing, narrowly qualified for the 1999 playoffs, making the field as the eighth seed in the Eastern Conference. They navigated past the Miami Heat, Atlanta Hawks and Indiana Pacers, becoming the first eighth seed in NBA history to reach the Finals, where they met the San Antonio Spurs, who beat them in five games. Sprewell enjoyed a good series for the most part, averaging 26.0 ppg. He tallied 35 points and grabbed 10 rebounds in the Knicks' 78-77 Game 5 loss, and was featured on the cover of the September 1999 issue of "SLAM Magazine".


title: Latrell Sprewell

text: Sprewell moved into the Knicks' starting lineup for the 1999–2000 season at small forward, and averaged 18.6 points, helping the Knicks to a 50–32 record, good enough for the third seed in the Eastern Conference, led by Sprewell, Ewing and shooting guard Allan Houston. The Knicks navigated past the Toronto Raptors in three hard-fought games and the Miami Heat in seven even harder-fought games in the first two rounds of the playoffs, en route to the Eastern Conference Finals against the Indiana Pacers. But their quest for back-to-back NBA Finals appearances came to an end when they lost to the Pacers in 6 games in the Eastern Conference Finals. Sprewell averaged 19.7 ppg in the series, and the Knicks gave him a five-year $62 million contract extension.


title: Latrell Sprewell

text: The 2000–01 season saw Sprewell step up as the Knicks' leader with Ewing traded to the Seattle SuperSonics, making his only All-Star appearance for the Knicks that year, scoring 17.7 points. But despite another impressive season from Sprewell, the Knicks lost in the first round to the Toronto Raptors in five games in the playoffs. In 2001–02 Sprewell averaged 19.4 ppg, including 49 points in a game against the Boston Celtics, one of three times he scored 40 or more points that season; but the Knicks missed the playoffs for the first time in 15 years.


title: Latrell Sprewell

text: Before the 2002–03 season, Sprewell reported to training camp with a broken hand, which he claimed occurred when he slipped on his yacht; the Knicks fined him a record $250,000 for failing to report the incident. He then sued the "New York Post" for claiming he had broken his hand in a fight. Sprewell lost the lawsuit.


title: Latrell Sprewell

text: That season, Sprewell made NBA history as he hit 9 of 9 three-point shots in one game, making the most three-pointers without a single miss for the first time en route to a season-high 38 points versus the Los Angeles Clippers. The record has since been tied twice by then-Chicago Bulls guard Ben Gordon. After that season, in which the Knicks missed the playoffs for the second year in a row, Sprewell was traded to the Minnesota Timberwolves in a four-team trade involving Keith Van Horn, Glenn Robinson, and Terrell Brandon.


title: Latrell Sprewell

text: In the 2003–04 season, Sprewell became part of the league's highest-scoring trio alongside superstar power forward Kevin Garnett and point guard Sam Cassell. With a 58–24 record, the Timberwolves qualified for the 2004 playoffs as the top seed in the Western Conference. They navigated past the Denver Nuggets in five games and the Sacramento Kings in seven in the first two rounds of the playoffs. In the Western Conference Finals they met the Los Angeles Lakers, who defeated them in six games, still the Timberwolves' only appearance in the conference finals. Sprewell finished third in team scoring at 16.8 ppg, behind Garnett's 24.2 and Cassell's 19.8.


title: Latrell Sprewell

text: On October 31, 2004, the Minnesota Timberwolves offered Sprewell a three-year, $21 million contract extension, a substantial pay cut. Claiming to feel insulted by the offer, he publicly expressed outrage, declaring, "I have a family to feed." He declined the extension and the Timberwolves offered him nothing more. Having once more drawn the ire of fans and sports media, Sprewell had the worst season of his career in the final year of his contract. In the summer of 2005, the Denver Nuggets, Cleveland Cavaliers and Houston Rockets all expressed interest in signing Sprewell, but none ended up signing him.


title: Latrell Sprewell

text: One month into the 2005–06 season and without a contract, Sprewell's agent, Bob Gist, said his client would rather retire than play for the NBA minimum salary, telling "Sports Illustrated", "Latrell doesn't need the money that badly. To go from being offered $7 million to taking $1 million, that would be a slap in the face." Several days later, Gist said that Sprewell planned to wait until "teams get desperate" around the trade deadline in February, and then sign with a contending team—an eventuality that never materialized. Gist said that Sprewell would not be interested in signing for any team's $5 million mid-level exception, calling that amount "a level beneath which [Sprewell] would not stoop or kneel!"


title: Latrell Sprewell

text: In March 2006, Sprewell was offered contracts by the Dallas Mavericks and San Antonio Spurs, both of which were considered at the time strong favorites to win the NBA Championship, but Sprewell failed to respond and remained a free agent as the season closed. The Los Angeles Lakers also showed some interest in him at the start of that season, but nothing came of it.


title: Latrell Sprewell

text: Over the course of his career, Sprewell started 868 of the 913 games he played in, averaging 18.8 ppg, 4.2 apg, and 4.1 rpg with playoff career averages of 19.7 ppg, 3.4 apg, and 4.3 rpg. He was an All-NBA First Team selection at the end of his second season and made the All-NBA Defensive second team that same season.


title: Latrell Sprewell

text: In October 1994, Sprewell's four-year old daughter was mauled in the family backyard by one of two pet pit bulls, having an ear bitten off and suffering bites to her face.


title: Latrell Sprewell

text: On August 30, 2006, Milwaukee police investigated a claim by a 21-year-old female that she and Sprewell were having consensual sex aboard his yacht when Sprewell began to strangle her. Police allegedly observed red marks on her neck. Police investigating the allegation searched Sprewell's yacht for evidence. On September 6, police declined to press charges. Sprewell then sought a restraining order along with "civil remedies" against the accuser.


title: Latrell Sprewell

text: On January 31, 2007, Sprewell's long-term companion sued him for $200 million for ending their relationship agreement. She claimed Sprewell agreed to support her and their four children through college.


title: Latrell Sprewell

text: On August 22, 2007, Sprewell's $1.5 million yacht was repossessed by a federal marshal. He had failed to continue paying for and insuring the vessel, for which he reportedly still owed approximately $1.3 million. In February 2008, the yacht was auctioned for $856,000 after Sprewell defaulted on the mortgage. Three months later, a Milwaukee-area home Sprewell owned went into foreclosure status. In July 2009, a Westchester County, New York mansion Sprewell owned went into foreclosure status, but that action was dismissed on motion of another party's attorney.


title: Latrell Sprewell

text: In 2011, Sprewell owed the state of Wisconsin $3.5 million in unpaid income taxes. On January 1, 2013, he was arrested for disorderly conduct after police received numerous complaints about loud music.


title: Latrell Sprewell

text: On September 8, 2017, Sprewell was involved in an altercation in a Milwaukee bar with Alexander Schenk. The altercation was broken up by local officers, and a citation was made to both parties.


title: Rob Garrison

text: Robert Scott Garrison (January 23, 1960 – September 27, 2019) was an American actor known for his role as Tommy in the 1984 film "The Karate Kid" and the second season of its spinoff "Cobra Kai".


