title: Lions for Lambs

text: "Lions for Lambs" holds a 27% approval rating on review aggregator website Rotten Tomatoes, based on 185 reviews, with a weighted average of 4.80/10. The site's consensus states: "Despite its powerhouse cast, "Lions for Lambs" feels like a disjointed series of lectures, rather than a sharp narrative, and ends up falling flat." On Metacritic, the film had an average score of 47 out of 100, based on 36 reviews. Audiences surveyed by CinemaScore gave the film a grade C on scale of A to F.


title: Lions for Lambs

text: Film critic Roger Ebert gave it two and a half stars, noting that at the beginning of the film the viewer is "under the delusion that it's going somewhere." As the film progresses, Ebert wrote that interest is lost, noting, "When we begin to suspect it's going in circles, our interest flags." Matt Pais of the "Chicago Tribune" also gave the film two and a half stars, and wrote in summation: "Redford and Streep give it their all, but Cruise is Cruise, and the go-nowhere 'Lions' is more of an imitation of life than a reflection on it." A "USA Today" review gave the film two and a half stars as well, in a negative review titled: "As entertainment, 'Lions' whimpers rather than roars." Reviewer Claudia Puig commented, "Though characters make some strong points, the film feels preachy and falls flat as entertainment." The "New York Post" gave the film one and a half stars, and did not recommend it, writing: "if you want to be bored by pompous-assery, 'Meet the Press' is free." "The Guardian" was more critical, giving the film only one star, and calling it "a muddled and pompous film about America's war on terror."


title: Lions for Lambs

text: Derek Elley of "Variety" wrote that though the film was "star-heavy", it felt like "the movie equivalent of an Off Broadway play," and "uses a lot of words to say nothing new." "The New York Times" also mentioned the amount of dialogue in the film, writing: "It's a long conversation, more soporific than Socratic, and brimming with parental chiding, generational conflict and invocations of Vietnam," and the "Los Angeles Times" described the lecturing in the film as "dull and self-satisfied." The subtitle of the review in the "Los Angeles Times" was: "As a matter of policy, 'Lions for Lambs' doesn't play." In a review entitled "Political drama feels more like a lecture" in "The Boston Globe", Wesley Morris wrote: "It does not feel good to report that a movie with Robert Redford, Meryl Streep, and Tom Cruise makes the eyelids droop. But that's what 'Lions for Lambs' does." Writing in the "Seattle Post-Intelligencer", reviewer William Arnold wrote positively of the segments of the film involving Robert Redford's character: "His character, who hopes to save America one slacker at a time, rings true; and his real-life conviction and his fears for democracy come through." Amy Biancolli of the "Houston Chronicle" highlighted Redford's direction of the film, commenting that it was not his best film, but it was "his bravest." Ray Bennett of "The Hollywood Reporter" described "Lions for Lambs" as "a well-made movie that offers no answers but raises many important questions."


title: Lions for Lambs

text: The film took in 6.7 million USD in its opening weekend and debuted at the number four spot. Despite a slow start, the film ultimately grossed $63 million worldwide, nearly doubling its budget.


title: Peter Wolf

text: Peter Wolf (born March 7, 1946) is an American musician best known as the lead vocalist of the J. Geils Band from 1967 to 1983 and as a solo artist.


title: Peter Wolf

text: Peter Wolf was born Peter Walter Blankfield on March 7, 1946 in The Bronx, New York, New York. He attended the High School of Music & Art, located in west Harlem, Manhattan, near the Apollo Theater. He often attended the Apollo, seeing many of the famous soul, rhythm & blues, and gospel artists who influenced him.


title: Peter Wolf

text: He moved to Boston, Massachusetts, to attend the School of the Museum of Fine Arts at Tufts on scholarship, where he studied painting. His first roommate was film director David Lynch.


title: Peter Wolf

text: In 1964, Wolf and fellow art students Paul Shapiro (guitar), Doug Slade (guitar), Joe Clark (bass), and Stephen Jo Bladd (drums) formed a music group, The Hallucinations. They performed at nightclubs in the Combat Zone area of Boston and developed a large following as one of the first bands to play at the Boston Tea Party. During this period, they appeared on bills with The Velvet Underground, Howlin' Wolf, Muddy Waters, Van Morrison (who became close with Wolf while residing in nearby Cambridge, Massachusetts), John Lee Hooker, and Sun Ra.


title: Peter Wolf

text: During his time performing with the Hallucinations, Wolf was asked to help establish Boston's radio station WBCN and became their first all-night deejay creating the moniker Woofa Goofa as his on-air personality. His show became a popular late night staple where he interviewed many of the well-known rock, blues, and jazz artists that were touring through Boston in the late 1960s.


title: Peter Wolf

text: In 1967, Wolf and Bladd joined the J. Geils Band. Wolf and keyboardist Seth Justman were responsible for most of the band's songwriting. During the early days of MTV, the band enjoyed heavy airplay of their videos "Centerfold" and "Love Stinks". They toured stadiums with the Rolling Stones and others. Following the success of "Freeze Frame", the other band members wanted to take the band in a new pop direction musically, but Wolf wanted to stick to a more roots-based direction so he was asked to leave in 1983. In the ensuing years the band has been nominated five times for the Rock and Roll Hall of Fame.


title: Peter Wolf

text: Wolf's first solo record "Lights Out" (1984) was produced with Michael Jonzun of the Jonzun Crew. The album features Adrian Belew, G. E. Smith, Elliot Randall, Yogi Horton, Mick Jagger, Elliot Easton, and Maurice Starr. The single "Lights Out" written with Don Covay became a hit the same year, peaking at No. 12 on the "Billboard" Hot 100.


title: Peter Wolf

text: In 1985, Wolf duetted with Aretha Franklin on the track "Push" from her album "Who's Zoomin' Who?" and also appeared on the Artists United Against Apartheid song, "Sun City". In 1987, Wolf released his second solo album "Come as You Are", with the title track notching Wolf another top-15 hit on the pop chart and a number one hit on the Mainstream Rock Chart. A later single "Can't Get Started" received radio play.


title: Peter Wolf

text: His album "Long Line" (1996) and "Fool's Parade" (1998) started his collaboration with singer/songwriter Kenny White producing. "Sleepless" (2002) featured guest appearances from Mick Jagger and Keith Richards and was highly praised by "Rolling Stone". as one of the 500 greatest albums of all time. Wolf has collaborated with Angelo Petraglia and long-time writing partner Will Jennings. Wolf's 2010 album "Midnight Souvenirs" won Album of the Year at the Boston Music Awards. On the album, Wolf performed duets with Shelby Lynne, Neko Case, and Merle Haggard. His eighth solo album, "A Cure for Loneliness", was released in April 2016.


title: Belém Tower

text: Belém Tower (, ), officially the Tower of Saint Vincent () is a 16th-century fortification located in Lisbon that served as a point of embarkation and disembarkation for Portuguese explorers and as a ceremonial gateway to Lisbon. It was built during the height of the Portuguese Renaissance, and is a prominent example of the Portuguese Manueline style, but it also incorporates hints of other architectural styles. The structure was built from lioz limestone and is composed of a bastion and a , four-storey tower.


title: Belém Tower

text: Since 1983, the tower has been a UNESCO World Heritage Site, along with the Jerónimos Monastery. It is often portrayed as a symbol of Europe's Age of Discoveries and as a metonym for Portugal or Lisbon, given its landmark status. It has incorrectly been stated that the tower was built in the middle of the Tagus and now sits near the shore because the river was redirected after the 1755 Lisbon earthquake. In fact, the tower was built on a small island in the Tagus river near the Lisbon shore.


title: Belém Tower

text: In the late 15th century, King John II had designed a defence system for the mouth of the Tagus that depended on the fortresses of Cascais and "São Sebastião" (or "Torre Velha") in Caparica on the south side of the river. These fortresses did not completely protect the river's mouth, and further protection was required. In his "Chronicle of John II" ("Chronica de D. Joao II"), which appeared in 1545, the author Garcia de Resende affirmed the king's opinion that the defences of Lisbon were inadequate, and that he had insisted on building fortifications along the entrance to the River Tagus to supplement the existing defences. To this end, he ordered the "making of a strong fort", but died before any plans were drawn. King Manuel I of Portugal revisited the proposal twenty years later and ordered the construction of a military fortification on the northern margin of the Tagus at Belém. In 1513, Lourenço Fernandes wrote a letter to his friends referring to the king's intention of constructing a tower near Restelo Velho, having determined it to be essential.


title: Belém Tower

text: The project was started on a basaltic rock outcrop a short distance from the riverbank, using some of the stone being collected to build the Monastery of Santa Maria de Belém. The tower was designed by military architect Francisco de Arruda, named "Master of the works of the Belém stronghold" by King Manuel, and in 1516 he began receiving 763 blocks and 504 stones for its construction, delivered by Diogo Rodrigues, treasurer for the project. As construction progressed, a man-of-war called the "Grande Nau" (Great Ship), a heavily armed, 1000–ton ship continued to guard the estuary at the mouth of the Tagus until the fort's completion.


title: Belém Tower

text: The building was finished in 1519, just two years before Manuel's death, and Gaspar de Paiva was temporarily stationed to command the fortress; his commission was made permanent on 15 September 1521, when he was appointed the first Captain-General, or alcalde, and the fortress was named the Castle of St Vincent ("Castelo de São Vicente de Belém"), in honour of the patron saint of Lisbon.


title: Belém Tower

text: In 1571, Francisco de Holanda advised the monarch that it was necessary to improve the coastal defences in order to protect the kingdom's capital. He suggested the construction of a "strong and impregnable" fort that could easily defend Lisbon and that the Belém Tower "should be strengthened, repaired and completed...that it has cost so much without being completed". D'Holanda designed an improved rectangular bastion with several turrets. In 1580, after a few hours of battle, the garrison stationed in the tower surrendered to Spanish forces under the command of the Duke of Alba. After this defeat, the dungeons of the tower served as a prison until 1830. It was also during the last quarter of the 16th century that the construction of the Philippine Barracks began. A rectangular two-storey space was constructed over the bastion, giving the tower the visual profile that it has retained to the present, with sculpted crosses of the Order of Christ and domed turrets.


title: Belém Tower

text: In 1589, Philip I of Portugal ordered Italian engineer Friar João Vicenzio Casale to build a well-defended fort to be constructed in place of the "useless castle of São Vicente". The engineer submitted three designs, proposing that the bastion would be surrounded by another bastion of greater dimensions, but the project never materialized.


