title: Manasseh of Judah

text: The Assyrian records are consistent with archaeological evidence of demographic trends and settlement patterns suggesting a period of stability in Judah during Manasseh's reign. Despite the criticisms of his religious policies in the biblical texts, archaeologists such as Israel Finkelstein and Neil Asher Silberman credit Manasseh with reviving Judah's rural economy, arguing that a possible Assyrian grant of most favoured nation status stimulated the creation of an export market. They argue that changes to the economic structure of the countryside would have required the cooperation of the "countryside aristocracy", with restoration of worship at the high places a "quid pro quo" for this. Apparent devastation of the fertile Shephelah, coupled with growth of the population of the highlands and the southeast of the kingdom (especially in the Beersheba valley) during Manasseh's reign, point to this possibility.


title: Manasseh of Judah

text: Olive oil production and export played a big role in the economy of the time. There is evidence in the Gaza area of entrepôt trade, and an apparently flourishing olive oil industry at Ekron. The construction or reconstruction of forts at sites such as Arad and Horvat Uza, explored by Nadav Na'aman and others, is also argued by Finkelstein and Silberman to be evidence in support of this thesis, as they would have been needed to protect the trade routes. However, Finkelstein and Silberman argue that the trade led to great disparities between rich and poor, which in turn gave rise to civil unrest. As a result, they speculate, the Deuteronomist author or editor of 2 Kings later reworked the traditions about Manasseh to portray his outward-looking involvement in trade as, effectively, apostasy.


title: Manasseh of Judah

text: There are three aspects of Manasseh's religious policy which the writer of "Kings" considered deplorable: the religious reaction which followed hard upon his accession; its extension by the free adoption of foreign cults; and the bitter persecution of the prophetic party.


title: Manasseh of Judah

text: According to Kings, Manasseh reversed the centralizing reforms of his father Hezekiah, and re-established local shrines, possibly for economic reasons. He restored polytheistic worship of Baal and Asherah () in the Temple, and sponsored the Assyrian astral cult throughout Judah. So zealous was he in his worship of the foreign gods, he is said to have participated in the sacrificial cult of Moloch which consisted of sacrificing young children or passing them through fire (2 Kings 21:6) His reign may be described as reactionary in relation to his father's, and "Kings" suggests that he may have executed supporters of his father's reforms. During Manasseh's half-century the popular worship was a medley of native and foreign cults, the influence of which was slow to disappear.


title: Manasseh of Judah

text: 2 Kings 21:10 suggests that several prophets combined their condemnation of Manasseh. The Pulpit Commentary identifies the prophets as probably Isaiah and Habakkuk and possibly Nahum and Zephaniah. Manasseh's response was to persecute those who had bitterly condemned the popular syncretism. The prophets were put to the sword (Jeremiah 2:30). Exegetical tradition relates that Isaiah, Manasseh's own grandfather, suffered a particularly painful execution, sawn in two under the king's orders. "Innocent blood" reddened the streets of Jerusalem. For many decades those who sympathized with prophetic ideas were in constant peril.


title: Manasseh of Judah

text: Arnold J. Toynbee considers that Manasseh was a pious conservative, defending the faith of his ancestors from Yahweh-only iconoclasts.


title: Manasseh of Judah

text: According to , Manasseh was on one occasion brought in chains to the Assyrian king, (possibly Esarhaddon), presumably for suspected disloyalty. The verse goes on to indicate that he was later treated well and restored to his throne. In the Chronicler's account, the severity of Manasseh's imprisonment brought him to repentance. Manasseh was restored to the throne, () and abandoned idolatry, removing the foreign idols () and enjoining the people to worship the Lord of Israel Yahweh. However, neither "Kings" nor Assyrian records mention this incident.


title: Manasseh of Judah

text: Thiele dates Manasseh's reign back from the dates of the reign of his grandson, Josiah. Josiah died at the hands of Pharaoh Necho II in the summer of 609 BC. By Judean reckoning, which began regnal years in the fall month of Tishri, this would be in the year 610/609 BC. Josiah reigned for 31 years (, ) and began to reign after the short two-year reign of Amon. Manasseh's last year, 33 years earlier, would be 643/642 BC.


title: Manasseh of Judah

text: The length of Manasseh's reign is given as 55 years in . Assuming non-accession reckoning, as he usually did for coregencies, Thiele determined 54 "actual" years back to 697/696 BC, as the year when the Hezekiah/Manasseh coregency began. Non-accession reckoning means that the first partial year of a king in office was counted twice, once for him and once for his predecessor, so that one year must be subtracted when measuring spans of time. An analysis of the data for Jeroboam II of Israel and Jehoshaphat of Judah, both of whom had coregencies, shows that their years were measured in this way.


title: Manasseh of Judah

text: Regarding the Hezekiah/Manasseh coregency, Thiele observes Manasseh began his reign when he was 12 years old (), and then comments, "A Hebrew lad when he reached the age of twelve was a "son of the law" and had become "gadol". He had then passed from the days of childhood to youth and was considered old enough to concern himself with the serious work of life ... "it is only to be expected that the king, facing the prospect of the termination of his reign within fifteen years [], would at the earliest moment give the heir-presumptive every advantage of training in leadership."


title: Manasseh of Judah

text: In rabbinic literature and Christian pseudepigrapha, Manasseh is accused of executing the prophet Isaiah, who was identified as the maternal grandfather of Manasseh.


title: Manasseh of Judah

text: The Prayer of Manasseh, a penitential prayer attributed to Manasseh, appears in some Christian Bibles, but is considered apocryphal by Jews, Roman Catholics and Protestants.


title: Manasseh of Judah

text: Manasseh is also made reference to in chapter 21 of 1 Meqabyan, a book considered canonical in the Ethiopian Orthodox Tewahedo Church, where he is used as an example of ungodly king.


title: Samuel Wilson

text: Samuel Wilson (September 13, 1766 – July 31, 1854) was an American meat packer who lived in Troy, New York, whose name is purportedly the source of the personification of the United States known as "Uncle Sam".


title: Samuel Wilson

text: Wilson was born in the historic town of Arlington, Massachusetts (known as Menotomy at the time, township of West Cambridge), to parents Edward and Lucy Wilson. Wilson is a descendant of one of the oldest families of Boston; through direct heritance of his grandfather Robert Wilson, originally from Greenock, Scotland, he was Scottish with a Massachusetts background. As a boy, he moved with his family to Mason, New Hampshire.


title: Samuel Wilson

text: While living in Mason at the young age of fourteen, Wilson joined the Continental Army on March 2, 1781. His duties while enlisted consisted of guarding and caring for cattle, and mending fences, as well as slaughtering and packaging meat; guarding meat was a priority during the war. It was not uncommon for enemies to tamper with and poison food sources. Wilson's service to the Army most likely came to an end around October 19, 1781, with the surrender of Cornwallis at the Siege of Yorktown.


title: Samuel Wilson

text: In 1789, at the age of 22, Samuel and his older brother Ebeneezer, age 27, relocated, by foot, to Troy, New York. The Wilson brothers were amongst the first pioneer settlers of the community, and Troy was attractive to earlier settlers for its proximity to the Hudson River. Samuel and his brother Ebeneezer partnered together and built several successful businesses. Both were employees of the city as well as successful entrepreneurs.


title: Samuel Wilson

text: After his relocation to Troy, Samuel drew upon his prosperous location. He purchased property on Mount Ida (now Prospect Park), closely located to the Hudson River. The combination of natural elements produced exceptional clay, ideal for brick making. This began a new business venture for Samuel Wilson. His bricks were the first native bricks of Troy. Many historical buildings in Troy include bricks made by Wilson. This was revolutionary during the 18th century. Many bricks during this period were imported from the Netherlands.


title: Samuel Wilson

text: On March 8, 1793, Samuel and his brother Ebeneezer leased the western half of lot 112, now 43 Ferry Street, from Jacob Vanderhyden for 30 shillings a year. This was the year the Wilson brothers began E & S Wilson, which was the Wilson brothers' introduction to the profitable meat business. Their slaughterhouse was located between Adams (now Congress) Street and Jefferson Street. The brothers took advantage of their prime location and built a dock at the foot of what is now Ferry Street. Having such access to the Hudson River enabled E & S Wilson to prosper.


title: Samuel Wilson

text: Wilson returned to Mason, New Hampshire, in 1797, to marry Betsey Mann, daughter of Captain Benjamin Mann. Samuel and Betsey were parents to four children, Polly (1797–1805), Samuel (1800–1807), Benjamin (1802–59), and Albert (1805–66).


title: Samuel Wilson

text: Wilson not only was a pioneer of Troy, he was active in the community, as well as an employee of the city. On April 12, 1808, he took an oath as Office Assessor. Four days later he took an Oath of Office as Path Master (now more commonly known as road commissioner).


title: Samuel Wilson

text: Wilson's career role during the War of 1812 is what he is most noted for today. The demand for a supply of meat for the troops had significantly increased. E & S Wilson's location and dock made the business ready and ideal.