title: Rob Garrison

text: Garrison started his acting career in the 1970s and continued steadily over the 1980s and 1990s. He acted in "Brubaker" (1980), "The Karate Kid" (1984), "The Karate Kid Part II" (1986), and "Iron Eagle" (1986). He also had roles in the television shows "Coach", "St. Elsewhere", "MacGyver," and "".


title: Rob Garrison

text: Garrison was born on January 23, 1960, and raised in Wheeling, West Virginia. He first became involved in acting at Wheeling Park High School and also had a small role in "Starship Invasions" (1977) before graduating in 1978. He then studied theater at Ohio University on a full scholarship, and received a small role as a convict in Robert Redford's prison film "Brubaker" (1980). After graduating from Ohio University in 1982, he was cast as Tommy in the 1984 film "The Karate Kid", although both he and William Zabka tried out for the role of Johnny. Garrison reprised this role during season 2 of the Netflix web series "Cobra Kai" in 2019. His "Karate Kid" character Tommy is remembered for delivering the line "Get him a body bag, yeah!" during the climactic fight between Ralph Macchio's Daniel LaRusso and Zabka's Johnny Lawrence in the original "Karate Kid" film. He later stated that the line, heard while his character is offscreen, was not a part of the original script: "My famous line, I never said that while filming. I looped that in two months later. I was in the recording booth with John [Avildsen] and he said he needed two seconds of something. I said, 'Get him a body bag!' on the first try. John said 'That's going to be a classic. You'll never be forgotten because of that line.'"


title: Rob Garrison

text: Garrison continued his acting career over the 1980s and 1990s, appearing in films such as "The Karate Kid Part II (cameo)" (1986) and "Iron Eagle" (1986). He also had roles in the television shows "Coach", "St. Elsewhere", "MacGyver" and "".


title: Rob Garrison

text: In the later part of Garrison's life, acting was no longer his full-time work and he was employed as a restaurant manager. He acted in the 2007 No More Kings music video "Sweep the Leg", which parodied "The Karate Kid", "The Pledge" (2011), and the short film "The Static" released in 2016.


title: Rob Garrison

text: Garrison interacted with his fans via social media and reprised the role of Tommy in the second season of "Cobra Kai", which was his last performance.


title: Rob Garrison

text: Garrison continued acting on stage in local theatre productions in Wheeling until his health began to fail him. He died on September 27, 2019, at the age of 59. He had been admitted to a West Virginia hospital for treatment of kidney and liver issues, where he had been hospitalized for a month until his organs shut down.


title: Pat Gelsinger

text: Patrick Paul Gelsinger (; born March 5, 1961) is an American business executive and engineer currently serving as CEO of Intel.


title: Pat Gelsinger

text: Based mainly in Silicon Valley since the late 1970s, Gelsinger graduated from Stanford University with a master's degree in engineering and was the chief architect of the i486 processor in the 1980s. Before returning to Intel, he was CEO of VMware and president and chief operating officer (COO) at EMC.


title: Pat Gelsinger

text: Gelsinger was raised on family farms by his parents, June and Paul Gelsinger, in rural Robesonia, in an Amish and Mennonite part of Pennsylvania. As a teenager, he received a high score on a Lincoln Tech electronics technology test, winning an early-admission scholarship. He then skipped his final year at Conrad Weiser High School and left home at 16 for college. There, he earned the remainder of high school credits for graduation and worked at WFMZ-TV Channel 69 as a technician, while obtaining an associate’s degree from Lincoln Tech in West Orange, New Jersey, in 1979. He moved to Silicon Valley to work at Intel as a quality-control technician, at age 18 in 1979. While at Intel, he earned a bachelor's degree in electrical engineering, graduating magna cum laude from Santa Clara University in 1983, then a master's degree in electrical engineering and computer science from Stanford University in 1985.


title: Pat Gelsinger

text: Gelsinger first joined Intel at 18 years old in 1979 just after earning an associate degree from Lincoln Tech. He spent much of his career with the company in Oregon, where he maintains a home. In 1987, he co-authored his first book about programming the 80386 microprocessor. Gelsinger was the lead architect of the 4th generation 80486 processor introduced in 1989. At age 32, he was named the youngest vice president in Intel's history. Mentored by Intel CEO Andrew Grove, Gelsinger became the company's CTO in 2001, leading key technology developments, including Wi-Fi, USB, Intel Core and Intel Xeon processors, and 14 chip projects. He launched the Intel Developer Forum conference as a counterpart to Microsoft's WinHEC.


title: Pat Gelsinger

text: In 2012, he became the CEO of VMware, where Gelsinger became a "seasoned CEO" and gained "new leadership skills."


title: Pat Gelsinger

text: Gelsinger rejoined Intel as their new CEO on February 15, 2021 after previously having a 30 year-long career at the company in various technical engineering and leadership roles. This followed reorganization pressure, due to languishing share prices, from its newest activist investor Third Point Management. Gelsinger leads Intel's course correction, including construction of two $20 billion Arizona manufacturing plants (fabs) for its planned expansion. Media reported positive responses to Gelsinger's appointment and credited the decision for driving Intel share prices up nearly 8%. On March 23, 2021, Intel shares rose over 6% following Gelsinger’s remarks regarding company strategy.


title: Pat Gelsinger

text: In May 2021, Gelsinger was interviewed by Lesley Stahl of "60 Minutes". Gelsinger stated that Intel plans to catch up with Taiwanese chip manufacturer TSMC and Korean chip manufacturer Samsung within the next five years. He announced a planned three and a half-billion dollar upgrade to Intel's fab in New Mexico.


title: Pat Gelsinger

text: In March 2022, Gelsinger personally announced the start of an entirely new fab build for roughly $20 billion near Magdeburg, Saxony-Anhalt, Germany to employ 7,000 people during construction work and 3,000 people in production work in 2027.


title: Pat Gelsinger

text: He was named a Fellow of the Institute of Electrical and Electronics Engineers in 2008 and serves as a director of the Semiconductor Industry Association (SIA). He is a member of the National Security Telecommunications Advisory Committee (NSTAC).


title: Pat Gelsinger

text: Gelsinger holds eight design patents, developed for communications, computer architecture and VLSI design.


title: Pat Gelsinger

text: In 2021, Gelsinger was appointed to serve on President Joe Biden's Council of Advisors on Science and Technology. In this position, he has advised Biden on the chips shortage and advocated for the passage of the CHIPS and Science Act. Gelsinger was a guest at Biden's State of the Union Address in March 2022. Biden has spoken in favor of Intel's investment in fabrication plants in the U.S. and has visited the $20 billion facility planned in Ohio alongside Gelsinger.


title: Pat Gelsinger

text: In October 2021, Gelsinger was inducted into Indiana Wesleyan University's Society of World Changers. While speaking on campus he received an honorary doctor of science degree and a bronze bust of Gelsinger was placed in the university's library rotunda. In 2022, he was awarded an honorary Doctorate of Engineering from The Ohio State University.