title: Belém Tower

text: A 1633 codex for the House of Cadaval was inserted into one of the floors, in one of the arches of the barracks, and in the four largest arches at the top of the southern façade. Similarly, a reference to the year 1655 was inscribed on a plaque placed on the northern wall of the cloister, which certified the tower's function as a customs control point and for navigation along the Tagus; vessels were obliged to pay a tax as they entered the harbour, which was imposed incrementally.


title: Belém Tower

text: Between 1780 and 1782, under the reign of Maria I of Portugal, General Guilherme de Valleré constructed the Fort of Bom Sucesso, whose battery was connected by a western corridor wall to the tower. When French forces invaded Lisbon during the Peninsular War, detachments of their troops were quartered in the tower from 1808 to 1814. After the French retreated, Lord Beresford advised that coastal artillery batteries should be reinforced along the Tagus, and specifically noted that stronger batteries should be placed on the sides of the tower's bastion, with carts placed to better protect the soldiers, since the walls were very low.


title: Belém Tower

text: King Miguel I (1828–1834) used the dungeons to imprison his liberal opponents, while another level was used as a custom house for ships until the duty on foreign ships was abolished in 1833. The tower received military upgrades in 1589 and 1809–1814.


title: Belém Tower

text: During the reign of Maria II, Almeida Garrett protested the site's degradation and under the persuasion of the Duke of Terceira, renovations were begun by military engineer António de Azevedo e Cunha. He demolished the Philippine barracks and extended revivalist elements in 1845–46 (such as the armoured merlons, the balustrade of the veranda along the southern façade, the laced fascia in the cloister and the niche with an image of the Virgin and Child).


title: Belém Tower

text: In 1865–67 a beacon was installed on the southeast terrace of the building and a telegraph service was started, while nearby a gas factory was built, producing smoke that prompted many protests. The first moves to preserve and rehabilitate the tower began in the latter part of the 20th century. First, the tower was transferred to the Ministry of Finance in 1940, which undertook small conservation works. Then the military quarters on the battlements were removed and the inner cloister was built. The architectural landscape designer António Viana Barreto began a three-year project in 1953 to integrate the tower with the local shoreline. In 1983 the site hosted the 17th European Exhibition on Art, Science and Culture, and various projects involving the building were undertaken, among them covering the cloister with a transparent plastic cupola. In the same year the Belém Tower was classified by UNESCO as a World Heritage Site.


title: Belém Tower

text: In the 1990s, the property was transferred to the "Instituto Português do Património Arquitectónico" (forerunner of IGESPAR), which began a full restoration of the building that lasted from February 1997 to January 1998; this included reinforcing the tower and bastion, reinforcing the south balcony supports with stainless steel rods and epoxy resin, treating the mortar joints, and general structural cleaning. The statues of Saint Vincent of Saragossa and the Archangel Michael received the same treatment. In 1999 the project received the "Europa Nostra" award for its restoration of the exterior. The Belém Tower was added on 7 July 2007 to the registry of the Seven Wonders of Portugal.


title: Belém Tower

text: The Belém Tower is situated on the northern bank of the Tagus River in the civil parish of Santa Maria de Belém, municipality of Lisbon, accessible at the western end of the "Avenida de Brasília" by a small bridge. Nearby are the Jeronimos Monastery to the east and the "Forte do Bom Sucesso" to the west, while to the north are the tower Governor's residence, the old Governor's residence for the Bom Successo fort, and the Chapel of São Jerónimo.


title: Belém Tower

text: The tower is isolated along the riverbank, between the dock of Bom Sucesso and Pedrouços, on a basaltic outcropping of rocks belonging to the geomorphological volcanic complex of Lisboa-Mafra. Although various guides have claimed that the tower was built in the middle of the Tagus, and now sits near the shore after the 1755 earthquake redirected the river, they are incorrect. The Portuguese Ministry of Culture and the Institute of Architectural Heritage indicate that the tower was constructed on a small island near the bank of the Tagus, opposite the shore of Restelo. As development extended the shoreline progressively, more and more of the northern bank crept southwards into the Tagus, the tower becoming integrated into the riverbank over time.


title: Belém Tower

text: The Belém Tower was built from a beige-white limestone local to the Lisbon area and thereabouts called "Lioz". The building is divided into two parts: the bastion and the four-story tower located on the north side of the bastion.


title: Belém Tower

text: The 16th-century tower is considered one of the principal works of the Portuguese Late Gothic Manueline style. This is especially apparent in its elaborate rib vaulting, crosses of the Order of Christ, armillary spheres and twisted rope, common to the nautically inspired organic Manueline style.


title: Belém Tower

text: The building's plan consists of a rectangular tower and an irregular, hexagonal bastion, with elongated flanks, that projects south into the river. It is basically a large articulated vertical space resting on a horizontal stone slab, covered by masonry enclosures. On the northeast angle of the structure, protected by a defensive wall with bartizans, is a drawbridge to access the bulwark, decorated in plant motifs, surmounted by the royal coat of arms and flanked by small columns, complemented with armillary spheres. The Manueline armillary spheres appear at the tower's entrance, symbolizing Portugal's nautical explorations, and were used on King Manuel I's personal banner to represent Portuguese discoveries during his rule. The decorative carved, twisted rope and elegant knots also point to Portugal's nautical history and are common elements of the Manueline style.


title: Belém Tower

text: On the outside of the lower bastion, the walls have spaces for 17 cannons with embrasures affording a view of the river. The upper tier of the bastion is crowned by a small wall with bartizans in strategic places, decorated by rounded shields with the cross of the Order of Christ encircling the platform. King Manuel I was a member of the Order of Christ, thus the cross of the Order of Christ is used numerous times on the parapets. These were a symbol of Manuel's military power, as the knights of the Order of Christ participated in several military conquests in that era. The bartizans, cylindrical turrets (guerites) in the corners that served as watchtowers, have corbels with zoomorphic ornaments and domes covered with ridges unusual in European architecture, topped with ornate finials. The bases of the turrets have images of beasts, including a rhinoceros. This rhinoceros is considered to be the first sculpture of such an animal in Western European art and probably depicts the rhinoceros that Manuel I sent to Pope Leo X in 1515.


title: Belém Tower

text: While the tower is predominantly Manueline in style, it also incorporates features of other architectural styles. It was built by the military architect Francisco de Arruda, who had already supervised the construction of several fortresses in Portuguese territories in Morocco. The influence of Moorish architecture is manifested in the delicate decorations, the arched windows, the balconies, and the ribbed cupolas of the watchtowers.


title: Belém Tower

text: The tower has four storeys, with fenestrations and battlements, the ground floor being occupied by a vaulted cistern. On the first floor, there is a south-facing rectangular door with arched windows on the east and north, and bartizans in the northeast and northwest corners. The southern part of the second floor is dominated by a covered veranda with a loggia ("matacães"), consisting of an arcade of seven arches, resting on large corbels with balusters. It is covered by laced stonework to form a porch, and its sloped roof ends in a sculpted twisted rope. The eastern, northern and western walls are occupied by double-arched enclosures, with the northeast and northwest corners occupied by statues of Saint Vincent of Saragossa and the archangel Michael in niches. The third floor has twin windows in the northern, eastern and western façades, with balusters, interspersed by two armillary spheres and large relief with the Royal coat of arms. The final floor is encircled by a terrace with shields of the Order of Christ, and a northern arched door and eastern arched window. The terrace is enclosed by a low wall with colonnaded pyramidal merlons with bartizans in the four corners. A similar terrace above this floor offers a view of the surrounding landscape.


title: Belém Tower

text: The interior of the bastion, with a circular staircase at the north end, has two contiguous halls with vaulted ceilings supported by masonry arches, as well as four storage lockers and sanitary facilities. On the ground floor bunker, the floor is inclined towards the outside, while the ceilings are supported by masonry pilasters and vaulted spines. Gothic rib vaulting is evident in this casemate, the rooms of the tower and the cupolas of the watchtowers on the bastion terrace. Peripheral compartments on the edges of the bunker allow the individual cannons to occupy their own space, with the ceiling designed with several asymmetrical domes of various heights. The ancillary storerooms were later used as prison cells.


title: Belém Tower

text: Two archways open to the main cloister in the north and south, while six broken arches stretch along the eastern and western parts of the cloister, interspersed with square pillars in the bastion interior, with gargoyle facets. The open cloister above the casemate, although decorative, was designed to dispel cannon smoke. The upper level is connected by a railing decorated with crosses of the Order of Christ, while at the terrace the space has rising columns topped with armillary spheres. This space could also be used for light calibre infantry. This was the first Portuguese fortification with a two-level gun emplacement and marks a new development in military architecture. Some of the decoration dates from the renovation of the 1840s and is Neo-Manueline in style, like the decoration of the small cloister on the bastion.


title: Belém Tower

text: On the southern portion of the cloister terrace is an image of the Virgin and Child. The statue of the Virgin of Belém, also referred to as "Nossa Senhora de Bom Successo" (Our Lady of Good Success), "Nossa Senhora das Uvas" (Our Lady of the Grapes) or the "Virgem da Boa Viagem" (Virgin of Safe Homecoming) is depicted holding a child in her right hand and a bunch of grapes in her left.


title: Belém Tower

text: The tower is about wide and tall. The first-floor interior contains the "Sala do Governador" (Governor's Hall), an octagonal space that opens into the cistern, while in the northeast and northwest corners are corridors that link to the bartizans. A small door provides access via a spiral staircase to the subsequent floors. On the second floor, the "Sala dos Reis" (King's Hall) opens to the loggia overlooking the river, while a small corner fireplace extends from this floor to the third floor fireplace in the "Sala das Audiências" (Audience Hall). The ceilings of all three floors are covered in hollow concrete slabs. The fourth floor chapel has a vaulted rib ceiling with niches emblematic of the Manueline style, supported by carved corbels.


title: Anatomy of a Murder

text: Anatomy of a Murder is a 1959 American courtroom drama and crime film produced and directed by Otto Preminger. The screenplay by Wendell Mayes was based on the 1958 novel of the same name written by Michigan Supreme Court Justice John D. Voelker under the pen name of Robert Traver. Voelker based the novel on a 1952 murder case in which he was the defense attorney.