title: Samuel Wilson

text: Secretary of War William Eustis made a contract with Elbert Anderson Jr. of New York City to supply and issue all rations necessary for the United States forces in New York and New Jersey for one year. Anderson ran an advertisement on October 6, 13, and 20 looking to fill the contract. E & S Wilson secured the contract for 2,000 barrels of pork and 3,000 barrels of beef for one year. The business held a staff of 200 men during this period.


title: Samuel Wilson

text: Wilson was appointed meat inspector for the U.S. Army. His duties included checking the freshness of meat and assuring that it was properly packaged and that the barrels were according to specification. Each barrel was required to be labeled. Each barrel was marked “E.A.-U.S.” This marking indicated Elbert Anderson, United States. The great majority of E & S Wilson's meat was shipped close by to a camp of 6,000 soldiers in Greenbush, New York. Many soldiers stationed in Greenbush were locals of Troy. They knew of or were acquainted with Sam Wilson and his nickname Uncle Sam, as well as his meat packing business. These soldiers recognized the barrels being from Troy and made an association between the "U.S." stamp and Uncle Sam. Over time, it is believed, anything marked with the same initials, as much Army property was, also became linked with his name.


title: Samuel Wilson

text: Wilson died July 31, 1854, at the age of 87. He was originally buried in Mt. Ida Cemetery, but later transferred to Oakwood Cemetery in Troy. Monuments mark his birthplace in Arlington, Massachusetts, and site of burial in Troy, New York. A New Hampshire historical marker (number 35) titled "Uncle Sam's House" marks his boyhood home in Mason, New Hampshire.


title: Samuel Wilson

text: Some scholars have pointed out that Wilson may not have been the original creator of the phrase, but may have had a significant role in spreading the name. While Wilson may or may not have been the original "Uncle Sam", the 87th United States Congress adopted the following resolution on September 15, 1961: "Resolved by the Senate and the House of Representatives that the Congress salutes Uncle Sam Wilson of Troy, New York, as the progenitor of America's National symbol of Uncle Sam."


title: 300 (comics)

text: 300 is a historically inspired 1998 comic book limited series written and illustrated by Frank Miller with painted colors by Lynn Varley.


title: 300 (comics)

text: The comic is a fictional retelling of the Battle of Thermopylae and the events leading up to it from the perspective of Leonidas of Sparta. "300" was particularly inspired by the 1962 film "The 300 Spartans", a film Miller watched as a young boy. The work was adapted in 2006 to a film of the same name.


title: 300 (comics)

text: In 2018, Dark Horse published "Xerxes: The Fall of the House of Darius and the Rise of Alexander", also written and drawn by Miller, acting as a prequel and sequel to the events of "300", depicting Xerxes I's rise to the throne, and the subsequent destruction of the Persian Empire under his descendant Darius III, by Alexander the Great.


title: 300 (comics)

text: Each page of the novel is illustrated as a double-page spread. When the series was gathered into hardcover form, the individual pages were twice as wide as a normal comic. Miller's art style for this project was similar to his "Sin City" work, although the addition of consistent color is an obvious difference.


title: 300 (comics)

text: "300" was initially published as a monthly five-issue comic book limited series by Dark Horse Comics, the first issue published in May 1998. The issues were titled "Honor", "Duty", "Glory", "Combat" and "Victory". The series won three Eisner Awards in 1999: "Best Limited Series", "Best Writer/Artist" for Frank Miller and "Best Colorist" for Lynn Varley. The work was collected as a hardcover volume in 1999.


title: 300 (comics)

text: The popularity of the film has boosted sales of the trade paperback edition. The 10th printing had an announced print run of 40,000 copies, with an 11th printing to follow. This is in addition to the 88,000 copies already sold since the initial volume was released in 1999.


title: 300 (comics)

text: In 480 BC, King Leonidas of Sparta gathers 300 of his best men to fight the upcoming Persian invasion. In what is likely a suicide mission, they and their allies plan to stop King Xerxes' invasion of Greece at the narrow cliffs of the "Hot Gates" (Thermopylae). The terrain prevents the Greeks from being overwhelmed by Xerxes' superior numbers (a military tactic usually called "defeat in detail").


title: 300 (comics)

text: Before the battle starts, Ephialtes, a deformed Spartan, begs Leonidas to let him fight but is rejected due to his hunchbacked form, which prevents him from lifting his shield high enough to be of use for the phalanx. Ephialtes becomes despondent due to Leonidas' refusal and throws himself off a cliff.


title: 300 (comics)

text: The Spartans and their allies successfully hold off the Persians for two days and nights. During a break in the fighting, Xerxes meets with Leonidas and offers wealth and power in exchange for his surrender. Leonidas declines, and battle continues. Meanwhile, Ephialtes awakes from his suicide attempt and decides to betray the Greeks by telling the Persians about the existence of a small pass that allows Xerxes to attack them from behind.


title: 300 (comics)

text: Learning of the Persian maneuvers the Greeks realize their position is indefensible, but the Spartans and a few others refuse to retreat. Before engaging the Persians for the last time, Leonidas orders one Spartan (Dilios) to return home so that he might survive to tell their story.


title: 300 (comics)

text: On the third day Xerxes has the Spartans surrounded, their remaining allies (Thespians) already dead. He gives Leonidas one final chance to surrender and kneel to him. After some hesitation, Leonidas finally complies and throws down his arms and kneels. This, however, is a trick by Leonidas, and signals Stelios, a loyal Spartan soldier, to jump from his back and kill a general. The Spartans fight. Leonidas throws his spear at Xerxes, intending to make the "God-King" bleed, and succeeds. The Spartans are killed to the last man by a storm of arrows.


title: 300 (comics)

text: The story then shifts about a year later and ends as now-Captain Dilios relates the heroic sacrifice of Leonidas and his Spartan comrades to his troops before the historic Battle of Plataea.


title: 300 (comics)

text: Writer Alan Moore has criticized "300" as being historically inaccurate, with particular reference to the characters' attitudes towards homosexuality:


title: 300 (comics)

text: Miller, in the letters page of the series, replied to accusations of homophobia from a reader regarding the phrase "Those boy-lovers":


title: 300 (comics)

text: Writer David Brin has also criticized "300" as being historically inaccurate, with particular reference to the bravery and efficacy of the non-Spartan Greeks:


title: 300 (comics)

text: During the Battle of Marathon, ten years previous to Thermopylae, the Spartans had been obligated to honor the Carneia, a religious festival during which military engagements were forbidden. Once the religious prohibition was lifted, the Spartan troops covered the 220 kilometers (140 mi) to Athens in a quick three days and arrived only one day after the battle had taken place. The Spartans toured the battlefield at Marathon, and agreed that the Athenians had won a great victory. Xerxes' invasion happened to coincide yet again with the celebration of the Carneia. This time, however, the Spartans chose not to hold back their entire army in deference to the festival, but instead sent an advance force of 300 men under Leonidas, who were to be reinforced by a full contingent of Spartan warriors after the festival concluded. It is impossible to know for certain whether this change in policy regarding the Carneia was based in shame about missing Marathon (as Brin suggests) or merely marked a reinterpretation of the military threat posed by the invading Persians. All Herodotus tells us is that the Spartan officials did not think that the engagement at Thermopylae would be decided so quickly and intended the main part of their force to arrive before the fighting broke out.


title: 300 (comics)

text: There are references to the Battle at Thermopylae in several of Frank Miller's other comic books. In "Sin City: The Big Fat Kill", Dwight McCarthy considers Leonidas' choice of "where to fight" and manages to loosely recreate the Spartan defense tactics by cornering the enemy gang in a tight alley; they then annihilate them with heavy gunfire and explosives. Also in "Hell and Back" when Wallace is drugged he sees his friend as Leonidas with a machine gun. In "The Dark Knight Returns" and "The Dark Knight Strikes Again", Miller's "omega" Batman stories, there are references to a character named "Hot Gates" (the literal translation of "Thermopylae"), an adult film star who first makes a version of Snow White, and then declares herself Dictator of Ohio.


title: 300 (comics)

text: In the Emmy Award-winning episode "Jack and the Spartans" of the cartoon "Samurai Jack", Jack meets a group of Spartan warriors fighting Aku's minions. This episode was partially inspired by Miller's comics.


title: 300 (comics)

text: In 2007, Zack Snyder directed a film adaptation of 300 with Frank Miller serving as executive producer to adapt his work for film. It used greenscreen technology to capture the comic book feel; the film is in fact notable for remaining extremely faithful to its source material as a result. It was released in both conventional cinemas and IMAX in 2007. In 2014, a sequel, "", was made, which is based on Frank Miller's mini-series "Xerxes".


title: Günter Grass

text: Günter Wilhelm Grass (born Graß; ; 16 October 1927 – 13 April 2015) was a German novelist, poet, playwright, illustrator, graphic artist, sculptor, and recipient of the 1999 Nobel Prize in Literature.