title: Pat Gelsinger

text: Gelsinger and his wife, Linda, are Christians who "support multiple worthy causes", including sponsorship of disaster relief medical teams. In 2013, Gelsinger co-founded Transforming the Bay with Christ (TBC), a coalition of business leaders, venture capitalists, non-profit leaders and pastors that aims to convert one million people over the next decade. He helped establish the Sacramento-area Christian institution William Jessup University, from which he also received an honorary doctorate, and was identified in "Money, Inc" magazine in 2018 as "among the most generous billionaires in the world." Gelsinger and his wife have 4 children.


title: Aspergillus

text: Aspergillus () is a genus consisting of several hundred mold species found in various climates worldwide.


title: Aspergillus

text: "Aspergillus" was first catalogued in 1729 by the Italian priest and biologist Pier Antonio Micheli. Viewing the fungi under a microscope, Micheli was reminded of the shape of an "aspergillum" (holy water sprinkler), from Latin "spargere" (to sprinkle), and named the genus accordingly. Aspergillum is an asexual spore-forming structure common to all "Aspergillus" species; around one-third of species are also known to have a sexual stage. While some species of "Aspergillus" are known to cause fungal infections, others are of commercial importance.


title: Aspergillus

text: "Aspergillus" is defined as a group of conidial fungi—that is, fungi in an asexual state. Some of them, however, are known to have a teleomorph (sexual state) in the Ascomycota. With DNA evidence, all members of the genus "Aspergillus" are members of the phylum Ascomycota.


title: Aspergillus

text: Members of the genus possess the ability to grow where a high osmotic pressure exists (high concentration of sugar, salt, etc.). "Aspergillus" species are highly aerobic and are found in almost all oxygen-rich environments, where they commonly grow as molds on the surface of a substrate, as a result of the high oxygen tension. Commonly, fungi grow on carbon-rich substrates like monosaccharides (such as glucose) and polysaccharides (such as amylose). "Aspergillus" species are common contaminants of starchy foods (such as bread and potatoes), and grow in or on many plants and trees.


title: Aspergillus

text: In addition to growth on carbon sources, many species of "Aspergillus" demonstrate oligotrophy where they are capable of growing in nutrient-depleted environments, or environments with a complete lack of key nutrients. "Aspergillus niger" is a prime example of this; it can be found growing on damp walls, as a major component of mildew.


title: Aspergillus

text: Several species of "Aspergillus", including "A. niger" and "A. fumigatus", will readily colonise buildings, favouring warm and damp or humid areas such as bathrooms and around window frames.


title: Aspergillus

text: Species of "Aspergillus" are important medically and commercially. Some species can cause infection in humans and other animals. Some infections found in animals have been studied for years, while other species found in animals have been described as new and specific to the investigated disease, and others have been known as names already in use for organisms such as saprophytes. More than 60 "Aspergillus" species are medically relevant pathogens. For humans, a range of diseases such as infection to the external ear, skin lesions, and ulcers classed as mycetomas are found.


title: Aspergillus

text: Other species are important in commercial microbial fermentations. For example, alcoholic beverages such as Japanese "sake" are often made from rice or other starchy ingredients (like manioc), rather than from grapes or malted barley. Typical microorganisms used to make alcohol, such as yeasts of the genus "Saccharomyces", cannot ferment these starches. Therefore, "koji" mold such as "Aspergillus oryzae" is used to first break down the starches into simpler sugars.


title: Aspergillus

text: Members of the genus are also sources of natural products that can be used in the development of medications to treat human disease. "Aspergillus" spp. are known to produce anthraquinone which has commercial importance due to its antibacterial and antifungal properties.


title: Aspergillus

text: Perhaps the largest application of "Aspergillus niger" is as the major source of citric acid; this organism accounts for over 99% of global citric acid production, or more than 1.4 million tonnes (>1.5 million US tons) per year. "A. niger" is also commonly used for the production of native and foreign enzymes, including glucose oxidase, lysozyme, and lactase. In these instances, the culture is rarely grown on a solid substrate, although this is still common practice in Japan, but is more often grown as a submerged culture in a bioreactor. In this way, the most important parameters can be strictly controlled, and maximal productivity can be achieved. This process also makes it far easier to separate the chemical or enzyme of importance from the medium, and is therefore far more cost-effective.


title: Aspergillus

text: "A. nidulans" ("Emericella nidulans") has been used as a research organism for many years and was used by Guido Pontecorvo to demonstrate parasexuality in fungi. Recently, "A. nidulans" was one of the pioneering organisms to have its genome sequenced by researchers at the Broad Institute. As of 2008, a further seven "Aspergillus" species have had their genomes sequenced: the industrially useful "A. niger" (two strains), "A. oryzae", and "A. terreus", and the pathogens "A. clavatus", "A. fischerianus" ("Neosartorya fischeri"), "A. flavus", and "A. fumigatus" (two strains). "A. fischerianus" is hardly ever pathogenic, but is very closely related to the common pathogen "A. fumigatus"; it was sequenced in part to better understand "A. fumigatus" pathogenicity.


title: Aspergillus

text: Of the 250 species of aspergilli, about 64% have no known sexual state. However, many of these species likely have an as yet unidentified sexual stage. Sexual reproduction occurs in two fundamentally different ways in fungi. These are outcrossing (in heterothallic fungi) in which two different individuals contribute nuclei, and self-fertilization or selfing (in homothallic fungi) in which both nuclei are derived from the same individual. In recent years, sexual cycles have been discovered in numerous species previously thought to be asexual. These discoveries reflect recent experimental focus on species of particular relevance to humans.


title: Aspergillus

text: "A. fumigatus" is the most common species to cause disease in immunodeficient humans. In 2009, "A. fumigatus" was shown to have a heterothallic, fully functional sexual cycle. Isolates of complementary mating types are required for sex to occur.


title: Aspergillus

text: "A. flavus" is the major producer of carcinogenic aflatoxins in crops worldwide. It is also an opportunistic human and animal pathogen, causing aspergillosis in immunocompromised individuals. In 2009, a sexual state of this heterothallic fungus was found to arise when strains of opposite mating types were cultured together under appropriate conditions.


title: Aspergillus

text: "A. lentulus" is an opportunistic human pathogen that causes invasive aspergillosis with high mortality rates. In 2013, "A. lentulus" was found to have a heterothallic functional sexual breeding system.


title: Aspergillus

text: "A. terreus" is commonly used in industry to produce important organic acids and enzymes, and was the initial source for the cholesterol-lowering drug lovastatin. In 2013, "A. terreus" was found to be capable of sexual reproduction when strains of opposite mating types were crossed under appropriate culture conditions.


title: Aspergillus

text: These findings with "Aspergillus" species are consistent with accumulating evidence, from studies of other eukaryotic species, that sex was likely present in the common ancestor of all eukaryotes.


title: Aspergillus

text: "A. nidulans", a homothallic fungus, is capable of self-fertilization. Selfing involves activation of the same mating pathways characteristic of sex in outcrossing species, i.e. self-fertilization does not bypass required pathways for outcrossing sex, but instead requires activation of these pathways within a single individual.


title: Aspergillus

text: Among those "Aspergillus" species that exhibit a sexual cycle, the overwhelming majority in nature are homothallic (self-fertilizing). This observation suggests "Aspergillus" species can generally maintain sex though little genetic variability is produced by homothallic self-fertilization. "A. fumigatus", a heterothallic (outcrossing) fungus that occurs in areas with widely different climates and environments, also displays little genetic variability either within geographic regions or on a global scale, again suggesting sex, in this case outcrossing sex, can be maintained even when little genetic variability is produced.