title: Anatomy of a Murder

text: The film stars James Stewart, Lee Remick, Ben Gazzara, Eve Arden, George C. Scott, Arthur O'Connell, Kathryn Grant, Brooks West (Arden's husband), Orson Bean, and Murray Hamilton. The judge was played by Joseph N. Welch, a real-life lawyer famous for dressing down Joseph McCarthy during the Army–McCarthy hearings. It has a musical score by Duke Ellington, who also appears in the film. It has been described by Michael Asimow, UCLA law professor and co-author of "Reel Justice: The Courtroom Goes to the Movies" (2006), as "probably the finest pure trial movie ever made".


title: Anatomy of a Murder

text: In 2012, the film was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".


title: Anatomy of a Murder

text: In the Upper Peninsula of Michigan, small-town lawyer Paul Biegler, a former district attorney who lost his re-election bid, spends most of his time fishing, playing the piano, and hanging out with his alcoholic friend and colleague Parnell McCarthy and sardonic secretary Maida Rutledge.


title: Anatomy of a Murder

text: One day, Biegler is contacted by Laura Manion, to defend her husband US Army Lieutenant Frederick "Manny" Manion, who has been arrested for the murder of innkeeper Bernard "Barney" Quill. Manion does not deny the murder, but claims that Quill raped his wife. Even with such a motivation, getting Manion cleared of murder would be difficult, but Manion claims to have no memory of the event, suggesting that he may be eligible for a defense of irresistible impulse—a version of a temporary insanity defense. It is strongly implied that Manion is pretending to insanity, having been guided to it as a potential defence by Biegler. Biegler's folksy speech and laid-back demeanor hide a sharp legal mind and a propensity for courtroom theatrics that keeps the judge busy maintaining control. However, the case for the defense does not go well, especially as local district attorney Mitch Lodwick is assisted by high-powered prosecutor Claude Dancer from the Attorney General's office.


title: Anatomy of a Murder

text: Furthermore, the prosecution tries at every instance to block any mention of Manion's motive for killing Quill. Biegler eventually manages to get the rape of Laura Manion into the record and Judge Weaver agrees to allow the matter to be part of the deliberations. During cross-examination, Dancer insinuates that Laura openly flirted with other men, including the man she claimed raped her. Psychiatrists give conflicting testimony to Manion's state of mind at the time that he killed Quill. Dancer says that Manion may have suspected Laura of cheating on him because he asked her, a Catholic, to swear on a rosary that Quill raped her. This raises doubt as to whether the act was consensual.


title: Anatomy of a Murder

text: Quill's estate is to be inherited by Mary Pilant, whom Dancer accuses of being Quill's mistress. McCarthy learns that Pilant is in fact Quill's daughter, a fact she is anxious to keep secret since she was born out of wedlock. Biegler, who is losing the case, tries to persuade Pilant that Al Paquette, the bartender who witnessed the murder, may know if Quill admitted to raping Laura but Paquette is covering this up, either because he loves Pilant or out of loyalty to Quill. Through Pilant, Biegler is unable to get Paquette to testify on behalf of Manion.


title: Anatomy of a Murder

text: During the trial, Laura claims that Quill tore off her underwear while raping her; the underwear wasn't found where she alleges the rape took place. Pilant, previously unaware of any details of the case, hears this during the trial and then tells Biegler and later testifies that she found the panties in the inn's laundry room the morning after the alleged rape. Biegler suggests Quill may have attempted to avoid suspicion by dropping the panties down the laundry chute located next to his room. Dancer tries to establish that Pilant's answers are founded on her jealousy. When Dancer asserts forcibly that Quill was Pilant's lover and that Pilant lied to cover this fact, Pilant shocks everyone by stating that Quill was her father. Manion is found "not guilty by reason of insanity". After the trial, Biegler decides to open a new practice, with a newly sober McCarthy as his partner.


title: Anatomy of a Murder

text: The next day, Biegler and McCarthy travel to the Manions' trailer park home to get Manion's signature on a promissory note which they hope will suffice as collateral for a desperately needed loan. It turns out the Manions have vacated the trailer park, the superintendent commenting that Laura Manion had been crying. Manion left a note for Biegler, indicating that his flight was "an irresistible impulse", the same justification Biegler used during the trial. Biegler states that Mary Pilant has retained him to execute Quill's estate; McCarthy says that working for her will be "poetic justice".


title: Anatomy of a Murder

text: On July 31, 1952, Lt. Coleman A. Peterson shot and killed Maurice Chenoweth in Big Bay, Michigan. Voelker was retained as defense attorney a few days later. The trial started on September 15, 1952, and Assistant Attorney General Irving Beattie assisted Marquette County Prosecuting Attorney Edward Thomas. Voelker used a rare version of the insanity defense called irresistible impulse that had not been used in Michigan since 1886. The jury deliberated for four hours on September 23, 1952, before returning a verdict of not guilty by reason of insanity. Two days later, after Peterson was examined by a psychiatrist who judged him sane, he was released. Peterson and his wife were divorced soon after the trial. Hillsdale Circuit Court Judge Charles O. Arch, Sr. tried the case because of the illness of a local judge.


title: Anatomy of a Murder

text: The film was shot in several locations in the Upper Peninsula of Michigan (Big Bay, Marquette, Ishpeming, and Michigamme). Some scenes were filmed in the Thunder Bay Inn in Big Bay, one block from the Lumberjack Tavern, the site of the 1952 murder that inspired much of the novel. The film was previewed on June 18, 1959, in Chicago, which "Variety" said was 21 days after filming had finished and a record for a big-budget film. It had its first screening at the Butler Theater in Ishpeming and the Nordic Theater in Marquette on June 29, 1959. The world premiere for the film was held on July 1, 1959, at the United Artists Theater in Detroit.


title: Anatomy of a Murder

text: The film examines the apparent fallibility of the human factor in jurisprudence. In various ways all of the human components—the counsels for defense and prosecution, the defendant and his wife, and the witnesses—have their own differing positions on what is right or wrong, and varying perspectives on integrity, justice, morality and ethics. The reliance on credibility of witnesses, and the "finding of facts" based upon those determinations, is the "Achilles heel" of the judicial process.


title: Anatomy of a Murder

text: One controversial legal issue in this film is possible witness coaching, a violation of legal canons. The only plausible legal defense Lt. Manion has—the insanity defense—is virtually spelled out to a befuddled Manion by his prospective counsel, who then temporarily suspends the conversation and suggests that Manion rethink his factual/legal position. Witness coaching by the prosecution is even more blatant as they call in other jail inmates awaiting sentencing to testify against Manion, which is portrayed as subornation of perjury to an extent. The first suggests that the defendant may be concealing the truth and manipulating his story in order to obtain the best possible verdict, and the latter that the prosecution dangled a possible lighter sentence through plea bargain as an incentive to perjury.


title: Anatomy of a Murder

text: The language used during the film startled Chicago, Illinois Mayor Richard J. Daley, and his police commissioner. As a result, the film was temporarily banned in the heavily Catholic city. Preminger filed a motion in federal court in Illinois and the mayor's decision was overturned. The film was allowed to be exhibited after the court determined that the clinical language during the trial was realistic and appropriate within the film's context. "Variety" claimed that the film contained words never before heard in American films with the Motion Picture Production Code seal such as "contraceptive", (sexual) "climax" and "spermatogenesis".


title: Anatomy of a Murder

text: In another federal lawsuit in Chicago, the daughter of the real-life murder victim from the 1952 case sued Dell Publishing and Columbia Pictures in July 1960 for libel over accusations that the book and movie "followed [the actual trial] too closely" and portrayed the two women in an unflattering light; the suit was dismissed less than a year later in May 1961.


title: Anatomy of a Murder

text: "Anatomy of a Murder" has been well received by members of the legal and educational professions. In 1989, the American Bar Association rated this as one of the 12 best trial films of all time. In addition to its plot and musical score, the article noted: "The film's real highlight is its ability to demonstrate how a legal defense is developed in a difficult case. How many trial films would dare spend so much time watching lawyers do what many lawyers do most (and enjoy least)—research?" The film has also been used as a teaching tool in law schools, as it encompasses (from the defense standpoint) all of the basic stages in the U.S. criminal justice system from client interview and arraignment through trial. The film was listed as 4 of 25 "Greatest Legal Movies" by the American Bar Association.


title: Anatomy of a Murder

text: The film grossed an estimated $11 million generating $5.5 million in theatrical rentals in the U.S. and Canada. It earned rentals of $8 million worldwide.


title: Anatomy of a Murder

text: Film critics have noted the moral ambiguity, where a small town lawyer triumphs by guile, stealth and trickery. The film is frank and direct. Language and sexual themes are explicit, at variance with the times (and other films) when it was produced. The black and white palette is seen as a complement to Michigan's harsh Upper Peninsula landscape. The film is "<nowiki>[m]</nowiki>ade in black-and-white but full of local color".


title: Anatomy of a Murder

text: Bosley Crowther, film critic for "The New York Times" said, "After watching an endless succession of courtroom melodramas that have more or less transgressed the bounds of human reason and the rules of advocacy, it is cheering and fascinating to see one that hews magnificently to a line of dramatic but reasonable behavior and proper procedure in a court. Such a one is "Anatomy of a Murder", which opened at the Criterion and the Plaza yesterday. It is the best courtroom melodrama this old judge has ever seen... . Outside of the fact that this drama gets a little tiring in spots—in its two hours and forty minutes, most of which is spent in court—it is well nigh flawless as a picture of an American court at work, of small-town American characters and of the average sordidness of crime."


title: Anatomy of a Murder

text: "Time" felt that it was well-paced, well-acted, and that the explicit language was warranted within the film's context.


title: Anatomy of a Murder

text: In June 2008, the American Film Institute revealed AFI's 10 Top 10, the best 10 films in 10 "classic" American film genres, after polling over 1,500 people from the creative community. "Anatomy of a Murder" was selected as the seventh best film in the courtroom drama genre.


title: Anatomy of a Murder

text: Rotten Tomatoes, a review aggregator, reports that 100% of 50 surveyed critics gave the film a positive review; the average rating was 8.70/10. The site's consensus states, "One of cinema's greatest courtroom dramas, "Anatomy of a Murder" is tense, thought-provoking, and brilliantly acted, with great performances from James Stewart and George C. Scott."


title: Anatomy of a Murder

text: The jazz score of "Anatomy of a Murder" was composed by Duke Ellington and Billy Strayhorn and played by Ellington's orchestra. Several of Ellington band's sidemen, including Jimmy Hamilton, Jimmy Johnson, Ray Nance, and Jimmy Woode appear, and Ellington himself plays the character Pie Eye.