title: Günter Grass

text: He was born in the Free City of Danzig (now Gdańsk, Poland). As a teenager, he served as a drafted soldier from late 1944 in the "Waffen-SS" and was taken as a prisoner of war by US forces at the end of the war in May 1945. He was released in April 1946. Trained as a stonemason and sculptor, Grass began writing in the 1950s. In his fiction, he frequently returned to the Danzig of his childhood.


title: Günter Grass

text: Grass is best known for his first novel, "The Tin Drum" (1959), a key text in European magic realism. It was the first book of his Danzig Trilogy, the other two being "Cat and Mouse" and "Dog Years". His works are frequently considered to have a left-wing political dimension, and Grass was an active supporter of the Social Democratic Party of Germany (SPD). "The Tin Drum" was adapted as a film of the same name, which won both the 1979 Palme d'Or and the Academy Award for Best Foreign Language Film. In 1999, the Swedish Academy awarded him the Nobel Prize in Literature, praising him as a writer "whose frolicsome black fables portray the forgotten face of history".


title: Günter Grass

text: Grass was born in the Free City of Danzig on 16 October 1927, to Wilhelm Grass (1899–1979), a Lutheran Protestant of German origin, and Helene Grass ("née" Knoff, 1898–1954), a Roman Catholic of Kashubian-Polish origin. He referred to himself as Kashubian. Grass was raised a Catholic and served as an altar boy when he was a child. His parents had a grocery store with an attached apartment in Danzig-Langfuhr (now Gdańsk-Wrzeszcz). He had a sister, Waltraud, born in 1930.


title: Günter Grass

text: Grass attended the Danzig gymnasium "Conradinum". In 1943, at age 16, he became a "Luftwaffenhelfer" (Air Force "helper"). Soon thereafter, he was conscripted into the "Reichsarbeitsdienst" (National Labour Service). In November 1944, shortly after his 17th birthday, Grass volunteered for submarine service with Nazi Germany's "Kriegsmarine", "to get out of the confinement felt as a teenager in his parents' house", which he considered stuffy Catholic lower middle-class.


title: Günter Grass

text: The Navy refused him and he was instead called up for the 10th SS Panzer Division Frundsberg in late 1944. Grass did not reveal until 2006 that he was drafted into the "Waffen-SS" at that time. His unit functioned as a regular "Panzer" Division, and he served with them from February 1945 until he was wounded on 20 April 1945. He was captured in Marienbad (now Mariánské Lázně, Czech Republic) and sent to a US prisoner-of-war camp in Bad Aibling, Bavaria.


title: Günter Grass

text: From 1946 to 1947, Grass worked in a mine and received training in stonemasonry. He studied sculpture and graphics at the "Kunstakademie Düsseldorf". He also was a co-founder of Group 47, organized by Hans Werner Richter. Grass worked as a writer, graphic designer, and sculptor, travelling frequently. In 1953 he moved to West Berlin and studied at the Berlin University of the Arts. From 1960, he lived in Berlin as well as part-time in Schleswig-Holstein. In 1961 he publicly objected to the erection of the Berlin Wall.


title: Günter Grass

text: In 1954 Grass married Anna Margareta Schwarz, a Swiss dancer, which ended in divorce in 1978. He and Schwarz had four children: Franz (born 1957), Raoul (1957), Laura (1961), and Bruno (1965). Separated in 1972, he began a relationship with Veronika Schröter and had a child with her, Helene (1974). He also had a child with Ingrid Kruger, Nele (1979). In 1979 he married Ute Grunert, an organist, to whom he was still married at his death. He had two stepsons from his second marriage, Malte and Hans. He had 18 grandchildren at his death.


title: Günter Grass

text: Grass's best-known work is "The Tin Drum" ("Die Blechtrommel"), published in 1959 (and adapted as a film of the same name by director Volker Schlöndorff in 1979). It was followed in 1961 by "Cat and Mouse" ("Katz und Maus"), a novella, and in 1963 by the novel "Dog Years" ("Hundejahre").


title: Günter Grass

text: The books are collectively called the Danzig Trilogy and focus on the rise of Nazism and how World War II affected Danzig (now Gdańsk, Poland), which was separated from Germany after World War I and became the Free City of Danzig ("Freie Stadt Danzig"). "Dog Years" (1965) is considered a sequel of sorts to "The Tin Drum", as it features some of the same characters. It portrays the area's mixed ethnicities and complex historical background in lyrical prose that is highly evocative.


title: Günter Grass

text: "The Tin Drum" established Grass as one of the leading authors of Germany, and also set a high bar of comparison for all of his subsequent works, which were often compared unfavorably to this early work by critics. Nonetheless, in West Germany of the late 1950s and early '60s the book could be controversial, and its "immorality" prompted the city of Bremen to revoke a prize it had bestowed upon him. When Grass received the Nobel Prize in literature in 1999 the Nobel Committee stated that the publication of "The Tin Drum" "was as if German literature had been granted a new beginning after decades of linguistic and moral destruction".


title: Günter Grass

text: The 1977 novel "The Flounder" ("Der Butt") is based on the folktale of "The Fisherman and His Wife", and deals with the struggle between the sexes. It has been read as an anti-feminist novel, since in the novel the magical flounder of the folk tale, now representing male triumphalism and the patriarchy is caught by a group of 1970s feminists, who put it on trial. The book interrogates male-female relations from the past and the present through the relationship between the narrator and his wife, who as the wife in the folk tale, insatiably craves more. In spite of the fact that the book could be read as a defense of women and a denouncement of male chauvinism, the book was harshly critiqued and rejected by feminists, partly due to its portrayal of violence, sexualization and objectification, and what the feminists perceived as male narcissism and gender essentialism.


title: Günter Grass

text: The 1999 book "My Century" ("Mein Jahrhundert") was an overview of the 20th-century's many brutal historic events, conveyed in short pieces, a mosaic of expression. In 2002, Grass returned to the forefront of world literature with "Crabwalk" ("Im Krebsgang"). This novella, one of whose main characters first appeared in "Cat and Mouse", was Grass's most successful work in decades. It dealt with the events of a refugee ship, full of thousands of Germans, being sunk by a Russian submarine, killing most on board. It was one of a number of works since the late 20th century that have explored the victimization of Germans in World War II.


title: Günter Grass

text: In 2006, Grass published the first volume in a trilogy of autobiographic memoirs. Titled "Peeling the Onion" ("Beim Häuten der Zwiebel"), it dealt with his childhood, war years, early efforts as a sculptor and poet, and finally his literary success with the publication of "The Tin Drum". In a prepublication interview Grass for the first time revealed that he had been a member of the Waffen-SS, and not only a "Flakhelfer" (anti-aircraft assistant) as he had long said. On being asked what caused the need for public confession and revelation of his past in the book he answered: "It was a weight on me, my silence over all these years is one of the reasons I wrote the book. It had to come out in the end."


title: Günter Grass

text: The interview and the book caused critics to accuse him of hypocrisy for having hidden this part of his past, while simultaneously being a strong voice for ethics and morality in the public debate. The book itself was also praised for its depictions of the German postwar generation and the social and moral development of a nation burdened simultaneously by destruction and a deep sense of guilt. Throughout the memoir Grass plays with the frailty of memory, for which the layers of the onion are a metaphor. Grass second-guesses his own memories, throws his own autobiographical statements into doubt and questions whether the person inhabiting his past was really him. This struggle with memory comes to represent the struggle of the German people during the same period with Germany's Nazi past.


title: Günter Grass

text: The second volume of the trilogy, "The Box" (German: "Die Box") was published in 2008; the third, "Grimms Wörter" ("Grimm's Words"), the title referring to the Brothers Grimm's "Deutsches Wörterbuch" ("German Dictionary"), in 2010.


title: Günter Grass

text: A main theme in Grass's work is World War II and its effects on Germany and the German people, including a critique of the forms of ideological reasoning that undergirded the Nazi regime. The place of the city of Danzig/Gdańsk and its ambiguous historical status in between Germany and Poland often stands as a symbol of the ambiguity between ethnic groups, also found in Grass's own heritage which includes both German and Slavic family members who fought on opposite sides of the war. His works also show a sustained concern for the marginal and marginalized subjects, such as Oskar Matzerath, the dwarf in "The Tin Drum" whose body was considered an aberration unworthy of life in the Nazi ideology, or with Roma and Sinti people who were also deemed impure and unworthy and subjected to eugenics and genocide.


title: Günter Grass

text: His literary style combines elements of magic realism, with a penchant for questioning and complicating questions of authorship by intermingling realistic autobiographical elements with unreliable narrators and fantastic events or happenings that creates irony or satirizes events to form social critiques.