title: Aspergillus

text: The simultaneous publication of three "Aspergillus" genome manuscripts in "Nature" in December 2005 established the genus as the leading filamentous fungal genus for comparative genomic studies. Like most major genome projects, these efforts were collaborations between a large sequencing centre and the respective community of scientists. For example, the Institute for Genome Research (TIGR) worked with the "A. fumigatus" community. "A. nidulans" was sequenced at the Broad Institute. "A. oryzae" was sequenced in Japan at the National Institute of Advanced Industrial Science and Technology. The Joint Genome Institute of the Department of Energy has released sequence data for a citric acid-producing strain of "A. niger". TIGR, now renamed the J. Craig Venter Institute, is currently spearheading a project on the "A. flavus" genome.


title: Aspergillus

text: "Aspergillus" is characterized by high levels of genetic diversity and, using protostome divergence as a scale, is as diverse as the Vertebrates phylum although both inter and intra-specific genome structure is relatively plastic. The genomes of some "Aspergillus" species, such as "A. flavus" and "A. oryzae", are more rich and around 20% larger than others, such as "A. nidulans" and "A. fumigatus". Several mechanisms could explain this difference, although the combination of segmental duplication, genome duplication, and horizontal gene transfer acting in a piecemeal fashion is well-supported.


title: Aspergillus

text: Genome sizes for sequenced species of "Aspergillus" range from about 29.3 Mb for "A. fumigatus" to 37.1 Mb for "A. oryzae", while the numbers of predicted genes vary from about 9926 for "A. fumigatus" to about 12,071 for "A. oryzae". The genome size of an enzyme-producing strain of "A. niger" is of intermediate size at 33.9 Mb.


title: Aspergillus

text: Some "Aspergillus" species cause serious disease in humans and animals. The most common pathogenic species are "A. fumigatus" and "A. flavus", which produces aflatoxin which is both a toxin and a carcinogen, and which can contaminate foods such as nuts. The most common species causing allergic disease are "A. fumigatus" and "A. clavatus". Other species are important as agricultural pathogens. "Aspergillus" spp. cause disease on many grain crops, especially maize, and some variants synthesize mycotoxins, including aflatoxin. "Aspergillus" can cause neonatal infections.


title: Aspergillus

text: "A. fumigatus" (the most common species) infections are primary pulmonary infections and can potentially become a rapidly necrotizing pneumonia with a potential to disseminate. The organism can be differentiated from other common mold infections based on the fact that it takes on a mold form both in the environment and in the host (unlike "Candida albicans" which is a dimorphic mold in the environment and a yeast in the body).


title: Aspergillus

text: Aspergillosis is the group of diseases caused by "Aspergillus". The most common species among paranasal sinus infections associated with aspergillosis is "A. fumigatus". The symptoms include fever, cough, chest pain, or breathlessness, which also occur in many other illnesses, so diagnosis can be difficult. Usually, only patients with already weakened immune systems or who suffer other lung conditions are susceptible.


title: Aspergillus

text: Fungal infections from Aspergillus spores remain one theory of sickness and untimely death of some early Egyptologists and tomb explorers. Ancient spores which grew on the remains of food offerings and mummies sealed in tombs and chambers may have been blown around and inhaled by the excavators, ultimately linked to the notion of the curse of the pharaohs.


title: Aspergillus

text: Aspergillosis of the air passages is also frequently reported in birds, and certain species of "Aspergillus" have been known to infect insects.


title: Aspergillus

text: Most people inhale "Aspergillus" into their lungs everyday. But it's generally only the immuno-compromised who get sick with Aspergillosis.


title: Triangle inequality

text: In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality. If , , and are the lengths of the sides of the triangle, with no side being greater than , then the triangle inequality states that


title: Triangle inequality

text: In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):


title: Triangle inequality

text: where the length of the third side has been replaced by the vector sum . When and are real numbers, they can be viewed as vectors in , and the triangle inequality expresses a relationship between absolute values.


title: Triangle inequality

text: In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although it may be proven without these theorems. The inequality can be viewed intuitively in either or . The figure at the right shows three examples beginning with clear inequality (top) and approaching equality (bottom). In the Euclidean case, equality occurs only if the triangle has a angle and two angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shortest distance between two points is a straight line.


title: Triangle inequality

text: In spherical geometry, the shortest distance between two points is an arc of a great circle, but the triangle inequality holds provided the restriction is made that the distance between two points on a sphere is the length of a minor spherical line segment (that is, one with central angle in ) with those endpoints.


title: Triangle inequality

text: The triangle inequality is a "defining property" of norms and measures of distance. This property must be established as a theorem for any function proposed for such purposes for each particular space: for example, spaces such as the real numbers, Euclidean spaces, the L spaces (), and inner product spaces.


title: Triangle inequality

text: Euclid proved the triangle inequality for distances in plane geometry using the construction in the figure. Beginning with triangle , an isosceles triangle is constructed with one side taken as and the other equal leg along the extension of side . It then is argued that angle has larger measure than angle , so side is longer than side . But , so the sum of the lengths of sides and is larger than the length of . This proof appears in Euclid's Elements, Book 1, Proposition 20.


title: Triangle inequality

text: For a proper triangle, the triangle inequality, as stated in words, literally translates into three inequalities (given that a proper triangle has side lengths , , that are all positive and excludes the degenerate case of zero area):


title: Triangle inequality

text: A mathematically equivalent formulation is that the area of a triangle with sides "a", "b", "c" must be a real number greater than zero. Heron's formula for the area is


title: Triangle inequality

text: In terms of either area expression, the triangle inequality imposed on all sides is equivalent to the condition that the expression under the square root sign be real and greater than zero (so the area expression is real and greater than zero).


title: Triangle inequality

text: The triangle inequality provides two more interesting constraints for triangles whose sides are "a, b, c", where "a" ≥ "b" ≥ "c" and formula_8 is the golden ratio, as


title: Triangle inequality

text: In the case of right triangles, the triangle inequality specializes to the statement that the hypotenuse is greater than either of the two sides and less than their sum.


title: Triangle inequality

text: The second part of this theorem is already established above for any side of any triangle. The first part is established using the lower figure. In the figure, consider the right triangle . An isosceles triangle is constructed with equal sides . From the triangle postulate, the angles in the right triangle satisfy:


title: Triangle inequality

text: An alternative proof (also based upon the triangle postulate) proceeds by considering three positions for point : (i) as depicted (which is to be proven), or (ii) coincident with (which would mean the isosceles triangle had two right angles as base angles plus the vertex angle , which would violate the triangle postulate), or lastly, (iii) interior to the right triangle between points and (in which case angle is an exterior angle of a right triangle and therefore larger than , meaning the other base angle of the isosceles triangle also is greater than and their sum exceeds in violation of the triangle postulate).


title: Triangle inequality

text: This theorem establishing inequalities is sharpened by Pythagoras' theorem to the equality that the square of the length of the hypotenuse equals the sum of the squares of the other two sides.