title: Anatomy of a Murder

text: Mervyn Cooke, in the "History of Film Music", asserts that despite being heard "in bits and pieces" the score "contains some of his most evocative and eloquent music... and beckons with the alluring scent of a femme fatale." Including small pieces by Billy Strayhorn, film historians recognize it "as a landmark—the first significant Hollywood film music by African Americans comprising non-diegetic music, that is, music whose source is not visible or implied by action in the film, like an on-screen band." The score avoids cultural stereotypes which previously characterized jazz scores and "rejected a strict adherence to visuals in ways that presaged the New Wave cinema of the '60s."


title: Anatomy of a Murder

text: The soundtrack album, containing 13 tracks, was released by Columbia Records on May 29, 1959. A CD was released on April 28, 1995, and reissued by Sony in a deluxe edition in 1999.


title: Anatomy of a Murder

text: "Detroit Free Press" music critic Mark Stryker concluded: "Though indispensable, I think the score is too sketchy to rank in the top echelon among Ellington-Strayhorn masterpiece suites like "Such Sweet Thunder" and "The Far East Suite", but its most inspired moments are their equal." The score employs a "handful of themes, endlessly recombined and re-orchestrated. Ellington never wrote a melody more seductive than the hip-swaying "Flirtibird", featuring the "irresistibly salacious tremor" by Johnny Hodges on the alto saxophone." A stalking back-beat barely contains the simmering violence of the main title music" The score is heavily dipped in "the scent of the blues and Ellington's orchestra bursts with color."


title: Anatomy of a Murder

text: The AllMusic review by Bruce Eder awarded the album 3 stars and called it "a virtuoso jazz score—moody, witty, sexy, and—in its own quiet way—playful".


title: Anatomy of a Murder

text: Ellington's score won three Grammy Awards in 1959, for "Best Performance by a Dance Band", "Best Musical Composition First Recorded and Released in 1959" and "Best Sound Track Album".


title: Anatomy of a Murder

text: After Traver's novel was published, St. Martin's Press planned to have it adapted for the stage, intending a Broadway production, which would then be made into a film. Before he died in December 1957, John Van Druten wrote a rough draft of the play adaptation. Some time after that, the publisher then made the film rights available, and these were purchased by Otto Preminger.


title: Anatomy of a Murder

text: Eventually, Traver's book was adapted for the stage in 1963 by Elihu Winer. It premiered at the Mill Run Theater in suburban Chicago, and was published in 1964 by Samuel French.


title: Anatomy of a Murder

text: The making of the film is the subject of the song, "Marquette County, 1959", by Great Lakes Myth Society. The lyrics read: "Jimmy Stewart came to Marquette County in 1959/ And he was shot for two months there/ And all the pines wept stardust for a while/ And the Duke would play his soundtrack there/ As Preminger had cast him in the film/ His character was Pie-Eye".


title: Anatomy of a Murder

text: On June 29, 2009, journalist and filmmaker John Pepin debuted "Anatomy '59: The Making of a Classic Motion Picture" on public television stations across the state of Michigan. The anchor station for those broadcasts was WNMU-TV in Marquette, Michigan. The documentary reviews the original incident that spawned the bestselling book "Anatomy of a Murder" by Robert Traver and the making of Otto Preminger's motion picture. Pepin's documentary debuted on the 50th anniversary of the world premiere of "Anatomy of a Murder" in Ishpeming and Marquette, Michigan; the date was also the birthday of John Voelker. Pepin grew up on Barnum Street in Ishpeming, the same street where Voelker lived and where the Mather Inn was located, which is where the stars of Preminger's film stayed during production. "Anatomy '59" features interviews with "Anatomy of a Murder" actors still alive in 2009, including Ben Gazzara, Kathryn Grant-Crosby, Orson Bean and Don Ross.


title: Anatomy of a Murder

text: "Anatomy of a Murder" was one of 25 films added to the National Film Registry in 2012. "The annual selections by the Library of Congress span more than a century of American filmmaking."


title: Gaucho (album)

text: Gaucho is the seventh studio album by the American rock band Steely Dan, released on November 21, 1980, by MCA Records. The sessions for "Gaucho" represent the band's typical penchant for studio perfectionism and obsessive recording technique. To record the album, the band used at least 42 different musicians, spent over a year in the studio, and far exceeded the original monetary advance given by the record label. In 1981, the album won the Grammy Award for Best Engineered Non-Classical Recording and received Grammy nominations for Album of the Year and Best Pop Performance by a Duo or Group with Vocals.


title: Gaucho (album)

text: During the two-year span in which the album was recorded, the band was plagued by a number of creative, personal and professional problems. MCA, Warner Bros. and Steely Dan had a three-way legal battle over the rights to release the album. After it was released, jazz musician Keith Jarrett was given a co-writing credit on the title track after threatening legal action over plagiarism of Jarrett's song "'Long As You Know You're Living Yours".


title: Gaucho (album)

text: "Gaucho" marked a significant stylistic change for the band, introducing a more minimal, groove and atmosphere-based format. The harmonically complex chord changes that were a distinctive mark of earlier Steely Dan songs are less prominent on "Gaucho", with the record's songs tending to revolve around a single rhythm or mood, although complex chord progressions were still present particularly in "Babylon Sisters" and "Glamour Profession". "Gaucho" proved to be Steely Dan's final studio album before a 20-year hiatus from the recording industry.


title: Gaucho (album)

text: Exceptional difficulties plagued the album's production. By 1978, Donald Fagen and Walter Becker had established themselves as the only two permanent members of Steely Dan, using a revolving cast of session musicians to record the songs they wrote together. However, the pair's working relationship began to strain, largely because of Becker's increasing drug use.


title: Gaucho (album)

text: During the course of the "Gaucho" sessions, Becker was hit by a car late one Saturday night while walking home to his apartment on the Upper West Side. Becker managed to push the woman he was out of harm's way, but sustained multiple fractures in one leg, a sprain in the other leg, and other injuries. During his six-month recovery, he suffered from secondary infections. While Becker was in the hospital, he and Fagen continued their musical collaborations via telephone.


title: Gaucho (album)

text: Becker's personal problems continued to mount when his girlfriend, Karen Roberta Stanley, died of a drug overdose at his home on January 30, 1980. Her family sued him for $17.5 million in January 1981, claiming that he had introduced the woman to cocaine, morphine, barbiturates, and heroin. The court later ruled in Becker's favor.


title: Gaucho (album)

text: According to "Stylus Magazine"s Mike Powell, "Gaucho" combines "bitter, poetic cynicism with freewheeling jazz-rock", while Stephen Thomas Erlewine from AllMusic says it "essentially replicates the smooth jazz-pop of "Aja", but with none of that record's dark, seductive romance or elegant aura". Similarly, rock historian Joe Stuessy suggests it is one in a series of Steely Dan albums that showed a progression of jazz influences in the band's sound, which was often described as "jazz-rock fusion". Music journalist and broadcaster Paul Sexton writes that, while "Aja" had "announced their ever-greater exploration of jazz influences", "Gaucho" is "their yacht rock masterpiece". In connection with the latter genre, Timothy Malcolm from "Houstonia" magazine says the album features "a number of yachty delights", while Erlewine highlights the title track as exemplary of the genre. Patrick Hosken from MTV News says that, like "Aja", "Gaucho" shows how "great yacht rock is also more musically ambitious than it might seem, tying blue-eyed soul and jazz to funk and R&B".


title: Gaucho (album)

text: Hal Leonard's "Best of Steely Dan" explains that "Gaucho" is "a concept album of seven interrelated tales about would-be hipsters." The lyrics of "Hey Nineteen" are about an aging hipster attempting to pick up a girl who is so young that she does not recognize "'Retha Franklin" playing on the stereo. The song closes with the ambiguous line, "The Cuervo Gold, the fine Colombian, make tonight a wonderful thing", leaving it up to the listener whether the narrator is consuming tequila and drugs with the love interest, or if he is in fact alone.


title: Gaucho (album)

text: Stewart Mason of AllMusic says that "Time Out of Mind" is "a barely veiled song about heroin, specifically a young man's first experience with the drug at the hands of a pretentious, pseudo-religious crank talking of 'chasing the dragon' with the 'mystical sphere direct from Lhasa.'" According to Ian MacDonald, "Two songs are about hookers, two more concern the doings of coke dealers, and a fifth depicts the denouement of a seedy marital dispute. What redeems it all is the humour and artistry. Lyrics exude class as well as underclass, while the music, whatever its guise or disguise, is immaculate".


title: Gaucho (album)

text: Keith Jarrett sued Becker and Fagen for copyright infringement over the title track of the album, claiming it plagiarized "'Long As You Know You're Living Yours" from his 1974 album "Belonging". As a result, Jarrett has since been included as a co-author of the track. In an interview after "Gaucho" was released, Fagen said that he loved the Jarrett track and had been strongly influenced by it.


title: Gaucho (album)

text: With 1977's "Aja", the duo had become accustomed to recording with (largely) Los Angeles-based session musicians. Sessions for "Gaucho" began in New York City during 1978. The transition to using New York City players during the "Gaucho" sessions proved difficult, because the musicians were unenthusiastic about Becker and Fagen's obsessive, perfectionist recording style.


title: Gaucho (album)

text: Fagen and Becker hired Mark Knopfler to play the guitar solo on "Time Out of Mind" after hearing him play on Dire Straits' hit single "Sultans of Swing". Several hours of Knopfler's playing were recorded at the session, but his contributions as heard on the record are limited to around forty seconds.


title: Gaucho (album)

text: The album's mixing sessions proved to be just as difficult as the recording sessions. It took Becker, Fagen, Nichols and Katz more than 55 attempts to complete a satisfactory mix of the 50-second fade-out of "Babylon Sisters".


title: Gaucho (album)

text: Even though the session players hired for "Gaucho" were amongst the most talented from both the East and West Coast session fraternities, Fagen and Becker were still not satisfied with the basic tracks for some of the songs, particularly with regard to the timing of the drum tracks. In a 2006 interview for "Sound On Sound Magazine", Donald Fagen stated that he and Becker told recording engineer Roger Nichols:


title: Gaucho (album)

text: According to Ken Micallef in an article in "Modern Drummer", the title song's drum track was assembled from 46 different takes. The drummer on the session, Jeff Porcaro, is quoted as saying:


title: Gaucho (album)

text: Drummer Bernard Purdie plays his signature half-time shuffle beat, the Purdie Shuffle, on "Babylon Sisters".