title: Günter Grass

text: Grass's work has tended to divide the critics into those who have considered his experiments and style to be sublime and those who have found it to be tied down by his political posturing. Particularly American critics such as John Updike have found the mixture of politics and social critique in his works to diminish its artistic qualities. In his various critiques of Grass's works, Updike wrote that Grass had been consumed by his "strenuous career as celebrity-author-artist-Socialist" and about one of his later novels that "he can't be bothered to write a novel; he just sends dispatches ... from the front lines of his engagement". Even if frequently critical of Grass, Updike considered him to be "one of the very, very few authors whose next novel one has no intention of missing".


title: Günter Grass

text: Grass's literary style has been widely influential. John Irving called Grass "simply the most original and versatile writer alive". And many have noted parallels between Irving's "A Prayer for Owen Meany" and "The Tin Drum". Similarly, Salman Rushdie has acknowledged a debt to Grass's work, particularly "The Tin Drum", and many parallels to Grass's work have been pointed out in his own oeuvre.


title: Günter Grass

text: Grass was for several decades a supporter of the Social Democratic Party of Germany and its policies. He took part in German and international political debate on several occasions. During Willy Brandt's chancellorship, Grass was an active supporter. Grass criticised left-wing radicals and instead argued in favour of the "snail's pace", as he put it, of democratic reform ("Aus dem Tagebuch einer Schnecke", literally "from the diary of a snail"). Books containing his speeches and essays were released throughout his literary career.


title: Günter Grass

text: In the 1980s, he became active in the peace movement and visited Calcutta for six months. A diary with drawings was published as "Zunge zeigen", an allusion to Kali's tongue.


title: Günter Grass

text: During the events leading up to the reunification of Germany in 1989–90, Grass argued for the continued separation of the two German states. He asserted that a unified Germany would be likely to resume its role as belligerent nation-state. This argument estranged many Germans, who came to see him as too much of a moralizing figure.


title: Günter Grass

text: In 2001, Grass proposed the creation of a German-Polish museum for art lost to other countries during the War. The Hague Convention of 1907 requires the return of art that had been evacuated, stolen or seized. Some countries refused to repatriate some of the looted art.


title: Günter Grass

text: On 4 April 2012, Grass's poem "What Must Be Said" ("Was gesagt werden muss") was published in several European newspapers. Grass expressed his concern about the hypocrisy of German military support (the delivery of a submarine) for an Israel that might use such equipment to launch nuclear warheads against Iran, which "could wipe out the Iranian people". And he hoped that many would demand "that the governments of both Iran and Israel allow an international authority free and open inspection of the nuclear potential and capability of both." In response, Israel declared him "persona non grata" in that country.


title: Günter Grass

text: According to Avi Primor, president of the Israel Council on Foreign Relations, Grass was the only important German cultural figure who had refused to meet with him when he served as Israeli ambassador to Germany. Primor noted: "One explanation for [Grass']s strange behaviour might be found in the fact that Grass (who despite his poem is probably not the bitter enemy of Israel that one would imagine) had certain personal difficulties with Israel." Primor said that during Grass's earlier visit to Israel, he "was confronted with the anger of an Israeli public that booed him in successive public appearances. To be sure, the Israeli protestors were not targeting Grass personally and their anger had nothing at all to do with his literature. It was the German effort to establish cultural relations with Israel to which they objected. Grass, however, did not see it that way and may well have felt personally slighted."


title: Günter Grass

text: Grass was a supporter of the Campaign for the Establishment of a United Nations Parliamentary Assembly, an organisation which campaigns for democratic reformation of the United Nations, and the creation of a more accountable international political system.


title: Günter Grass

text: On 26 April 2012, Grass wrote a poem criticizing European policy for the treatment of Greece in the European debt crisis. In "Europe's Disgrace", Grass accuses Europe of condemning Greece to poverty, a country "whose mind conceived Europe".


title: Günter Grass

text: Just a few days before he died Grass completed his last book, "Vonne Endlichkait". The title is in East Prussian dialect, the native dialect of Grass, and means "About Finitude". According to his publisher Gerhard Steidl, the book was "a literary experiment", combining short prose texts, poems and a pencil drawings by the writer. The book was published in August 2015.


title: Günter Grass

text: Grass received dozens of international awards; in 1999, he was awarded the highest literary honour: the Nobel Prize in Literature. The Swedish Academy noted him as a writer "whose frolicsome black fables portray the forgotten face of history". His literature is commonly categorised as part of the German artistic movement known as "Vergangenheitsbewältigung", roughly translated as "coming to terms with the past."


title: Günter Grass

text: In 1965, Grass received the Georg Büchner Prize; in 1993 he was elected an Honorary Fellow of the Royal Society of Literature In 1995, he received the Hermann Kesten Prize.


title: Günter Grass

text: Representatives of the city of Bremen joined to establish the Günter Grass Foundation with the aim of establishing a centralized collection of his numerous works, especially his many personal readings, videos and films. The Günter Grass House in Lübeck houses exhibitions of his drawings and sculptures, an archive and a library.


title: Günter Grass

text: In 1992, he received the Hidalgo Prize, awarded by the National Association of Spain "Presencia Gitana", in recognition of his defense of the Romani People.


title: Günter Grass

text: In 2012, Grass received the award European of the Year from the European Movement Denmark (Europabevægelsen) honoring his political debates in European affairs.


title: Günter Grass

text: In August 2006, in an interview about his forthcoming book, "Peeling the Onion", Grass said that he had been a member of the "Waffen-SS" in World War II. Prior to that, he had been considered a typical member of the "Flakhelfer generation", one of those too young to see much fighting or to be involved with the Nazi regime beyond its youth organizations.


title: Günter Grass

text: On 15 August 2006, "Spiegel Online" published three 1946 documents from US forces verifying Grass's "Waffen-SS" membership.


title: Günter Grass

text: After an unsuccessful attempt to volunteer for the U-boat fleet in 1942, at age 15, Grass was conscripted into the "Reichsarbeitsdienst" (Reich Labor Service). He was called up for the "Waffen-SS" in 1944. Grass was trained as a tank gunner and fought with the 10th SS Panzer Division Frundsberg until its surrender to US forces at Marienbad.


title: Günter Grass

text: In 2007, Grass published an account of his wartime experience in "The New Yorker", including an attempt to "string together the circumstances that probably triggered and nourished my decision to enlist." To the BBC, Grass said in 2006: "It happened as it did to many of my age. We were in the labour service and all at once, a year later, the call-up notice lay on the table. And only when I got to Dresden did I learn it was the Waffen-SS."


title: Günter Grass

text: Joachim Fest—German journalist, historian and biographer of Adolf Hitler—remarked, to the German weekly "Der Spiegel", on Grass's disclosure: "After 60 years, this confession comes a bit too late. I can't understand how someone who for decades set himself up as a moral authority, a rather smug one, could pull this off."


title: Günter Grass

text: As Grass was for many decades an outspoken left-leaning critic of Germany's failure to deal with its Nazi past, his statement caused a great stir in the press. Rolf Hochhuth said it was "disgusting" that this same "politically correct" Grass had publicly criticized Helmut Kohl and Ronald Reagan's visit to a military cemetery at Bitburg in 1985, because it contained graves of "Waffen-SS" soldiers. In the same vein, the historian Michael Wolffsohn accused Grass of hypocrisy in not earlier disclosing his SS membership.


title: Günter Grass

text: Others defended Grass, saying his involuntary "Waffen-SS" membership came very early in his life, resulting from his being drafted shortly after his seventeenth birthday. They noted he had always—after the war was lost—been publicly critical of Germany's Nazi past. For example, novelist John Irving criticised those who would dismiss the achievements of a lifetime because of a mistake made as a teenager.


title: Günter Grass

text: Grass's biographer described the controversy as resulting in "the end of a moral institution". Lech Wałęsa initially criticized Grass for keeping silent about his "Waffen-SS" membership for 60 years. He later withdrew his criticism after reading Grass's letter to the mayor of Gdańsk, saying that Grass "set the good example for the others." On 14 August 2006, the ruling party of Poland, Law and Justice, called on Grass to relinquish his honorary citizenship of Gdańsk. Jacek Kurski, a Law and Justice politician said, "It is unacceptable for a city where the first blood was shed, where World War II began, to have a Waffen-SS member as an honorary citizen." But, according to a 2010 poll ordered by city's authorities, the vast majority of Gdańsk citizens did not support Kurski's position. The mayor of Gdańsk, Paweł Adamowicz, said that he opposed submitting the affair to the municipal council because it was not for the council to judge history.


title: Günter Grass

text: An avid pipe smoker for most of his adult life, Grass died of a lung infection on 13 April 2015 in a Lübeck hospital at the age of 87. He was buried in a private family observance on 25 April in Behlendorf, 15 miles south of Lübeck, where he had lived since 1995.


title: Günter Grass

text: American novelist John Irving delivered the main eulogy at a memorial service for Grass on 10 May in the Theater Lübeck. Among those who attended were German President Joachim Gauck, former Chancellor Gerhard Schröder, federal Commissioner for Culture Monika Grütters, film director Volker Schlöndorff, and Paweł Adamowicz, mayor of Gdańsk. Grütters, in remarks to mourners, noted that Grass through his work championed the independence of artists and of art itself. Adamowicz said Grass had "bridged the chasm between Germany and Poland", and praised the novelist's "unwillingness to compromise".