title: Triangle inequality

text: Consider a triangle whose sides are in an arithmetic progression and let the sides be , , . Then the triangle inequality requires that


title: Triangle inequality

text: The first of these quadratic inequalities requires to range in the region beyond the value of the positive root of the quadratic equation , i.e. where is the golden ratio. The second quadratic inequality requires to range between 0 and the positive root of the quadratic equation , i.e. . The combined requirements result in being confined to the range


title: Triangle inequality

text: When the common ratio is chosen such that it generates a right triangle that is always similar to the Kepler triangle.


title: Triangle inequality

text: The triangle inequality can be extended by mathematical induction to arbitrary polygonal paths, showing that the total length of such a path is no less than the length of the straight line between its endpoints. Consequently, the length of any polygon side is always less than the sum of the other polygon side lengths.


title: Triangle inequality

text: Consider a quadrilateral whose sides are in a geometric progression and let the sides be , , , . Then the generalized polygon inequality requires that


title: Triangle inequality

text: The left-hand side polynomials of these two inequalities have roots that are the tribonacci constant and its reciprocal. Consequently, is limited to the range where is the tribonacci constant.


title: Triangle inequality

text: This generalization can be used to prove that the shortest curve between two points in Euclidean geometry is a straight line.


title: Triangle inequality

text: No polygonal path between two points is shorter than the line between them. This implies that no curve can have an arc length less than the distance between its endpoints. By definition, the arc length of a curve is the least upper bound of the lengths of all polygonal approximations of the curve. The result for polygonal paths shows that the straight line between the endpoints is the shortest of all the polygonal approximations. Because the arc length of the curve is greater than or equal to the length of every polygonal approximation, the curve itself cannot be shorter than the straight line path.


title: Triangle inequality

text: The converse of the triangle inequality theorem is also true: if three real numbers are such that each is less than the sum of the others, then there exists a triangle with these numbers as its side lengths and with positive area; and if one number equals the sum of the other two, there exists a degenerate triangle (that is, with zero area) with these numbers as its side lengths.


title: Triangle inequality

text: In either case, if the side lengths are "a, b, c" we can attempt to place a triangle in the Euclidean plane as shown in the diagram. We need to prove that there exists a real number "h" consistent with the values "a, b," and "c", in which case this triangle exists.


title: Triangle inequality

text: By the Pythagorean theorem we have and according to the figure at the right. Subtracting these yields . This equation allows us to express in terms of the sides of the triangle:


title: Triangle inequality

text: which holds if the triangle inequality is satisfied for all sides. Therefore there does exist a real number "h" consistent with the sides "a, b, c", and the triangle exists. If each triangle inequality holds strictly, "h" > 0 and the triangle is non-degenerate (has positive area); but if one of the inequalities holds with equality, so "h" = 0, the triangle is degenerate.


title: Triangle inequality

text: The area of a triangular face of a tetrahedron is less than or equal to the sum of the areas of the other three triangular faces. More generally, in Euclidean space the hypervolume of an -facet of an -simplex is less than or equal to the sum of the hypervolumes of the other facets.


title: Triangle inequality

text: Much as the triangle inequality generalizes to a polygon inequality, the inequality for a simplex of any dimension generalizes to a polytope of any dimension: the hypervolume of any facet of a polytope is less than or equal to the sum of the hypervolumes of the remaining facets.


title: Triangle inequality

text: In some cases the tetrahedral inequality is stronger than several applications of the triangle inequality. For example, the triangle inequality appears to allow the possibility of four points , , , and in Euclidean space such that distances


title: Triangle inequality

text: However, points with such distances cannot exist: the area of the 26–26–26 equilateral triangle is , which is larger than three times , the area of a 26–14–14 isosceles triangle (all by Heron's formula), and so the arrangement is forbidden by the tetrahedral inequality.


title: Triangle inequality

text: that is, the norm of the sum of two vectors is at most as large as the sum of the norms of the two vectors. This is also referred to as subadditivity. For any proposed function to behave as a norm, it must satisfy this requirement.


title: Triangle inequality

text: The triangle inequality is useful in mathematical analysis for determining the best upper estimate on the size of the sum of two numbers, in terms of the sizes of the individual numbers.


title: Triangle inequality

text: There is also a lower estimate, which can be found using the "reverse triangle inequality" which states that for any real numbers and :


title: Triangle inequality

text: for all , , in . That is, the distance from to is at most as large as the sum of the distance from to and the distance from to .


title: Triangle inequality

text: The triangle inequality is responsible for most of the interesting structure on a metric space, namely, convergence. This is because the remaining requirements for a metric are rather simplistic in comparison. For example, the fact that any convergent sequence in a metric space is a Cauchy sequence is a direct consequence of the triangle inequality, because if we choose any and such that and , where is given and arbitrary (as in the definition of a limit in a metric space), then by the triangle inequality, , so that the sequence is a Cauchy sequence, by definition.


title: Triangle inequality

text: This version of the triangle inequality reduces to the one stated above in case of normed vector spaces where a metric is induced via , with being the vector pointing from point to .


title: Triangle inequality

text: The reverse triangle inequality is an elementary consequence of the triangle inequality that gives lower bounds instead of upper bounds. For plane geometry, the statement is:


title: Triangle inequality

text: This implies that the norm formula_50 as well as the distance function formula_51 are Lipschitz continuous with Lipschitz constant , and therefore are in particular uniformly continuous.


title: Triangle inequality

text: By applying the cosine function to the triangle inequality and reverse triangle inequality for arc lengths and employing the angle addition and subtraction formulas for cosines, it follows immediately that


title: Triangle inequality

text: With these formulas, one needs to compute a square root for each triple of vectors that is examined rather than for each pair of vectors examined, and could be a performance improvement when the number of triples examined is less than the number of pairs examined.


title: Triangle inequality

text: The Minkowski space metric formula_58 is not positive-definite, which means that formula_59 can have either sign or vanish, even if the vector "x" is non-zero. Moreover, if "x" and "y" are both timelike vectors lying in the future light cone, the triangle inequality is reversed:


title: Triangle inequality

text: A physical example of this inequality is the twin paradox in special relativity. The same reversed form of the inequality holds if both vectors lie in the past light cone, and if one or both are null vectors. The result holds in "n" + 1 dimensions for any "n" ≥ 1. If the plane defined by "x" and "y" is spacelike (and therefore a Euclidean subspace) then the usual triangle inequality holds.


title: Quartile

text: In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or "quarters", of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three main quartiles are as follows:


title: Quartile

text: Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides information about both the center and the spread of the data. Knowing the lower and upper quartile provides information on how big the spread is and if the dataset is skewed toward one side. Since quartiles divide the number of data points evenly, the range is not the same between quartiles (i.e., "Q"-"Q" ≠ "Q"-"Q") and is instead known as the interquartile range (IQR). While the maximum and minimum also show the spread of the data, the upper and lower quartiles can provide more detailed information on the location of specific data points, the presence of outliers in the data, and the difference in spread between the middle 50% of the data and the outer data points.