title: Gaucho (album)

text: "The Second Arrangement" had been a favorite of producer Gary Katz and Nichols. In late December 1979, after weeks of working on a particular recording of the track, approximately three-quarters of the song was accidentally erased by an assistant engineer who had been asked by Katz to ready the track for listening. The band attempted to re-record the track, but eventually abandoned the song entirely.


title: Gaucho (album)

text: Steely Dan biographer Brian Sweet has written that the group abandoned the song in favor of focusing on "Third World Man". "The Second Arrangement" was never played live by Steely Dan until a rarities show on September 17, 2011, and a studio recording of the song remains unreleased. However, a handful of demo and outtake recordings of the song exist in bootleg form.


title: Gaucho (album)

text: In addition to "The Second Arrangement", a number of songs were written for the album which were not included in the final release. Some of them were included on a bootleg titled "The Lost Gaucho", which features recordings from early in the sessions for the album. Song titles include "Kind Spirit", "Kulee Baba", "The Bear" and "Talkin' About My Home", as well as "The Second Arrangement". An early version of "Third World Man", with alternate lyrics, is included under the title "Were You Blind That Day". That recording dates from the "Aja" sessions.


title: Gaucho (album)

text: In 2020, Cimchie Nichols, the daughter of engineer Roger Nichols, said that the family had discovered three cassettes that may include working mixdowns of "The Second Arrangement."


title: Gaucho (album)

text: During a guitar clinic in 2011, Larry Carlton said of "Third World Man": "When "Billboard" magazine came out ... about Gaucho, it's writing about the news 'Steely Dan released ... bla bla bla ... and great guitar solo by Larry Carlton', and I said, 'but I didn't play on "Gaucho"!, they'd cut it in New York, I didn't play on it!'. So I found out later: they had finished mixing in New York, and one of the second engineers erased one of their master tracks. So "Third World Man" was in the can from "The Royal Scam" and they had to reach back into the old tapes and find something to finish the album, and that's how I ended up on "Gaucho" playing "Third World Man".


title: Gaucho (album)

text: The cover art is based upon a wall plaque entitled "Guardia Vieja – Tango" (Old Guard – Tango), located in a southside Buenos Aires promenade known as "Caminito", by Argentine artist .


title: Gaucho (album)

text: Just prior to the album's release, the band members had another argument with MCA over the retail list price. MCA made Steely Dan, along with Tom Petty and the Heartbreakers' "Hard Promises" and the Olivia Newton-John/Electric Light Orchestra "Xanadu" soundtrack, a test case for its new "superstar pricing" policy, whereby new albums by top-selling artists would sell for $9.98, one dollar more than those of other artists. Steely Dan opposed this idea, fearful that the fans would place blame on them.


title: Gaucho (album)

text: The album was greeted with mostly positive reviews. "Rolling Stone"'s Ariel Swartley said of the album: "After years of hibernation in the studio, the metamorphosis that began with "The Royal Scam" is complete. Steely Dan have perfected the aesthetic of the tease." "The New York Times" gave "Gaucho" a positive review, later deeming it the best album of 1980, beating out Talking Heads’ "Remain in Light" and Joy Division's "Closer". The album also received a positive review from the "Montreal Gazette".


title: Gaucho (album)

text: Not all reviews were positive. The second edition of "The Rolling Stone Album Guide" gave "Gaucho" a rating of 1 star out of 5; critic Dave Marsh called it "the kind of music that passes for jazz in Holiday Inn lounges, with the kind of lyrics that pass for poetry in freshman English classes." Pete Bishop of "The Pittsburgh Press" found it "too well-crafted, too artificially sophisticated", and lacking in spontaneity. "The Village Voice"s Robert Christgau remarked, "Even the song with Aretha in it lends credence to rumors that the LP was originally entitled "Countdown to Lethargy"." In 2000 it was voted number 504 in Colin Larkin's "All Time Top 1000 Albums".


title: Gaucho (album)

text: In a retrospective review for AllMusic, Stephen Thomas Erlewine wrote that "Gaucho", while sonically similar to "Aja", features musical performances that have been overly rehearsed to the point of lacking emotional resonance, as well as inferior songwriting, excepting the highlights "Babylon Sisters", "Time Out of Mind" and "Hey Nineteen", which "make the remainder of the album's glossy, meandering fusion worthwhile". David Sakowski of "PopMatters" reappraised the album as a "classic" that was largely "lost in the shadow of "Aja" and the changing tides of music".


title: Gaucho (album)

text: Following the release of "Gaucho" in 1980, jazz pianist Keith Jarrett sued the band for copyright infringement. "Gaucho's" title track, credited to Donald Fagen and Walter Becker, bore a resemblance to Jarrett's "Long As You Know You're Living Yours" from Jarrett's 1974 album "Belonging". In an interview with "Musician" magazine, Becker and Fagen were asked about the similarity between the two pieces of music, and Becker told "Musician" that he loved the Jarrett composition while Fagen said they had been influenced by it. After their comments were published, Jarrett sued, and Becker and Fagen were legally obliged to add his name to the credits and provide Jarrett with publishing royalties.


title: Gaucho (album)

text: The album reached #9 on the U.S. Album Chart and was certified Platinum. "Hey Nineteen" reached #10 on the U.S. Singles Chart, and went to #1 in Canada. The album reached #27 on the UK Albums Chart.


title: Marwari people

text: The Marwari or Marwadi (Hindi: मारवाड़ी, Urdu: مارواڑی) are an Indian ethnic group that originate from the Rajasthan region of India. Their language, also called Marwari, comes under the umbrella of Rajasthani languages, which is part of the Western Zone of Indo-Aryan languages.


title: Marwari people

text: They have been a highly successful business community, first as inland traders during the era of Rajput kingdoms, and later also as investors in industrial production and other sectors. Today, they control many of the country's largest media groups. Although spread throughout India, historically they have been most concentrated in Kolkata, Mumbai, Chennai, Delhi, Nagpur, Pune and the hinterlands of central and eastern India.


title: Marwari people

text: The term "Marwari" once referred to the area encompassed by the former princely state of Marwar, also called the Jodhpur region of southwest Rajasthan in India. The Jodhpur region includes the present districts of Barmer, Jalore, Jodhpur, Nagaur, Pali and parts of Sikar. It has evolved to be a designation for the Rajasthani people in general but it is used particularly with reference to certain jātis that fall within the Bania community. The most prominent among these communities, are the Agrawals, Khandelwals, Maheshwaris and Oswals. It is possible that the association of the "Marwari" term with Jodhpur owes more to the high status of that place in pre-independence India.


title: Marwari people

text: Dwijendra Tripathi believes that the term "Marwari" was probably used by the traders only when they were outside their home region; that is, by the diaspora. Anne Hardgrove also supports this argument, saying that the Marwari identity could only exist in the context of a diaspora who came "from" somewhere and that until they migrated they had no such designation.


title: Marwari people

text: Marwari traders have historically been migratory in habit. The possible causes of this trait include the proximity of their homeland to the major Ganges - Yamuna trade route; movement to escape famine; and the encouragement given to them by various rulers of northern India who saw advantages in having their skills in banking and finance.


title: Marwari people

text: The pattern of Marwari migration became increasingly divergent following the decline in wars between Rajput kingdoms, which the Marwaris had helped to finance, and the decreasing influence of the community over the North Indian caravan trading routes that resulted from the British establishing themselves in the region. The changed focus of migration was also encouraged by the British, who established or patronised new trading routes and centres, as well as by the decline in the political significance of the Rajput courts whose famed conspicuous consumption had been supported by Marwari money. The community welcomed the relative safety that the British presence offered, as well as the commercial and legal frameworks that they provided and which were more favourable to Marwari activities than the systems prevalent during the earlier period of Mughal and Rajput rule.


title: Marwari people

text: After the decline of Mughal authority, Marwari traders, bankers and financiers migrated to the growing British power in Calcutta. There were particularly significant population shifts to Bombay between 1835-1850 and Kolkata from the 1870s, as well as to Madras.


title: Marwari people

text: A considerable number of Marwari business groups made their fortune on speculative markets in the nineteenth and early twentieth century.


title: Marwari people

text: Although maintaining close and public ties with the British authorities, members of the Marwari business community were early financial supporters of the Indian National Congress, often in secret.


title: Marwari people

text: In 1956, the All-India Marwari Federation opposed a linguistic organisation of states whilst buying up regional language newspapers in Maharashtra, Tamil Nadu and Andhra Pradesh. Today, they control many of the country's largest media groups.


title: Marwari people

text: The community's influence over the Indian economy declined following the country's 1991 economic reforms. From a peak of controlling 24 per cent of economic activity in 1990, it had fallen to less than 2 per cent in 2000. This reflects the growth of new industries outside of commodities trading and primary production. The figure for 2000 is considered to be lower than the position in 1939, when the community first began its resurgence.


title: Marwari people

text: Marwari, or Marrubhasha, as it is referred to by Marwaris, is the traditional, historical, language of the Marwari ethnicity. The Marwari language is closely related to the Rajasthani language. The latter evolved from the Old Gujarati (also called "Old Western Rajasthani", "Gujjar Bhakha" or "Maru-Gurjar"), language spoken by the people in Gujarat and Rajasthan. It has been noted that throughout the state of Rajasthan, people avoid identifying their language by name, preferring to identify themselves as speaking "Rajasthani" with Marwari literature and taught as Rajasthani until secondary level.


title: Marwari people

text: Marwaris have been known for a tightly knit social solidarity, described by Selig Harrison in 1960 as "indissoluble under the impact of the strongest regional solvents". According to Hardgrove, "The main duty for Marwari women, it would seem, is to provide a stable household life for their husbands, sons and brothers-in-law", although she acknowledges that some such women have in recent years been attempting to carve out roles in the wider world through engagement in charitable ventures and even running their own businesses.


title: Biot–Savart law

text: In physics, specifically electromagnetism, the Biot–Savart law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb's law in electrostatics. When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.


title: Biot–Savart law

text: The Biot–Savart law is used for computing the resultant magnetic field B at position r in 3D-space generated by a flexible current "I" (for example due to a wire). A steady (or stationary) current is a continual flow of charges which does not change with time and the charge neither accumulates nor depletes at any point. The law is a physical example of a line integral, being evaluated over the path "C" in which the electric currents flow (e.g. the wire). The equation in SI units is


title: Biot–Savart law

text: The formulations given above work well when the current can be approximated as running through an infinitely-narrow wire. If the conductor has some thickness, the proper formulation of the Biot–Savart law (again in SI units) is:


title: Biot–Savart law

text: where formula_1 is the vector from dV to the observation point formula_2, formula_3 is the volume element, and formula_4 is the current density vector in that volume (in SI in units of A/m).