title: Sriimurali

text: Sriimurali (born 17 December 1981), also known simply as Murali, is an Indian actor who works predominantly in Kannada cinema. After making his debut in 2003 in "Chandra Chakori", he appeared in "Kanti" as the eponymous lead, a performance that won him the Karnataka State Film Award for Best Actor in 2004. His performance in the 2014 Kannada film "Ugramm" received unanimous praise and emerged as a major success.


title: Sriimurali

text: Sriimurali was born on 17 December 1981 in Bangalore, Karnataka, in a family of film people. His father S. A. Chinne Gowda is a film producer and brother Vijay Raghavendra, an actor. Actor Rajkumar was his uncle and actors Shiva Rajkumar and Puneeth Rajkumar his cousins. He married his Telugu girlfriend, Vidya from Andhra, on 11 May 2008. They have a son and a daughter together, who are non-identical twins. Vidya is the sister of Prashanth Neel, a director in Kannada cinema, and Aadarsh Balakrishna, an actor in Telugu Cinema.


title: Sriimurali

text: Sriimurali made his debut in films in 2003 with a romance film, "Chandra Chakori". The film performed well and his performance received praise. In "Kanti" set in the backdrop of the Karnataka–Maharashtra border dispute, he played the eponymous lead of a college student who, on falling in love with a Marathi girl, gets embroiled politically. His performance won him the Karnataka State Film Award for Best Actor.


title: Sriimurali

text: Sriimurali then appeared in films such as "Siddu", "Shambu", "Yashwant" and "Preethigaagi", which did not perform well at the box office. In 2008, he appeared in "Minchina Ota", produced by his father, also starring brother Vijay Raghavendra. He also takes care of the production responsibilities of his family banner "Sowbhagya Pictures", under which several films produced by his father were made such as "Sevanthi Sevanthi" and "Ganesha Mathe Bandha".


title: Sriimurali

text: After a hit "Chandra Chakori", Sri Murali could not keep up the expectations of the audiences and all of his consecutive films were flops.


title: Sriimurali

text: Prashanth Neel (Murali's brother in law) came up with an action drama story in 2008, exclusively for taking off Sri Murali's career again on a high note. The movie was initially named "Nandhe" and later changed to "Ugramm". It took nearly 4–5 years for completion of the project, which marked Neel's directorial debut. The film was released in 2014. In the film, Sri Murali played the role of Agastya, a mechanic, who protects Nithya (played by Haripriya) from being caught alive by goons, and takes on the mafia. The film emerged as a critical and commercial success with his performance receiving acclaim. A. Sharadhaa of "The Indian Express" wrote: "This is definitely a 'comeback' film for Murali, a carefully thought-out project for him by the director. Murali is smarter than he looks and tougher than people expected him to be." He received his first nominations for Best Actor in Filmfare Awards South and SIIMA Awards. Following the massive success of the film, it was reported that he was flooded with offers for film totaling to 67, all of which he rejected.


title: Satish Dhawan Space Centre

text: Satish Dhawan Space Centre - SDSC (formerly Sriharikota Range - SHAR) is a rocket launch centre (spaceport) operated by Indian Space Research Organisation (ISRO). It is located in Sriharikota, Tirupati district of Andhra Pradesh. Sriharikota Range was renamed in 2002 after ISRO's former chairman Satish Dhawan.


title: Satish Dhawan Space Centre

text: Sriharikota island was chosen in 1969 for a satellite launching station. The centre became operational in 1971 when an RH-125 sounding rocket was launched. The first attempted launch of an orbital satellite, Rohini 1A aboard a Satellite Launch Vehicle, took place on 10 August 1979, but due to a failure in thrust vectoring of the rocket's second stage, the satellite's orbit decayed on 19 August 1979. SHAR was named as 'Satish Dhawan Space Centre SHAR' (SDSC), on 5 September 2002, in memory of Satish Dhawan, former chairman of the ISRO.


title: Satish Dhawan Space Centre

text: The SHAR facility now consists of two launch pads, with the second built in 2005. The second launch pad was used for launches beginning in 2005 and is a universal launch pad, accommodating all of the launch vehicles used by ISRO. The two launch pads will allow multiple launches in a single year, which was not possible earlier. India's lunar orbiter Chandrayaan-1 launched from the centre at 6:22 AM IST on 22 October 2008. India's first Mars orbiter Mangalyaan was launched from the centre on 5 November 2013, which was successfully placed into Mars orbit on 24 September 2014.


title: Satish Dhawan Space Centre

text: Initially under Indian Human Spaceflight Programme existing launch facilities will be augmented to meet the target of launching a crewed spacecraft called "Gaganyaan".


title: Satish Dhawan Space Centre

text: Satish Dhawan Space Centre (SHAR) is located in Sriharikota, a spindle-shaped barrier island on the east coast of Andhra Pradesh. Features like a good launch azimuth corridor for various missions, nearness to the equator (benefiting eastward launches), and large uninhabited area for a safety zone make it an ideal spaceport.


title: Satish Dhawan Space Centre

text: SHAR covers a total area of about with a coastal length of . Prior to its acquisition for ISRO by the Government of India, it was a firewood plantation of Eucalyptus and Casuarina trees. This island is affected by both south-westerly and north-easterly monsoons, but heavy rains come only in October and November. Thus many clear days are available for out-door static tests and launchings.


title: Satish Dhawan Space Centre

text: SHAR is linked to Sullurupeta by a road across Pulicat Lake. Sullurupeta has connectivity with other parts of India by Indian Railways and is on a National Highway 16 (India) that connects it to Chennai (about south) and Kolkata.


title: Satish Dhawan Space Centre

text: Originally known as the Sriharikota Range (SHAR) and later named after Satish Dhawan. It is India's primary orbital launch site to this day. First flight-test of 'Rohini-125', a small sounding rocket which took place on 9 October 1971 was the first rocket launch from SHAR. Since then technical, logistic and administrative infrastructure have been enhanced. Together with the northerly Balasore Rocket Launching Station, the facilities are operated under the ISRO Range Complex (IREX) headquartered at SHAR.


title: Satish Dhawan Space Centre

text: The range became operational when three Rohini 125 sounding rockets were launched on 9 and 10 October 1971. Previously, India used Thumba Equatorial Rocket Launching Station (TERLS), at Thiruvananthapuram, on the south-western coast of India, to launch sounding rockets. The first test launch of the complete SLV-3 rocket occurred in August 1979 but it was only partially successful following a malfunction in the second-stage guidance system. SHAR facilities worked satisfactorily during the SLV-3 preparation and launch. On 18 July 1980 the SLV-3 successfully launched India's third satellite. Out of the four SLV launches from SHAR, two were successful.


title: Satish Dhawan Space Centre

text: The ASLV orbital launcher was integrated vertically, beginning with motor and subassembly preparations in the Vehicle Integration Building (VIB) and completed on the pad within the 40 m tall Mobile Service Structure. The first ASLV launch from SHAR took place in 1987 and resulted in a failure. Eventually, out the four ASLV launches from 1987 to 1994, only one was successful.


title: Satish Dhawan Space Centre

text: The Polar Satellite Launch Vehicle launch complex was commissioned during 1990. It has a 3,450 tonne, 76.5 m high Mobile Service Tower (MST) which provides the SP-3 payload clean room. The solid propellant motors for the PSLV are processed by SHAR, which also carries out launch operations. The first launch of the PSLV took place on 20 September 1993.


title: Satish Dhawan Space Centre

text: The first launch of India's Geosynchronous Satellite Launch Vehicle (GSLV) was successfully completed on 18 April 2001. GSLV, with its own cryogenic upper stage, has enabled the launch of communications satellites of the class up to 2 tonnes. The next variant of GSLV is GSLV Mk III with its own cryogenic high-thrust engine and stage capable of launching communications satellites of the 4-ton class.


title: Satish Dhawan Space Centre

text: The SDSC has two operational orbital launch pads. SHAR is ISRO's satellite launching base and additionally provides launch facilities for the full range of Rohini sounding rockets. The Vehicle Assembly, Static Test and Evaluation Complex (VAST, previously STEX) and the Solid Propellant Space Booster Plant (SPROB) are located at SHAR for casting and testing solid motors. The site also has a Telemetry, Tracking, Range Instrumentation, & Control centre for Range Operation (RO), Liquid Propellant Storage and Servicing Facilities (LSSF), the Management Service Group and Sriharikota Common Facilities. The PSLV launch complex was commissioned in 1990. It has a 3,450 tonne, 76.5 m high Mobile Service Tower (MST) which provides the SP-3 payload clean room.