title: Quartile

text: If we have an ordered dataset formula_1, we can interpolate between data points to find the formula_2th empirical quantile if formula_3 is in the formula_4 quantile. If we denote the integer part of a number formula_5 by formula_6, then the empirical quantile function is given by,


title: Quartile

text: To find the first, second, and third quartiles of the dataset we would evaluate formula_10, formula_11, and formula_12 respectively.


title: Quartile

text: If we define a continuous probability distributions as formula_13 where formula_14 is a real valued random variable, its cumulative distribution function (CDF) is given by,


title: Quartile

text: The CDF gives the probability that the random variable formula_14 is less than the value formula_17. Therefore, the first quartile is the value of formula_17 when formula_19, the second quartile is formula_17 when formula_21, and the third quartile is formula_17 when formula_23. The values of formula_17 can be found with the quantile function formula_25 where formula_26 for the first quartile, formula_27 for the second quartile, and formula_28 for the third quartile. The quantile function is the inverse of the cumulative distribution function if the cumulative distribution function is monotonically increasing.


title: Quartile

text: There are methods by which to check for outliers in the discipline of statistics and statistical analysis. Outliers could be a result from a shift in the location (mean) or in the scale (variability) of the process of interest. Outliers could also be evidence of a sample population that has a non-normal distribution or of a contaminated population data set. Consequently, as is the basic idea of descriptive statistics, when encountering an outlier, we have to explain this value by further analysis of the cause or origin of the outlier. In cases of extreme observations, which are not an infrequent occurrence, the typical values must be analyzed. In the case of quartiles, the Interquartile Range (IQR) may be used to characterize the data when there may be extremities that skew the data; the interquartile range is a relatively robust statistic (also sometimes called "resistance") compared to the range and standard deviation. There is also a mathematical method to check for outliers and determining "fences", upper and lower limits from which to check for outliers.


title: Quartile

text: After determining the first and third quartiles and the interquartile range as outlined above, then fences are calculated using the following formula:


title: Quartile

text: where "Q" and "Q" are the first and third quartiles, respectively. The lower fence is the "lower limit" and the upper fence is the "upper limit" of data, and any data lying outside these defined bounds can be considered an outlier. Anything below the Lower fence or above the Upper fence can be considered such a case. The fences provide a guideline by which to define an outlier, which may be defined in other ways. The fences define a "range" outside which an outlier exists; a way to picture this is a boundary of a fence, outside which are "outsiders" as opposed to outliers. It is common for the lower and upper fences along with the outliers to be represented by a boxplot. For a boxplot, only the vertical heights correspond to the visualized data set while horizontal width of the box is irrelevant. Outliers located outside the fences in a boxplot can be marked as any choice of symbol, such as an "x" or "o". The fences are sometimes also referred to as "whiskers" while the entire plot visual is called a "box-and-whisker" plot.


title: Quartile

text: When spotting an outlier in the data set by calculating the interquartile ranges and boxplot features, it might be simple to mistakenly view it as evidence that the population is non-normal or that the sample is contaminated. However, this method should not take place of a hypothesis test for determining normality of the population. The significance of the outliers vary depending on the sample size. If the sample is small, then it is more probable to get interquartile ranges that are unrepresentatively small, leading to narrower fences. Therefore, it would be more likely to find data that are marked as outliers.


title: Quartile

text: The Excel function "QUARTILE(array, quart)" provides the desired quartile value for a given array of data, using Method 3 from above. In the "Quartile" function, array is the dataset of numbers that is being analyzed and quart is any of the following 5 values depending on which quartile is being calculated.


title: Quartile

text: In order to calculate quartiles in Matlab, the function "quantile(A,p)" can be used. Where A is the vector of data being analyzed and p is the percentage that relates to the quartiles as stated below.


title: Enschede

text: Enschede (; known as in the local Twents dialect) is a municipality and city in the eastern Netherlands in the province of Overijssel and in the Twente region. The eastern parts of the urban area reaches the border of the German city of Gronau.


title: Enschede

text: The municipality of Enschede consisted of the city of Enschede until 1935, when the rural municipality of Lonneker, which surrounded the city, was annexed after the rapid industrial expansion of Enschede which began in the 1860s and involved the building of railways and the digging of the Twentekanaal. The proposal for consolidation began in 1872, per the Tubantia newspaper article on 22 Jun 1872 that referenced a committee of 5 to oversee a study. They were: J. Mosman (Johannes Theodorus Mosman), H. Fikkert, H. G. Blijdenstein J. Bz., C. C. Schleucker, and G. J. van Heek.


title: Enschede

text: In sports and culture, Enschede is known for being home to football club FC Twente, one-time Dutch champions, and the University of Twente.


title: Enschede

text: The municipality of Enschede works together in the Twente Region and has been a participant in the EUREGIO, the first regional cross-border partnership in Europe, since its foundation in 1958.


title: Enschede

text: Enschede lies in the eastern part of Overijssel and is the easternmost city of more than 140,000 inhabitants in the Netherlands. The city lies a few kilometres from Germany, which borders the municipality. A few small rivers flow through or surround the city, such as the Roombeek and Glanerbeek.


title: Enschede

text: Enschede contains five official city districts (""Stadsdelen""). Note that they also include surrounding villages in the municipality:


title: Enschede

text: Like most of the Netherlands, Enschede features an oceanic climate (Cfb in the Köppen classification), however, winters tend to be less mild than the rest of the Netherlands due to its inland location. Although the former military airport is derelict and plans to revive the place were canceled in 2012, the Royal Netherlands Meteorological Institute still maintains a weather station there.


title: Enschede

text: The early history of Enschede is largely unknown, but a settlement existed around the Old Marketplace in early medieval times. The name of this settlement is mentioned as "Anescede" or Enscede meaning either "near the border" (with Bentheim) or "near the Es" and sported a church, a marketplace and a fortified aristocratic house.


title: Enschede

text: Enschede was granted city rights around 1300 which were confirmed in 1325 by Bishop Jan III van Diest and henceforth was allowed to protect itself with a wall. Because a stone wall was too expensive (since stone had to be imported), Enschede had a system of ditches, palisades and hedges instead, which is still reflected in the street-names "Noorderhagen" and "Zuiderhagen" (North Hedge and South Hedge, respectively). The city plan of this era is still recognisable in the street-pattern. The city was spared destruction in 1597 at its capture during the Eighty Years' War when after a short siege, the Spanish garrison surrendered the city and the defences were razed.


title: Enschede

text: Because the medieval city was largely built of wood and stone houses were the exception, fire was a constant risk and a series of fires in 1517, 1750 and again on 7 May 1862 earned the people from Enschede the nickname "Brandstichters" (arsonists).


title: Enschede

text: The last fire coincided with the start of the growth of the city into a large production center of textiles, originally as a cottage industry, but since the start of the 19th century on an industrial scale, especially the manufacture of "bombazijn" (a mixture of cotton and linen) proved a successful export. One such factory to have produced textiles in the late 19th century is the Hardick & Seckel Factory.


title: Enschede

text: The industrialisation stimulated a large increase in population, which by 1894 had reached an estimated 18,267: nineteenth-century urban growth was at first rather chaotic. The names of the slums (like "De Krim" and "Sebastopol") are still notorious, although they have long since been torn down. In 1907 the "laissez faire" mentality was dropped and Enschede was the first city in the Netherlands to draw up an official expansion-plan, incorporating the surrounding municipality of Lonneker.