title: Biot–Savart law

text: In the case of a point charged particle "q" moving at a constant velocity v, Maxwell's equations give the following expression for the electric field and magnetic field:


title: Biot–Savart law

text: where formula_10 is the unit vector pointing from the current (non-retarded) position of the particle to the point at which the field is being measured, and θ is the angle between formula_11 and formula_12.


title: Biot–Savart law

text: These equations were first derived by Oliver Heaviside in 1888. Some authors call the above equation for formula_7 the "Biot–Savart law for a point charge" due to its close resemblance to the standard Biot–Savart law. However, this language is misleading as the Biot–Savart law applies only to steady currents and a point charge moving in space does not constitute a steady current.


title: Biot–Savart law

text: The Biot–Savart law can be used in the calculation of magnetic responses even at the atomic or molecular level, e.g. chemical shieldings or magnetic susceptibilities, provided that the current density can be obtained from a quantum mechanical calculation or theory.


title: Biot–Savart law

text: The Biot–Savart law is also used in aerodynamic theory to calculate the velocity induced by vortex lines.


title: Biot–Savart law

text: In the aerodynamic application, the roles of vorticity and current are reversed in comparison to the magnetic application.


title: Biot–Savart law

text: In Maxwell's 1861 paper 'On Physical Lines of Force', magnetic field strength H was directly equated with pure vorticity (spin), whereas B was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability μ to be a measure of the density of the vortex sea. Hence the relationship,


title: Biot–Savart law

text: B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the vortices.


title: Biot–Savart law

text: The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the B vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.


title: Biot–Savart law

text: In aerodynamics the induced air currents form solenoidal rings around a vortex axis. Analogy can be made that the vortex axis is playing the role that electric current plays in magnetism. This puts the air currents of aerodynamics (fluid velocity field) into the equivalent role of the magnetic induction vector B in electromagnetism.


title: Biot–Savart law

text: In electromagnetism the B lines form solenoidal rings around the source electric current, whereas in aerodynamics, the air currents (velocity) form solenoidal rings around the source vortex axis.


title: Biot–Savart law

text: Hence in electromagnetism, the vortex plays the role of 'effect' whereas in aerodynamics, the vortex plays the role of 'cause'. Yet when we look at the B lines in isolation, we see exactly the aerodynamic scenario insomuch as B is the vortex axis and H is the circumferential velocity as in Maxwell's 1861 paper.


title: Biot–Savart law

text: "In two dimensions", for a vortex line of infinite length, the induced velocity at a point is given by


title: Biot–Savart law

text: where is the strength of the vortex and "r" is the perpendicular distance between the point and the vortex line. This is similar to the magnetic field produced on a plane by an infinitely long straight thin wire normal to the plane.


title: Biot–Savart law

text: This is a limiting case of the formula for vortex segments of finite length (similar to a finite wire):


title: Biot–Savart law

text: In a magnetostatic situation, the magnetic field B as calculated from the Biot–Savart law will always satisfy Gauss's law for magnetism and Ampère's law:


title: Biot–Savart law

text: In a "non"-magnetostatic situation, the Biot–Savart law ceases to be true (it is superseded by Jefimenko's equations), while Gauss's law for magnetism and the Maxwell–Ampère law are still true.


title: Biot–Savart law

text: Initially, the Biot–Savart law was discovered experimentally, then this law was derived in different ways theoretically. In The Feynman Lectures on Physics, at first, the similarity of expressions for the electric potential outside the static distribution of charges and the magnetic vector potential outside the system of continuously distributed currents is emphasized, and then the magnetic field is calculated through the curl from the vector potential. Another approach involves a general solution of the inhomogeneous wave equation for the vector potential in the case of constant currents. The magnetic field can also be calculated as a consequence of the Lorentz transformations for the electromagnetic force acting from one charged particle on another particle. Two other ways of deriving the Biot–Savart law include: 1) Lorentz transformation of the electromagnetic tensor components from a moving frame of reference, where there is only an electric field of some distribution of charges, into a stationary frame of reference, in which these charges move. 2) the use of the method of retarded potentials.


title: Carolina Herrera

text: Carolina Herrera (born María Carolina Josefina Pacanins y Niño; 8 January 1939) is a Venezuelan-American fashion designer known for her personal style, and for dressing various First Ladies, including Jacqueline Onassis, Laura Bush, Michelle Obama, and Melania Trump.


title: Carolina Herrera

text: María Carolina Josefina Pacanins y Niño was born on 8 January 1939, in Caracas, Venezuela, to Guillermo Pacanins Acevedo, an air force officer and former governor of Caracas, and María Cristina Niño Passios. Her socialite grandmother introduced her to the world of fashion, taking young Carolina to shows by Balenciaga and buying her outfits at Lanvin and Dior. She has said, "My eye was accustomed to seeing pretty things."


title: Carolina Herrera

text: In 1965, Herrera began her career working as a publicist for Emilio Pucci, a Florentine Marquis himself and a close family friend. She began working at Pucci's Caracas boutique, and moved to New York in 1980. Frequently associating with Mick and Bianca Jagger and Andy Warhol, at Studio 54, she became well known for her dramatic style. She first appeared on the International Best Dressed List in 1972, then was elected to its Hall of Fame in 1980. In 1981, her friend Diana Vreeland, then Editor-in-Chief of "Vogue" suggested that Carolina design a clothing line. She did so, having samples made in Caracas, and debuted her collection at Manhattan's Metropolitan Club to critical acclaim. A well known Park Avenue boutique, Martha's, agreed to showcase her clothing in their prominent windows. Upon this initial success, she returned to Caracas and raised capital to fund a more formal launch. Her first runway show in 1980 included future supermodel Iman. Carolina Herrera presents her Ready-to-Wear Collection semiannually at Mercedes-Benz Fashion Week in New York.


title: Carolina Herrera

text: The company has been based in New York City since 1980, and in 1981 the brand received recognition from several key publications, including "Women's Wear Daily" and "Tatler", with particular early attention to her well designed sleeves. A few of her most notable clients have included Jacqueline Kennedy Onassis, who asked her to design the dress for her daughter Caroline's wedding, Diana, Duchess of Cadaval, who asked her to design the dress for her marriage with Prince Charles-Philippe of Orléans, Duke of Anjou, and actress Renée Zellweger.


title: Carolina Herrera

text: In the late 1980s, Spanish fragrance company Puig licensed the Carolina Herrera name to develop and market a line of perfumes. In 1995, the firm acquired the Carolina Herrera fashion business, retaining her as Creative Director. In 2008, they launched a ready-to-wear brand called CH Carolina Herrera; as of 2012, there were 18 Carolina Herrera and CH Carolina Herrera boutiques in the world, and her lines were carried in 280 stores in 104 countries. As of 2011, her daughters Carolina Jr. and Patricia Lansing participated in the creative direction and design. In February 2016, it was reported by "WWD" that the fragrance side of the business had more than 25,000 points of sale across the globe while the CH brand included 129 freestanding stores.


title: Carolina Herrera

text: In 2015, the first advert for the brand was released, featuring models Elisabeth Erm and Joséphine Le Tutour.


title: Carolina Herrera

text: In July 2016, Herrera announced the release of her new women's fragrance to be available for purchase in September, her biggest fragrance launch in 14 years. The scent is called 'Good Girl' and Karlie Kloss is the face of the fragrance.


title: Carolina Herrera

text: In 2018, Herrera showed her last line for her eponymous brand and handed creative directorship of the brand over to Wes Gordon.


title: Carolina Herrera

text: In 2008, Herrera was awarded the Geoffrey Beene Lifetime Achievement Award from the Council of Fashion Designers of America, and "Womenswear Designer of the Year" in 2004. Herrera is a recipient of The International Center in New York's Award of Excellence as well as Spain's Gold Medal for Merit in the Fine Arts, which was presented to her in 2002 by King Juan Carlos I. She was awarded the Gold Medal of the Queen Sofía Spanish Institute in 1997.


title: Carolina Herrera

text: She received the Fashion Group International Superstar Award, the Style Awards Designer of the Year in 2012 and the "Mercedes-Benz Presents" title for her 2011 collection. She has been on the cover of "Vogue" seven times.


title: Carolina Herrera

text: Since 2004, she has been a member of the board of directors of jewelry designer Mimi So, and since 1999 on the board of the CFDA.


title: Carolina Herrera

text: In 2005, she received the Golden Plate Award of the American Academy of Achievement during the International Achievement Summit in New York City.


title: Carolina Herrera

text: In 1957, at the age of 18, Herrera married Guillermo Behrens Tello, a Venezuelan landowner. Before their eventual divorce in 1964, they became the parents of two daughters:


title: Carolina Herrera

text: In 1968, in Caracas, she married Reinaldo Herrera Guevara, who had inherited the Spanish title The in 1962 upon his father's death. Reinaldo was the host of "Buenos Días", a Venezuelan morning-television news program and the elder son of Don Reinaldo Herrera Uslar, 4th Marquis of Torre Casa, a prominent Venezuelan sugarcane plantation owner, aristocrat and art collector. Therefore, by marriage, Carolina held the title The Marquise consort of Torre Casa, until it was retracted in 1992, as Reinaldo had issued no son. Her husband is a special-projects editor of "Vanity Fair" magazine. Together, they have two daughters, and six grandchildren, including:


title: Earl Hindman

text: Earl John Hindman (; October 20, 1942  – December 29, 2003) was an American actor, best known for his role as the kindly unseen neighbor Wilson W. Wilson, Jr. on the television sitcom "Home Improvement" (1991–99).


title: Earl Hindman

text: Hindman was born in Bisbee, Arizona, the son of Eula and Burl Latney Hindman, who worked in the oil pipeline business. He studied acting at the University of Arizona.


title: Earl Hindman

text: Hindman played villains in two 1974 thrillers, "The Taking of Pelham One Two Three" and "The Parallax View". He also appeared in the films "Who Killed Mary What's 'Er Name?" (1971), "Greased Lightning" (1977), "The Brink's Job" (1978), "Taps" (1981), "Murder in Coweta County" (1983), and played the part of J.T. in the Lawrence Kasdan film "Silverado" (1985).


title: Earl Hindman

text: Hindman's most famous pre-"Home Improvement" role was as Bob Reid in "Ryan's Hope". He played the role from 1975 to 1984 and later returned for its final episodes in 1988–89. Hindman's wife (Molly McGreevy) was also on the soap 1977–81 as Polly Longworth, best friend to media tycoon Rae Woodard.


title: Earl Hindman

text: On May 21, 1976, Hindman married Molly McGreevy, with whom he later acted on "Ryan's Hope". McGreevey later became an Episcopal priest.


title: Damian Chapa

text: Chapa's ancestry is of Mexican, Italian, German and Native American descent. He now calls San Antonio, Texas home.


title: Damian Chapa

text: Chapa played the part of evangelist Leroy Jenkins in the 2002 film "The Calling". Perhaps his most notable film role is that of Miklo Velka in Taylor Hackford's "Blood In Blood Out". He appeared as Ken Masters in Raúl Juliá's final film "Street Fighter", based on the video game "".


title: Damian Chapa

text: In 2011 Damian Chapa was arrested in Madrid and later transferred to a Munich jail to await a court appearance on a charge of the alleged rape of former girlfriend Roxanna Foell. He was subsequently released and exonerated and paid several thousand euros by the German government in September 2011 after being held in custody wrongfully for seven weeks. Chapa has apparently since filed a $1.3 million lawsuit for damages against Foell.