title: Satish Dhawan Space Centre

text: The Solid Propellant Space Booster Plant (SPROB) processes large size propellant grains for the satellite launch vehicles. The Vehicle Assembly & Launching Facility (VALF), Solid Motor Preparation & Environmental Testing Facility (SMP&ETF) tests and qualifies different types of solid motor for launch vehicles. The control centre at SHAR houses computers and data processing, closed circuit television, real-time tracking systems and meteorological observation equipment. It is linked to eight radars located at Sriharikota and the five stations of ISRO's Telemetry, Tracking & Command Network (ISTRAC).


title: Satish Dhawan Space Centre

text: The propellant production plant produces composite solid propellant for rocket motors of ISRO using ammonium perchlorate (oxidiser), fine aluminium powder (fuel) and hydroxyl terminated polybutadiene (binder). The solid motors processed here include those for the first-stage booster motor of the Polar Satellite Launch Vehicle (PSLV) — a five segmented motor of diameter and length, weighing with a thrust level of .


title: Satish Dhawan Space Centre

text: Rocket motors and their subsystems have to be rigorously tested and evaluated on ground before they are declared flight worthy. The facilities at SDSC are used for testing solid rocket motors, both at ambient conditions and simulated high altitude conditions. Besides these, there are facilities for conducting vibration, shock, constant acceleration and thermal/humidity tests.


title: Satish Dhawan Space Centre

text: SDSC has infrastructure for launching satellites into low Earth orbit, polar orbit and geo-stationary transfer orbit. The launch complexes provide support for vehicle assembly, fueling, checkout and launch operations. The centre also has facilities for launching sounding rockets for atmospheric studies. The mobile service tower, launch pad, preparation facilities for different launch stages & spacecraft, storage, transfer and servicing facilities for liquid propellants, etc., are the principal parts of the PSLV/GSLV launch complex.


title: Satish Dhawan Space Centre

text: For supporting the GSLV Mark III, additional facilities were set up at SDSC. A new plant (SPP) is set up to process heavier class boosters with 200 tonnes of Solid propellant. The static test complex is being augmented for qualifying the S-200 booster. Other new facilities include a Solid Stage Assembly Building, Satellite Preparation and Filling Facility and Hardware Storage buildings. The existing liquid propellant and cryogenic propellant storage and filling systems, Propellant Servicing Facilities will also be augmented. The range instrumentation system will be enhanced further.


title: Satish Dhawan Space Centre

text: SDSC also has a S band Doppler weather radar that contributes to India Meteorological Department radar network and serves as a stand-in for Doppler weather radar in Chennai.


title: Satish Dhawan Space Centre

text: ISRO opened a viewing gallery at the Satish Dhawan Space Centre in March 2019. The gallery faces the two launchpads and can accommodate 5,000 people giving the general public the opportunity to witness rocket launches. The launch of PSLV-C45 on 1 April 2019 was the first launch that allowed spectators into the gallery.


title: Satish Dhawan Space Centre

text: The SLV3 Launch Pad began operation in 1979 and was decommissioned in 1994. It was used by two launch vehicles of the ISRO: the Satellite Launch Vehicle (SLV) and the Augmented Satellite Launch Vehicle (ASLV). Initially it was built for launching SLV-3s but was later also used as an ASLV launch complex. The first launch from this pad occurred on 10 August 1979, and was that of the first experimental flight of SLV-3 carrying the Rohini Technology Payload satellite. The last flight was of ASLV on 4 May 1994 carrying SROSS-C2.


title: Satish Dhawan Space Centre

text: The First Launch Pad began operation in 1993. It is currently used to launch the Polar Satellite Launch Vehicle, and formerly used by the Geosynchronous Satellite Launch Vehicle. It is one of two operational orbital launch pads at the site, the other being the Second Launch Pad, which opened in 2005. The first launch from this pad occurred on 20 September 1993, and was the maiden flight of the Polar Satellite Launch Vehicle carrying the IRS-1E satellite. The maiden flight of the Small Satellite Launch Vehicle also occurred from this pad on 7 August 2022.


title: Satish Dhawan Space Centre

text: The First Launch Pad is undergoing major expansion with PIF (PSLV Integration Facilities) project worth . Once complete, the first launch pad is expected to cater to around 15 launches per year.


title: Satish Dhawan Space Centre

text: The Second Launch Pad was designed, supplied, erected and commissioned by MECON Limited, a Government of Indian Enterprise, located at Ranchi (Jharkhand, India) during the period March 1999 to December 2003. It cost about at that time. The second launch pad with associated facilities was built in 2005. However it became operational on 5 May 2005 with the launching of PSLV-C6. MECON's sub-contractors for this project including Inox India, HEC, Tata Growth, Goderej Boyce, Simplex, Nagarjuna Construction, Steelage, etc. The other Launch Pad being the First Launch Pad. It is used by Polar Satellite Launch Vehicles, Geosynchronous Satellite Launch Vehicles, GSLV Mark III and is intended for India's first crewed space mission.


title: Satish Dhawan Space Centre

text: The first launch from the pad occurred on 5 May 2005, and was of a Polar Satellite Launch Vehicle carrying the CARTOSAT-1 and HAMSAT satellites. India's 1st Moon Mission, Chandrayan-I was launched from this launch pad on 22 October 2008. Its follow-up mission Chandrayaan-2 was also launched from this launch pad on 22 July 2019.


title: Satish Dhawan Space Centre

text: This launch pad is intended to be used for future Indian rockets like the Unified Launch Vehicle and GSLV Mark III as well as the older ones like Polar Satellite Launch Vehicle and Geosynchronous Satellite Launch Vehicle. The launch pad will be used for the India's future human space missions. One of the main reasons of building this launch pad is that it will increase the frequency of orbital launches by ISRO.


title: Satish Dhawan Space Centre

text: In 2018, it was reported that the launch of India's first crewed orbital spacecraft "Gaganyaan" is scheduled to be launch from the third launch pad before 2022. However, in November 2019, ISRO released tenders for augmentation of Second Launch Pad for Gaganyaan project.


title: Vigan

text: Vigan, officially the City of Vigan (; ), is a 4th class component city and capital of the province of Ilocos Sur, Philippines. According to the 2020 census, it has a population of 53,935 people.


title: Vigan

text: Located on the western coast of the large island of Luzon, facing the South China Sea, it is a UNESCO World Heritage Site and it is one of the few Spanish colonial towns left in the Philippines whose old structures have mostly remained intact.It is well known for its sett pavements and a unique architecture of the Spanish Philippines colonial era which fuses Native Philippine and Oriental building designs and construction, with colonial Spanish architecture that is still abundant in the area, mainly the Bahay na Bato houses and an Earthquake Baroque church. Former Philippine president Elpidio Quirino, the sixth President of the Philippines, was born in Vigan, at the former location of the Provincial Jail (his father was a warden); he resided in the Syquia Mansion. The entire city of Vigan was later inscribed as a UNESCO World Heritage City after being declared as a UNESCO World Heritage Site. It is a member of the Organization of World Heritage Cities (OWHC).


title: Vigan

text: In May 2015, Vigan City was officially recognized as one of the New7Wonders Cities together with Beirut, Doha, Durban, Havana, Kuala Lumpur and La Paz. New7Wonders Foundation president and founding member Bernard Weber led a ceremony held at St. Paul Cathedral where he handed a bronze plaque to former Vigan Mayor Eva Grace Singson-Medina, signifying the heritage city's election as one of the world's wonder cities.


title: Vigan

text: The area of Vigan was originally a settlement of traders coming from the Fujian Province, China. At the time of Spanish colonisation, the Chinese settlers, whose language was Southern Min (Min Nan, often referred to as "Hokkien" by most Filipinos), referred to the area as "Bee Gan" (), which means "Beautiful Shore." Since the Spanish conquistadors interchanged V and the B to refer to the /b/ sound, they spelled the Hokkien Chinese name "Bee Gan" as "Vigan", which is the name used to this day.


title: Vigan

text: Vigan's Chinese heritage is still evident from the numerous elite Chinese creole families who come from the area, many of whom adopted Hispanic family names. Others, such as the Syquia family, have retained Chinese-derived surnames, though most, if not all, of the Christian Chinese creole families fully Hispanicised themselves culturally.


title: Vigan

text: The most commonly known source of the city's name is from the Biga'a plant, which once grew abundantly along the banks of the Mestizo River, from which captain Juan de Salcedo derived the city's name (after a misunderstanding with the locals, thinking he was asking the name of the plants).


title: Vigan

text: The city's full name at the time of its Spanish foundation was "Villa Fernandina", or "Town of Ferdinand", in honor of Prince Ferdinand, the firstborn son of King Philip II of Spain. As the city grew, and the seat of the Archdiocese of Nueva Segovia transferred to Vigan, it was later renamed "Ciudad Fernandina de Vigan" ("Ferdinand's City of Vigan/Fernandine City of Vigan").


title: Vigan

text: Due to silting of the Mestizo River, Vigan City is no longer separated from the mainland, therefore no longer an island. The city is unique in the Philippines because it is one of many extensive surviving Philippine historic cities, dating back to the 16th century.