title: Enschede

text: During World War II, Enschede was one of the first Dutch cities to be captured by German troops, being the city closest to Germany. Resistance members helped many of the Jews from Enschede to hide on farms in the vicinity. Out of approximately 1300 Jews in Enschede, 500 were saved (38.5%), compared to less than 20% in the rest of the Netherlands. This higher survival rate is attributed to three members of the Jewish Council of Enschede, Sig Menko, Gerard Sanders and Isidoor Van Dam who took the initiative, against the advice of the Jewish Council of Amsterdam, of urging their community to go into hiding and not to answer the call-up of the Germans for "labour in the East." Another notable hero of the era was Enschede Pastor Leendert Overduin, who saved hundreds of Jewish children and adults, with help from his sister and others, through a network of safehouses in and around Enschede.


title: Enschede

text: Enschede was bombed on several occasions, most notably on October 10, 1943, and February 22, 1944. During the first raid the nearby airport (then "Fliegerhorst Twente") was a target of opportunity for the VIII Bomber Command during a raid on rail- and waterways in Münster. 141 people died and many houses were damaged. The latter mission named Enschede as a target of opportunity during Big Week after bombers had been recalled due to adverse weather.


title: Enschede

text: In the sixties of the 20th century, the textile industry was completely lost, at the cost of approximately 30,000 jobs. Most of the large factory complexes were demolished in the 1970s and 1980s, some were renovated and given a new purpose. For example, homes were built in the former factories of Jannink and Van Heek. In addition, part of the Jannink complex was converted into a museum. Enschede developed into a service city.


title: Enschede

text: In the 1970s the textile production in Enschede came to a halt, due to fierce competition from mainly the Far East. This had a profound effect on the populace. Enschede became one of the poorest municipalities in the Netherlands and went bankrupt. Large areas of industrial wasteland came to mark the city. With the support of the national government, this property was acquired and rebuilt. The city center was rendered a car-free zone.


title: Enschede

text: In 1961 it was announced a third technical university would be founded, placed on an estate on the western border of Enschede. This green campus called Drienerlo was donated by the city of Enschede. Building was complete in 1964, when the first and only full-facility university of the Netherlands was realised.


title: Enschede

text: On 13 May 2000, a fireworks storage depot in Enschede exploded, destroying part of the neighborhood of Roombeek and killing 23 people, including 4 firemen. In 2001 a referendum confirmed the proposal of the city council to expand the built-up area into the Usseler Es, an area of historic cultural significance and of geological importance, as it was here that the Usselo horizon was discovered. The renovations at Roombeek were finished in the year 2012. The place where the factory used to be is now a monument.


title: Enschede

text: The Alpha Tower was completed in 2008 and this tower block with 91 apartments spread over 29 floors, with a height of 101 meters, is the tallest building in Enschede. In the period 1995–2010, Enschede grew by approximately 10,000 inhabitants, but since then the growth has stagnated.


title: Enschede

text: Enschede has a large Assyrian community, the first Assyrians came to Enschede in the 1970s, primarily from Turkey (Tur Abdin). That is why there are today three Syriac Orthodox Churches in Enschede which meets the spiritual needs of the approximately over 10,000 Assyrians of the city.


title: Enschede

text: During the festivities of Carnival which happens in either February or March, Enschede is renamed as Krekkelstad, which means "cricket town" in English.


title: Enschede

text: The city is a former centre of textile production. When this industry left the area for cheaper production centers in South-East Asia, Enschede became one of the poorest municipalities in the Netherlands. More educated and wealthy citizens have historically migrated to the Randstad region; decades of renovation work in the city center have been carried out with the goal of making Enschede more attractive to this group.


title: Enschede

text: Modern shopping centers and department stores that until recently were only found in much larger cities have been opened. Enschede is host to many yearly festivals and the Old Market Square is often the venue for events, live music and other activities on the weekend.


title: Enschede

text: The proximity to Germany has, historically, been another major factor in the city's economic activity, ranging from the smuggling of coffee and tobacco in the 19th and 20th century, to large numbers of Germans, who visit the city's shops and weekly markets. Therefore, many natives of Enschede speak German more or less fluently.


title: Enschede

text: The city is co-operating with the nearby municipalities of Almelo, Borne and Hengelo as "Netwerkstad Twente". A draft law plan to merge Enschede with Hengelo and Almelo was defeated in parliament under the influence of opposition from the other towns.


title: Enschede

text: Grolsch beer is brewed in Enschede, and the tyre manufacturer Apollo Vredestein B.V. head office and a factory is in the city. It is one of the most important employers of the region.


title: Enschede

text: There are several museums in Enschede, among them the Rijksmuseum Twenthe for art. A museum of natural history and a museum dedicated to the history of the textiles industry, both closed in January 2007, have merged, and have reopened in April 2008 in new premises on a new location under the name TwentseWelle (Source/Well of Twente). The new location is situated in Roombeek, where a fireworks disaster took place in 2000. The new museum is located partly in a renovated old textile factory, in reference to Enschede's textile history, and partly in an adjourning new building, designed by the Amsterdam-based firm SeARCH (project architect: Bjarne Mastenbroek). Besides museums there are also several art spaces, the most prominent being Villa de Bank and TETEM. The latter focuses on art and technology, and aims to be accessible for a wide public.


title: Enschede

text: De Museumfabriek (formerly TwensteWelle) is a museum in the Roombeek district that arose from a merger of three institutions: Natuurmuseum Enschede, Van Deinse Instituut and Fabriekcomplex Jannink. In this museum, the cultural-historical heritage of Twente is linked to the natural-historical heritage, a unique combination for the Netherlands. The museum was opened in April 2008 by the then Queen Beatrix.


title: Enschede

text: The German-Dutch relationship is characteristic of music culture, which arose through cooperation in the border region and the dominant textile industry in the 19th and 20th centuries. Especially during the period of reversal after the World War I, a close German-Dutch cultural cooperation developed in Gronau and Enschede, which became increasingly important from string quartets, salon orchestras and hot dance music bands to symphony orchestras and an operetta company ("Enschedesch Opera en Operette Gezelschap") with their own performances. At the same time, jazz also found enthusiastic supporters from 1920 onwards.


title: Enschede

text: The three major concert stages for classical music in Enschede – the Muziekcentrum, the Twentse Schouwburg and the Grote Kerk – have been operating under the name Podium Twente since September 2002 and since September 2011 under the name Wilminktheater en Muziekcentrum Enschede. There is a varied offer of concerts, theater, youth and youth performances and the like to visit.


title: Enschede

text: In November 2008 the Nationaal Muziekkwartier opened its doors in Enschede. A new large theatre, pop stage Atak, the ArtEZ Conservatory, the Orkest van het Oosten (now the Dutch Symphony Orchestra), the Twente Music School, the Nationale Reisopera (now the Nederlandse Reisopera) and Podium Twente (now Wilminktheater en Muziekcentrum Enschede) have settled in this dominant building opposite the Central Station in Enschede. There will be a new large square, the Willem Wilminkplein.