The Queen Elizabeth II Platinum Jubilee Medal () or The Queen's Platinum Jubilee Medal is a commemorative medal created to mark the 70th anniversary of Queen Elizabeth II's accession in 1952.


title: Queen Elizabeth II Platinum Jubilee Medal

text: The medal is being awarded in the United Kingdom to people who work in public service, including the Armed Forces, the emergency services, and the prison services. In Canada, six of the country's 10 provinces are issuing their own medals; the first time in Canadian history that a royal occasion has been commemorated on provincial medals. Outstanding volunteers, members of the Canadian Armed Forces and emergency services, and other people who have made a positive impact on society have been deemed eligible to receive the medals, with particular focus in some provinces on the response to the COVID-19 pandemic, reconciliation with First Nations and Inuit, and protection of the environment. The Queen's Caribbean realms have also instituted a medal programme for the Platinum Jubilee. Examples of those eligible there are members of the emergency services who responded during hurricanes and the COVID-19 pandemic and of the defence and police forces.


text: The medal, made of nickel silver, has the Ian Rank-Broadley effigy of Her Majesty on the obverse. The reverse shows the helm, crest, and mantling of the royal coat of arms of the United Kingdom used outside Scotland. The ribbon has silver edges, representing the Silver Jubilee; the blue from the ribbon of the Golden Jubilee medal; and the red from the Diamond Jubilee ribbon. Worcestershire Medal Service is manufacturing the medal.


text: The government of Canada opted not to produce a platinum jubilee medal, despite having issued medals for royal jubilees since at least Queen Victoria's in 1897. The decision was criticized by the Royal Canadian Legion and the Monarchist League of Canada. In response, the provinces of Prince Edward Island, Nova Scotia, New Brunswick, Manitoba, Alberta, and Saskatchewan instituted a provincial platinum jubilee medal to mark the Queen's seventy years on the Canadian throne.


text: On 3 November 2022, the Governor General signed an Order in Council approving all the provincial Platinum Jubilee Medals to the order of precedence in the Canadian Honours System after all the medals under the heading "Other Medals" in section 1 of the Canadian Orders, Decorations and Medals Directive, 1998.


text: The designs of the medals are similar in all the provinces that produced one, differing only in each depicting the shield of the particular province's coat of arms, as well as the province's official flower (the wild rose for Alberta, prairie crocus for Manitoba, purple violet for New Brunswick, mayflower for Nova Scotia, pink lady's slipper for Prince Edward Island, and western red lily for Saskatchewan). All are silver in colour, 32mm in diameter, and with a ring suspension. The obverse depicts the same crowned effigy of the Queen that was previously used for the Canadian Queen Elizabeth II Diamond Jubilee Medal, while the reverse displays the Queen's royal cypher with the dates of the Queen's reign, 1952 and 2022, on either side at the top. The provincial shield of arms is in the centre, on both sides of which are renderings of the official flower of the province, and, appearing at the base, is the motto "VIVAT REGINA" ("long live the Queen!").


text: The ribbon uses a new arrangement of the blue, red, and white colours found in the ribbons of the Queen Elizabeth II Coronation Medal, Queen Elizabeth II Silver Jubilee Medal, Queen Elizabeth II Golden Jubilee Medal, and Queen Elizabeth II Diamond Jubilee Medal.


text: The Queen Elizabeth II Platinum Jubilee Recognition Act was introduced in the Legislature of Alberta on 22 February 2022 and received royal assent on 24 March of the same year. The act included the creation of a medal to be awarded to 7,000 Albertans who have made significant contributions to society. Three minimum criteria were set for the medal recipients; the nominee must: be a Canadian citizen or permanent resident with a tangible link to Alberta at the time the medal is granted; have made a significant contribution to Canada, Alberta, or to a particular Alberta region or community;and have been alive on 6 February 2022.


text: On 28 April 2022, Lieutenant Governor Janice Filmon and Premier Heather Stefanson announced the creation of the Queen's Platinum Jubilee Medal for Manitoba, the design of which was unveiled on 2 June in the same year.


text: A total of 1,000 medals will be awarded at ceremonies held throughout the province during the Platinum Jubilee year. There are three minimum criteria for the medal recipients: be a resident of Manitoba or have a link to Manitoba at the time of the grant of the medal; have made a contribution to Canada, Manitoba, or to a particular region or community; and be alive on 6 February 2022.


text: The Queen Elizabeth II Platinum Jubilee Medal (New Brunswick) will be awarded to 3,000 deserving individuals; one third of the total medals are specifically intended for those who have made outstanding contributions to the province's COVID-19 pandemic response. The program was launched on 2 June 2022 and will be administered by the Office of Protocol of New Brunswick.


text: Nominees must reside in the province or have a tangible link to New Brunswick; have been alive as of 6 February 2022; and must have made a significant contribution to New Brunswick or to a particular region, community, or field. A specific focus is placed on those individuals who have played a significant role in New Brunswick's COVID-19 pandemic response at the local level over an extended period of time; made a tangible contribution to New Brunswick's reconciliation efforts with Indigenous peoples; made a contribution to New Brunswick's diversity and inclusion goals; provided volunteer service at the local level; served or are serving in the Canadian Armed Forces, Royal Canadian Mounted Police, and other emergency services; and/or made a positive impact on the preservation of the environment.


text: On 30 March 2022, Lieutenant Governor Arthur J LeBlanc announced the establishment of the Queen's Platinum Jubilee Medal for Nova Scotia. Five thousand medals will be awarded across the province until 5 February 2023. LeBlanc announced on 2 June that the Queen had approved the design of the medal. On the same day, the names of the first 70 recipients were released and the inaugural investiture ceremony took place at the Westin Nova Scotian hotel in Halifax on 4 August.


text: To be eligible for the medal, a person must be a resident of Nova Scotia or have a strong direct connection with the province; have made a significant contribution to Canada, Nova Scotia, or to a particular region or community; and have been alive on 6 February 2022.


text: The Queen Elizabeth II Platinum Jubilee Medal programme in Prince Edward Island will see a total of 584 medals being distributed to Islanders. The programme will run to the end of the Queen's Platinum Jubilee Year, 5 February 2023.


text: Eligible recipients must reside in the province or have a tangible link to Prince Edward Island; have made a significant contribution to Prince Edward Island, a region, community, or a field; and been alive on 6 February 2022. Medals will be awarded to those who also have devoted themselves to making the province a better place and have made a significant contribution, which may include having provided volunteer service at the local level; contributed to the province's reconciliation efforts with indigenous peoples; contributed to the province's diversity and inclusion goals, including the promotion of the Acadian and Francophone community; served, or are serving, in the Canadian Armed Forces, Royal Canadian Mounted Police, and/or emergency services; and/or made a positive impact on the preservation of the environment.


text: Lieutenant Governor Russell Mirasty announced on 30 March 2022 the creation of the Queen Elizabeth II Platinum Jubilee Medal (Saskatchewan), which will honour significant contributions and achievements throughout Saskatchewan. 7,000 medals will be awarded throughout the province during the jubilee year.


text: On 30 August, 70 Saskatchewanians were presented with jubilee medals by Lieutenant Governor Russ Mirasty at the inaugural investiture ceremony which took place at the Regency Ballroom in the Hotel Saskatchewan, Regina.


text: The three minimum criteria for the medal recipients are be a resident of Saskatchewan or have a link to Saskatchewan at the time of the grant of the medal; have made a contribution to Canada, Saskatchewan, or to a particular region or community; and be alive on 6 February 2022.


text: The obverse bears the same effigy of the Queen as does the British medal circumscribed by the words PLATINUM JUBILEE HM QUEEN ELIZABETH II. The ribbon of the Caribbean medal is similar to the British version, with silver edges, representing the Silver Jubilee; the blue from the ribbon of the Golden Jubilee medal; and the red from the Diamond Jubilee medal ribbon.


text: During their visit to Antigua and Barbuda on 25 April, the Earl and Countess of Wessex and Forfar presented Platinum Jubilee medals to three people at Government House to recognise their service to national security.


text: Serving frontline members for their service during Hurricanes Eta and Iota, and more recently, to those who served during the COVID-19 pandemic.


text: In Jamaica, Platinum Jubilee medals will be awarded to members of the Jamaica Defence Force, the Jamaica Constabulary Force, the Department of Correctional Services, the Jamaica Fire Brigade and the Emergency Medical Services.


text: On 29 July 2022, Governor-General Sir Patrick Allen, presented Jubilee medals during the Armed Forces Day Parade at Up Park Camp in Kingston. A total of 1056 members of the Jamaica Defence Force, including one woman, were acknowledged with the Queen's Platinum Jubilee Medal. This was awarded to service members of the Regular and Reserve Force, who completed 18 years of service on 6 February 2022.


title: N-sphere

text: In mathematics, an -sphere or a hypersphere is a topological space that is homeomorphic to a "standard" -"sphere", which is the set of points in -dimensional Euclidean space that are situated at a constant distance from a fixed point, called the "center". It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the center. When the sphere has unit radius, it is usual to call it the unit -sphere or simply the -sphere for brevity. In terms of the standard norm, the -sphere is defined as


title: N-sphere

text: The dimension of -sphere is , and must not be confused with the dimension of the Euclidean space in which it is naturally embedded. An -sphere is the surface or boundary of an -dimensional ball.