title: Vigan

text: Vigan was a coastal trading post long before the Spaniards arrived; Chinese traders sailing from the South China Sea came to "Isla de Vigan" (Island of Vigan) via the Mestizo River that surrounded it. On board their ships were seafaring merchants who came to trade goods from other Asian kingdoms in exchange for gold, beeswax, and other mountain products brought by the indigenous peoples from the Cordillera region.


title: Vigan

text: In the book "The Philippine Island" (Vol. III, p. 276, Blair and Robertson) two letters from Governor-General Guido de Lavezaris to King Philip II of Spain mention: "It seemed best to send Captain Juan de Salcedo with 70 or 80 soldiers to explore the coast of Los Ilocanos on the shores of the river called Bigan." The Spaniards led by Salcedo marched north from Manila on May 20, 1572. They arrived in Vigan on June 13, 1572. Tirad Pass, declared a National Shrine, had been the last stand of the Filipino Revolutionary Forces under General Emilio Aguinaldo during the same period.


title: Vigan

text: Thus, after the successful expedition and the exploration of the North, Juan de Salcedo founded "Villa Fernandina de Vigan" in honor of King Philip II's son, Prince Ferdinand, who died at the age of four. From Vigan, Salcedo rounded the tip of Luzón and proceeded to pacify Camarines, Albay, and Catanduanes. As a reward for his services to the King of Spain, Salcedo was awarded the old province of Ilocos, which consisted of the modern provinces of Ilocos Norte, Ilocos Sur, Abra, La Union and part of Mountain Province as his hacienda (estate), and was accorded the title of "Justicia Mayor de esta Provincia de Ylocos" (Province Mayor of Ilocos).


title: Vigan

text: In 1574, Salcedo returned to the capital of his "encomienda" (trusteeship), Vigan, bringing with him his soldiers and some Augustinian missionaries to pioneer the evangelization of the Ilocos region. He established a Spanish city for the purpose of controlling the neighboring country.


title: Vigan

text: Governor General Gómez Pérez Dasmariñas, in his account of "encomienda" dated in Manila on May 31, 1591, states: "The town of Vigan called "Villa Fernandina" consisted of Spanish settlers; a priest; a Justice Alcalde Mayor (Governor); and a Deputy. The King collects 800 tributes (equivalent to 3,200 subjects)." During this period, Vigan was composed of 19 "barrio"s (districts).


title: Vigan

text: Between 1645 and 1660, Vigan was divided into 21 "Cabezas de Barrio" (Town Mayors) as mentioned in the "Libro de Casamiento" (Book of Marriage); from the records of the parish house of Vigan found in its archives. Separated from the indigenous population, the Chinese migrants were residents in a neighbourhood called El Pariancillo, los Sangleyes del parian (The Sangleyes of the Parian); and the Spanish settlers were residents in a town called "Los Españoles de la Villa" (The Town Spaniards).


title: Vigan

text: During the Philippine Revolution, revolutionary forces under Manuel Tinio, supported by the Ilocano rebels, attacked and defeated the Spanish colonial forces and captured the city in the Siege of Vigan. During the Philippine–American War, American forces led by Commander McCracken and Lt. Col. James Parker occupied the town in Nov. 1899.


title: Vigan

text: At the start of World War II, Vigan was one of the first places in the Philippines invaded by Japan on December 10, 1941. In 1945, combined U.S. and Philippine Commonwealth ground troops, aided by Ilocano resistance fighters, defeated the Japanese Imperial forces and liberated Vigan.


title: Vigan

text: In 1999, Vigan was listed by UNESCO as the best preserved example of Spanish colonial towns in Asia. Its architecture is the conglomeration of cultural elements from the Philippines, China, and Spain, making it unique in the world.


title: Vigan

text: On December 27, 2000, then President Joseph Estrada signed Republic Act No. 8988, that "revalidated and recognized" Vigan's city status granted by virtue of the Royal Decree of September 7, 1757, issued by Ferdinand VI, King of Spain. This legislation serves as Vigan's present city charter. The charter did not provide a clause for a plebiscite and the law took effect in January 2001.


title: Vigan

text: On July 27, 2022, a 7.0 magnitude earthquake struck parts of Luzon, damaging the city's UNESCO World Heritage sites including the Vigan Cathedral and old-century houses, as well as few power lines toppled along Calle Crisologo.


title: Vigan

text: Vigan is situated in the northern part of Luzon, the Philippines’ largest island. It serves as the capital of Ilocos Sur and has been a major political and trading center since before the Spanish colonizers arrived in the Philippines.


title: Vigan

text: It is away from Manila, away from Laoag City, and away from San Fernando, La Union, the regional capital of Ilocos Region.


title: Vigan

text: Its of land consists mostly of plains with gentle hills. Its boundaries on the north, east, south, and west are the municipalities of Bantay, Santa, Caoayan, and Santa Catalina, respectively. The South China Sea is on its southwest portion.


title: Vigan

text: Majority of its land, 60 percent of it, is used for agriculture. Around 32 percent is made up of residential area, nearly three percent are for commercial and industrial use, and around one percent is for institutional purposes. There are also forest reserves and fishponds included in Vigan's land area.


title: Vigan

text: Vigan is made up of 39 barangays. Thirty of them are classified as rural, but they occupy only 2,366 hectares. The remaining nine are classified as "poblacion" barangays and are together 144.75 hectares big.


title: Vigan

text: The barangays of Pagburnayan, Paoa, and Tamag are on the area of rolling plains. On the other hand, portions of Barangays Tamag and the barangays of Bulala and Salindeg are found on the city's hilly parts.


title: Vigan

text: Its most dominant hill feature is the Vigan Gap Hill in the eastern part, just 10 kilometers away from the city. Vigan used to be separated from the rest of the mainland by the rivers of Abra, Mestizo and Govantes, making it an island during that time. The Govantes River cuts the current Vigan plain from North to South.


title: Vigan

text: The large Abra and Mestizo rivers, together with the rivers of Bantay, Bantaoay, Nauman and Santo Tomas serve as part of a network that drain the Vigan plains. These rivers are not only important in safekeeping the city from floods, they also served as important ways of transport for trade-related activities from the 15th century to the 19th century, that helped make Vigan a thriving center. The most vital of these rivers is said to be the Mestizo River which was used by the small vessels to transport goods and people.


title: Vigan

text: The land area of Vigan is generally flat. Slopes of 20 are found at Barangay V, Tamag, and Paoa. There are no forest reserves in the city in terms of potential and raw materials. Bamboo is the only forest product in Vigan.


title: Vigan

text: There are five soil types in the city. First, the "Bantay Loam", located at the southern portion of Raois, has a land area of 36.67 hectares, and is good as pastureland. The second, "Umingan sandy", with a land area of 1191.57 hectares, is good for upland rice and vegetables. The third, "San Manuel clay loam", which is best for bananas, cotton and vegetables, has an area of 1244.57 hectares. The fourth, "Bantog clay"—considered as the most significant type for soil, and the best clay material for making pots, jars and all earthenware, has a land area of 31.65 hectares. The fifth, "beach sand", with a land area of 7.28 hectares, is generally found on the shores of all the beaches of Vigan, and is best for coconut plantation.


title: Vigan

text: Vigan is politically subdivided into 39 barangays. These barangays are headed by elected officials: Barangay Captain, Barangay Council, whose members are called Barangay Councilors. All are elected every three years.


title: Vigan

text: The sedimentary and metamorphic rocks that are present in the city are alluvium, fluviatile, lacustrine, paludal and beach deposits such as coral, stools, and beach rock. These are predominantly found along the coastal areas of Vigan. An important non-metallic mineral resource found in Vigan is the kind of clay that is used in making earthen jars locally called "burnay." Earthenware of different uses and sizes are made of this kind of clay. Known as "Bantog clay", the mineral is the basic material in making bricks. These bricks are the original materials in building the Hispanic houses of Vigan.


title: Vigan

text: Vigan is situated in a Quaternary Age sedimentary plain called the Vigan-Bantay Plain which is part of the Ilocos coastal plain. The Vigan-Bantay Plain is bounded on the east by a moderately rugged Miocene sediments consisting of interbedded sandstones and shale to very rugged Meta-volcanics and Meta sediment topography; on the south is the Municipality of Santa where the north–south trending fault terminates; to the west is the South China Sea; while the northern boundary opens to the northern extension of the Ilocos coastal plain.


title: Vigan

text: The central part of the plain is characterized by a dissected ridge of Plio-Pleistocene age that trends in a northeast–southwest direction. The ridge divides the Vigan-Bantay Plain into northern and southern plains.


title: Vigan

text: The northern part of the plain is drained by minor rivers namely: Bantaoay, Santo Tomas, and Nauman rivers, while the Abra River is the main drainage network of the southern portion of the plain. The Abra River meanders into the hinterland but exhibits a braided pattern across the plain.


title: Vigan

text: The drainage network of the eastern margin of Vigan-Bantay plain consist of deeply cut valleys whose pattern is strongly controlled by main faulting trends, particularly those in the northerly and easterly directions.