title: Enschede

text: In December 2012, the Serious Request action from national radio station 3FM took place in Enschede, which collected more than 12.2 million euros (almost US$16.2 million).


title: Enschede

text: The University of Twente ("Universiteit Twente"), a university with mostly technical studies, is located in Enschede. It is one of the four technical universities in the Netherlands (besides Delft University of Technology, Eindhoven University of Technology and the Wageningen University and Research Centre). The Universiteit Twente is also the only large-campus university in the Netherlands.


title: Enschede

text: The university has courses in pure technical studies such as Applied Physics, Applied Mathematics, Mechanical Engineering, Electrical Engineering, Chemical Engineering, Informatics/Computer Science and Industrial Engineering and also offers study programmes in Communication, Psychology, Economic Sciences, International Business Administration, Public Administration, Applied Medicine and Biomedical Technology; the latter attract a broader public. Since 2006, the programmes of European Studies, Advanced Technology, Creative Technology and ATLAS University College have been added to the university's offerings.


title: Enschede

text: The Faculty of Geo-Information Science and Earth Observation of the University of Twente, with former name International Institute for Aerospace Survey and Earth Sciences, (known by its abbreviation ITC) runs MSc, Master's, Diploma and PhD courses in Geo-Information Science for developing countries. Students from all over the world attend the ITC. Enschede also has an academy of arts and design combined with a conservatory named ArtEZ.


title: Enschede

text: Enschede is also home to one of the three campuses of Saxion University of Applied Sciences ("Saxion Hogeschool"), a polytechnical school offering internationally recognized Bachelor's degrees and Master's degrees in a wide range of fields, including engineering, economics, social work, investigations and health care. The other campuses are located in Deventer and Apeldoorn.


title: Enschede

text: The Medisch Spectrum Twente (MST) hospital is one of the largest top-clinical hospitals of the Netherlands and features important tertiary care departments, fulfilling a supraregional role. It includes a level I trauma center as well. The hospital is strongly involved in higher medical education, with up to 300 medical students following their internships in the hospital at any given time, closely working together with the University of Twente's Technical Medicine program training a new type of technically specialized doctors.


title: Enschede

text: Enschede is a terminus station of the Nederlandse Spoorwegen (NS) railway lines from the west. Trains operate to Hengelo, Almelo, Zwolle, Deventer, Apeldoorn, Amersfoort Centraal, Hilversum, Amsterdam Zuid, Schiphol Airport, Utrecht Centraal and Den Haag Centraal.


title: Enschede

text: To the east there is a line to Gronau, Germany, which has two more stations in the Netherlands: Enschede De Eschmarke and Glanerbrug. The latter two have low ridership. The line is served by


title: Enschede

text: DB Regionalbahn Westfalen (part of the German Deutsche Bahn), to Münster and to Dortmund, each on an hourly interval and alternating half-hours in the service to Gronau.


title: Enschede

text: There is no track connection between the two systems. The through line had been retained for eventual NATO use during the Cold War even after through passenger service was ended (September 1981), although it was in serious disrepair in later years. With the renewal of service to Germany (May 2001) the track was severed; there is a gap of about 30 centimeters between them.


title: Enschede

text: Enschede is situated at the south-east terminus of the Twentekanaal. There is also a network of bus lines connecting nearly every part of the city with the centre. Enschede also has bus connections to nearby towns and cities, like Hengelo, Oldenzaal and south towards Haaksbergen, Neede and Eibergen. The city lines are operated by Syntus, under the Twents-branche. The interlocal lines are exploited by Syntus and Arriva.


title: Enschede

text: Previously, Enschede had a combined regional civil airport, Enschede Airport, and Airbase Twenthe of the Royal Netherlands Air Force. The latter was closed in 2007; the former was closed in 2008. However, It remains in operation for business air traffic flying via a charter or private jet, and recreational flights.


title: Enschede

text: Around the center districts of Enschede is a complete ring road with a length of approximately 8 km, which is popularly called "de singel". This was constructed in the period between 1916 and 1929. Most major arterial roads connect to the canal. Enschede is connected to the national road network by means of the A/N35 and the N18. Below and on the edge of the center are various parking facilities, the most famous and largest of which is the Van Heekgarage, which is located under the Van Heekplein. At the end of 2012, construction of an additional entrance and exit at Kuipersdijk was started as the South entrance. Van Heekgarage is the largest underground parking garage in the Netherlands with a capacity of 1650 cars.


title: Enschede

text: Enschede's association football club is FC Twente. Twente were the 2010 Eredivisie champions but were relegated to the second-tier league, the Eerste Divisie, after the 2017-18 season. Since the 2019–2020 season, they are back in the Eredivisie. De Grolsch Veste Stadium is the club's home base and has a capacity of 30,205 spectators.


title: Enschede

text: Enschede has the second oldest marathon in Europe, and the oldest marathon in the Netherlands: the Enschede Marathon. This has been run annually since 1947. Since 2017 there is a new course. The student rowing club D.R.V. Euros has produced several national champions and one Olympic Champion. DOS-WK played until 2006 in the highest competition of korfball, the 'Korfbal League'.Enschede (from Old Church to University) is the final stage of the Batavierenrace, a footrace relay beginning in Nijmegen, contested mostly by university student teams and claimed to be the largest relay races in the world, with 8000 participants. Enschede built the second indoor speed skating arena in the country, IJsbaan Twente.


title: Enschede

text: Enschede has the second oldest marathon in Europe, and the oldest marathon in the Netherlands: the Enschede Marathon. This has been run annually since 1947. Since 2017 there is a new course. Enschede is also the finish place of the Batavierenrace every year. The Batavierenrace is the world's largest relay race, followed by the largest student party in the Benelux. The race runs from Nijmegen to Enschede. Every year, more than 8,000 students from all over the Netherlands participate in this event.


title: Specific impulse

text: Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse is exactly proportional to the effective exhaust gas velocity.


title: Specific impulse

text: A propulsion system with a higher specific impulse uses the mass of the propellant more efficiently. In the case of a rocket, this means less propellant needed for a given delta-v, so that the vehicle attached to the engine can more efficiently gain altitude and velocity.


title: Specific impulse

text: In an atmospheric context, specific impulse can include the contribution to impulse provided by the mass of external air that is accelerated by the engine in some way, such as by an internal turbofan or heating by fuel combustion participation then thrust expansion or by external propeller. Jet engines breathe external air for both combustion and by-pass, and therefore have a much higher specific impulse than rocket engines. The specific impulse in terms of propellant mass spent has units of distance per time, which is a notional velocity called the "effective exhaust velocity". This is higher than the "actual" exhaust velocity because the mass of the combustion air is not being accounted for. Actual and effective exhaust velocity are the same in rocket engines operating in a vacuum.


title: Specific impulse

text: Specific impulse is inversely proportional to specific fuel consumption (SFC) by the relationship for SFC in kg/(N·s) and for SFC in lb/(lbf·hr).


title: Specific impulse

text: The amount of propellant can be measured either in units of mass or weight. If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to have units of speed, specifically the effective exhaust velocity. As the SI system is mass-based, this type of analysis is usually done in meters per second. If a force-based unit system is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time (seconds). These two formulations differ from each other by the standard gravitational acceleration ("g") at the surface of the earth.