title: N-sphere

text: For , the -spheres that are differential manifolds can be characterized (up to a diffeomorphism) as the simply connected -dimensional manifolds of constant, positive curvature. The -spheres admit several other topological descriptions: for example, they can be constructed by gluing two -dimensional Euclidean spaces together, by identifying the boundary of an -cube with a point, or (inductively) by forming the suspension of an -sphere. The 1-sphere is the 1-manifold that is a circle, which is not simply connected. The 0-sphere is the 0-manifold, which is not even connected, consisting of two points.


title: N-sphere

text: For any natural number , an -sphere of radius is defined as the set of points in -dimensional Euclidean space that are at distance from some fixed point , where may be any positive real number and where may be any point in -dimensional space. In particular:


title: N-sphere

text: The above -sphere exists in -dimensional Euclidean space and is an example of an -manifold. The volume form of an -sphere of radius is given by


title: N-sphere

text: where is the Hodge star operator; see for a discussion and proof of this formula in the case . As a result,


title: N-sphere

text: The space enclosed by an -sphere is called an -ball. An -ball is closed if it includes the -sphere, and it is open if it does not include the -sphere.


title: N-sphere

text: Topologically, an -sphere can be constructed as a one-point compactification of -dimensional Euclidean space. Briefly, the -sphere can be described as , which is -dimensional Euclidean space plus a single point representing infinity in all directions.


title: N-sphere

text: In particular, if a single point is removed from an -sphere, it becomes homeomorphic to . This forms the basis for stereographic projection.


title: N-sphere

text: The volume of the unit -ball is maximal in dimension five, where it begins to decrease, and tends to zero as tends to infinity. Furthermore, the sum of the volumes of even-dimensional -balls of radius can be expressed in closed form:


title: N-sphere

text: The 0-ball consists of a single point. The 0-dimensional Hausdorff measure is the number of points in a set. So,


title: N-sphere

text: The unit 1-sphere is the unit circle in the Euclidean plane, and this has circumference (1-dimensional measure)


title: N-sphere

text: The region enclosed by the unit 1-sphere is the 2-ball, or unit disc, and this has area (2-dimensional measure)


title: N-sphere

text: Analogously, in 3-dimensional Euclidean space, the surface area (2-dimensional measure) of the unit 2-sphere is given by


title: N-sphere

text: The "surface area", or properly the -dimensional volume, of the -sphere at the boundary of the -ball of radius is related to the volume of the ball by the differential equation


title: N-sphere

text: We can also represent the unit -sphere as a union of products of a circle (1-sphere) with an -sphere. Let and , so that and . Then,


title: N-sphere

text: where denotes the double factorial, defined for odd natural numbers by and similarly for even numbers .


title: N-sphere

text: where is the gamma function, which satisfies , , and , and so , and where we conversely define "x"! = for every "x".


title: N-sphere

text: The recurrences can be combined to give a "reverse-direction" recurrence relation for surface area, as depicted in the diagram:


title: N-sphere

text: We may define a coordinate system in an -dimensional Euclidean space which is analogous to the spherical coordinate system defined for 3-dimensional Euclidean space, in which the coordinates consist of a radial coordinate , and angular coordinates , where the angles range over radians (or over degrees) and ranges over radians (or over degrees). If are the Cartesian coordinates, then we may compute from with:


title: N-sphere

text: There are some special cases where the inverse transform is not unique; for any will be ambiguous whenever all of are zero; in this case may be chosen to be zero.


title: N-sphere

text: To express the volume element of -dimensional Euclidean space in terms of spherical coordinates, first observe that the Jacobian matrix of the transformation is:


title: N-sphere

text: The determinant of this matrix can be calculated by induction. When , a straightforward computation shows that the determinant is . For larger , observe that can be constructed from as follows. Except in column , rows and of are the same as row of , but multiplied by an extra factor of in row and an extra factor of in row . In column , rows and of are the same as column of row of , but multiplied by extra factors of in row and in row , respectively. The determinant of can be calculated by Laplace expansion in the final column. By the recursive description of , the submatrix formed by deleting the entry at and its row and column almost equals , except that its last row is multiplied by . Similarly, the submatrix formed by deleting the entry at and its row and column almost equals , except that its last row is multiplied by . Therefore the determinant of is


title: N-sphere

text: Similarly the surface area element of the -sphere of radius , which generalizes the area element of the 2-sphere, is given by


title: N-sphere

text: The natural choice of an orthogonal basis over the angular coordinates is a product of ultraspherical polynomials,


title: N-sphere

text: The standard spherical coordinate system arises from writing as the product . These two factors may be related using polar coordinates. For each point of , the standard Cartesian coordinates


title: N-sphere

text: This says that points in may be expressed by taking the ray starting at the origin and passing through formula_38, rotating it towards formula_39 by formula_40, and traveling a distance formula_41 along the ray. Repeating this decomposition eventually leads to the standard spherical coordinate system.


title: N-sphere

text: Polyspherical coordinate systems arise from a generalization of this construction. The space is split as the product of two Euclidean spaces of smaller dimension, but neither space is required to be a line. Specifically, suppose that and are positive integers such that . Then . Using this decomposition, a point may be written as


title: N-sphere

text: Here formula_44 and formula_45 are the unit vectors associated to and . This expresses in terms of formula_46, formula_47, , and an angle . It can be shown that the domain of is if , if exactly one of and is 1, and if neither nor are 1. The inverse transformation is


title: N-sphere

text: These splittings may be repeated as long as one of the factors involved has dimension two or greater. A polyspherical coordinate system is the result of repeating these splittings until there are no Cartesian coordinates left. Splittings after the first do not require a radial coordinate because the domains of formula_44 and formula_45 are spheres, so the coordinates of a polyspherical coordinate system are a non-negative radius and angles. The possible polyspherical coordinate systems correspond to binary trees with leaves. Each non-leaf node in the tree corresponds to a splitting and determines an angular coordinate. For instance, the root of the tree represents , and its immediate children represent the first splitting into and . Leaf nodes correspond to Cartesian coordinates for . The formulas for converting from polyspherical coordinates to Cartesian coordinates may be determined by finding the paths from the root to the leaf nodes. These formulas are products with one factor for each branch taken by the path. For a node whose corresponding angular coordinate is , taking the left branch introduces a factor of and taking the right branch introduces a factor of . The inverse transformation, from polyspherical coordinates to Cartesian coordinates, is determined by grouping nodes. Every pair of nodes having a common parent can be converted from a mixed polar–Cartesian coordinate system to a Cartesian coordinate system using the above formulas for a splitting.


title: N-sphere

text: Polyspherical coordinates also have an interpretation in terms of the special orthogonal group. A splitting determines a subgroup


title: N-sphere

text: This is the subgroup that leaves each of the two factors formula_52 fixed. Choosing a set of coset representatives for the quotient is the same as choosing representative angles for this step of the polyspherical coordinate decomposition.


title: N-sphere

text: In polyspherical coordinates, the volume measure on and the area measure on are products. There is one factor for each angle, and the volume measure on also has a factor for the radial coordinate. The area measure has the form:


title: N-sphere

text: Suppose we have a node of the tree that corresponds to the decomposition and that has angular coordinate . The corresponding factor depends on the values of and . When the area measure is normalized so that the area of the sphere is 1, these factors are as follows. If , then


title: N-sphere

text: Just as a two-dimensional sphere embedded in three dimensions can be mapped onto a two-dimensional plane by a stereographic projection, an -sphere can be mapped onto an -dimensional hyperplane by the -dimensional version of the stereographic projection. For example, the point on a two-dimensional sphere of radius 1 maps to the point on the -plane. In other words,


title: N-sphere

text: Likewise, the stereographic projection of an -sphere of radius 1 will map to the -dimensional hyperplane perpendicular to the -axis as


title: N-sphere

text: To generate uniformly distributed random points on the unit -sphere (that is, the surface of the unit -ball), gives the following algorithm.


title: N-sphere

text: Generate an -dimensional vector of normal deviates (it suffices to use , although in fact the choice of the variance is arbitrary), . Now calculate the "radius" of this point:


title: N-sphere

text: An alternative given by Marsaglia is to uniformly randomly select a point in the unit -cube by sampling each independently from the uniform distribution over , computing as above, and rejecting the point and resampling if (i.e., if the point is not in the -ball), and when a point in the ball is obtained scaling it up to the spherical surface by the factor ; then again is uniformly distributed over the surface of the unit -ball. This method becomes very inefficient for higher dimensions, as a vanishingly small fraction of the unit cube is contained in the sphere. In ten dimensions, less than 2% of the cube is filled by the sphere, so that typically more than 50 attempts will be needed. In seventy dimensions, less than formula_62 of the cube is filled, meaning typically a trillion quadrillion trials will be needed, far more than a computer could ever carry out.


title: N-sphere

text: With a point selected uniformly at random from the surface of the unit -sphere (e.g., by using Marsaglia's algorithm), one needs only a radius to obtain a point uniformly at random from within the unit -ball. If is a number generated uniformly at random from the interval and is a point selected uniformly at random from the unit -sphere, then is uniformly distributed within the unit -ball.


title: N-sphere

text: Alternatively, points may be sampled uniformly from within the unit -ball by a reduction from the unit -sphere. In particular, if is a point selected uniformly from the unit -sphere, then is uniformly distributed within the unit -ball (i.e., by simply discarding two coordinates).


title: N-sphere

text: If is sufficiently large, most of the volume of the -ball will be contained in the region very close to its surface, so a point selected from that volume will also probably be close to the surface. This is one of the phenomena leading to the so-called curse of dimensionality that arises in some numerical and other applications.


title: N-sphere

text: The octahedral 1-sphere is a square (without its interior). The octahedral 2-sphere is a regular octahedron; hence the name. The octahedral "n"-sphere is the topological join of "n" + 1 pairs of isolated points. Intuitively, the topological join of two pairs is generated by drawing a segment between each point in one pair and each point in the other pair; this yields a square. To join this with a third pair, draw a segment between each point on the square and each point in the third pair; this gives a octahedron.


title: Against All Odds (1984 film)

text: Against All Odds is a 1984 American romantic neo-noir thriller film directed by Taylor Hackford and starring Rachel Ward, Jeff Bridges and James Woods alongside Jane Greer, Alex Karras, Richard Widmark and Dorian Harewood. A remake of "Out of the Past" (1947), a film in which Greer played the femme fatale, this film's plot is about an aging American football star who is hired by a mobster to find his girlfriend.