title: Vigan

text: Vigan is being drained by the Vigan River and Bantay River, respectively, on the north and on the south by Mestizo River whose water discharge comes from the Bantaoay head waters.


title: Vigan

text: The relief of the Vigan-Bantay plain is actively level to undulating with a slope ranging from 0% to 8%. Vigan in particular is generally in level with several hills in Barangays Tamag, Bulala, and Salindeg, sometimes reaching about 50 meters in elevation and has a slope ranging from 3% to 8%.


title: Vigan

text: The eastern margin of the plain characterized by a steep to very steep slope, about 40% to 60%, the relief often reaches an elevation of more that 600 meters especially the northerly and easterly portion.


title: Vigan

text: The dominant topographic feature in the eastern margin of the town is the Vigan Gap Hill where the continuously shifting Vigan River cuts its way. The Gap Hill is located approximately 10 kilometers east of Vigan.


title: Vigan

text: The city of Vigan falls under (tropical savanna), which is characterized by two pronounced seasons – the dry season which starts from the month of November and ends in April; and the wet season which spans the months of May to October. The average annual rainfall is and the heaviest registered rainfall is .


title: Vigan

text: The average temperature is 26 °C. The average warmest temperature is 30.9 °C and the average coldest temperature is 21.1 °C. An average of 7-10 typhoons visit Vigan annually. The average relative humidity is 81%.


title: Vigan

text: Vigan, belonging to the first congressional district of the province of Ilocos Sur, is governed by a mayor designated as its local chief executive and by a city council as its legislative body in accordance with the Local Government Code. The mayor, vice mayor, and the councilors are elected directly by the people through an election which is being held every three years.


title: Vigan

text: When Juan de Salcedo founded Vigan in 1572, he decided to pattern its urban plan with that of Intramuros, the walled city in Manila.


title: Vigan

text: The urban planners of the Spanish government also followed a basic pattern that can be observed in most old towns in the country, whose establishment dates back to the Spanish colonial period. This pattern is detailed in the "Ley de las Indias," the Law of the Indies, and was put into force in the 18th century. Under the Law of the Indies streets were to follow a grid pattern, the center of which being a plaza or central park.


title: Vigan

text: In Vigan, the central park is the Plaza Salcedo. Next to it are the administrative buildings—the Casa Real or provincial administrative office, and the "municipio" (municipal hall). A stone's throw away are the religious buildings—the seminary of the archdiocese, the Arzobispado (Archbishop's Palace), and the St. Paul's Cathedral. Beside these religious structures is the church-run school, the Saint Paul College, known in its early days as the "Colegio de Niñas." After the full transfer of the said school to the neighboring towns of Bantay and San Vicente, the building was handed over to the Archdiocese of Nueva Segovia and is currently being occupied by a retail store chain, with only a commemorative plaque at the building's entrance and the old "ROSARY COLLEGE" concrete sign at its rear reminding visitors of its past (the school's old logo, once found at the building's facade, has been removed sometime later).


title: Vigan

text: A unique thing is the existence of another plaza, the "Plaza Burgos", which is immediately beside the St. Paul's Cathedral. After the first tier emanating from Plaza Salcedo are the houses of prominent residents that now make up the preserved heritage houses of Vigan. This urban plan remained relatively intact despite wars and natural calamities that have been endured by Vigan since its foundation.


title: Vigan

text: The major changes to the original urban landscape were caused by fires. The Casa Real was replaced with a provincial capitol building during the American period when the original structure burned down. The archdiocese seminary was also destroyed by fire in 1968, and it lay in ruins until the late 1990s, when part of a shopping mall was built on the site.


title: Vigan

text: The residential areas were not spared. Some of the houses on Crisologo Street were casualties of fire during the Japanese period; several houses on Quezon Avenue were destroyed by fire as well in 1952; while in 1971, some houses near Plaza Burgos burned down as well. The houses along Crisologo Street that were burned were later reconstructed faithfully following the architecture of the former structures.


title: Vigan

text: Presently, there are other major areas of activities other than the two plazas, though these are still where most recreation and shopping are done. One may also go to the southern part of the city to reach the commercial area and public market. The current Public Market is a new one, as the old one (formerly the Imelda Socio-Commercial Complex), on the same site, was (also) destroyed by fire. A new mall (opened in December 2017) has risen from the site of the city's first Public Market, found in the center of the business district, after being the site of some business establishments and a tricycle-for-hire terminal.


title: Vigan

text: Popular sites include Calle Crisologo located in the Mestizo district- the old quarters of the city. Syquia Mansion Museum, Plaza Salcedo's Dancing Fountain, Padre Burgos House, and the National Museum of the Philippines. Nearby is the Bantay Church Bell Tower. Of special note is the Hotel Luna, which houses an extensive collection of art, including La Mandolinera by Jose Luna. Centuries-old Sta. Maria Church, designated also as a UNESCO World Heritage Site.


title: Vigan

text: Modes of transport within the city are purely land-based. Vehicles for public use include jeepneys, tricycles, vans-for-hire (or PUVs/public utility vehicles) and "calesa"s (horse-drawn vehicles). Buses, mini-buses and jeepneys provide transportation to and from Vigan. The metro Vigan transport system is mostly served by tricycles, which are color- and number-coded to identify their municipality of origin.


title: Vigan

text: Vigan City is well-served by a network of roads and a major highway that connects to Manila North Road, the highway leading to Manila and the rest of the country. Major bus companies such as Dominion Bus Lines, Viron Transit, Partas, and Aniceto/St. Joseph operate terminals in Vigan. GMW Florida Transport operates a terminal in Bantay, just outside Vigan. Bus companies such as Maria de Leon and Fariñas pass by Vigan on their way to Laoag. They operate direct and/or indirect bus services from Vigan City to points in Luzon, mostly to Manila, Baguio, and Laoag and vice versa. There are also independent bus operators plying the Laoag-Vigan-Carmen and Vigan-Abra routes, and have a joint terminal found at the New Vigan Public Market Annex. A taxi service started operating in 2019, just before the COViD-19 pandemic struck.


title: Vigan

text: A secondary airport called Vigan Airport (also known as Mindoro Airport) is located at Barangay Mindoro. It has one asphalted runway, 900 meters long and 30 meters wide. The airport was once a dormant asset of the city for it does not generate revenue, with only chartered and private planes using it; it is currently being upgraded and is on its way toward commercialization.


title: Quadratic form

text: In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,


title: Quadratic form

text: is a quadratic form in the variables and . The coefficients usually belong to a fixed field , such as the real or complex numbers, and one speaks of a quadratic form over . If formula_2, and the quadratic form takes zero only when all variables are simultaneously zero, then it is a definite quadratic form, otherwise it is an isotropic quadratic form.


title: Quadratic form

text: Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric, second fundamental form), differential topology (intersection forms of four-manifolds), and Lie theory (the Killing form).


title: Quadratic form

text: Quadratic forms are not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadratic form is one case of the more general concept of homogeneous polynomials.


title: Quadratic form

text: Quadratic forms are homogeneous quadratic polynomials in "n" variables. In the cases of one, two, and three variables they are called unary, binary, and ternary and have the following explicit form:


title: Quadratic form

text: The theory of quadratic forms and methods used in their study depend in a large measure on the nature of the coefficients, which may be real or complex numbers, rational numbers, or integers. In linear algebra, analytic geometry, and in the majority of applications of quadratic forms, the coefficients are real or complex numbers. In the algebraic theory of quadratic forms, the coefficients are elements of a certain field. In the arithmetic theory of quadratic forms, the coefficients belong to a fixed commutative ring, frequently the integers Z or the "p"-adic integers Z. Binary quadratic forms have been extensively studied in number theory, in particular, in the theory of quadratic fields, continued fractions, and modular forms. The theory of integral quadratic forms in "n" variables has important applications to algebraic topology.


title: Quadratic form

text: Using homogeneous coordinates, a non-zero quadratic form in "n" variables defines an ("n"−2)-dimensional quadric in the ("n"−1)-dimensional projective space. This is a basic construction in projective geometry. In this way one may visualize 3-dimensional real quadratic forms as conic sections.


title: Quadratic form

text: An example is given by the three-dimensional Euclidean space and the square of the Euclidean norm expressing the distance between a point with coordinates and the origin:


title: Quadratic form

text: A closely related notion with geometric overtones is a quadratic space, which is a pair , with "V" a vector space over a field "K", and a quadratic form on "V". See below for the definition of a quadratic form on a vector space.


title: Quadratic form

text: The study of particular quadratic forms, in particular the question of whether a given integer can be the value of a quadratic form over the integers, dates back many centuries. One such case is Fermat's theorem on sums of two squares, which determines when an integer may be expressed in the form , where "x", "y" are integers. This problem is related to the problem of finding Pythagorean triples, which appeared in the second millennium B.C.


title: Quadratic form

text: In 628, the Indian mathematician Brahmagupta wrote "Brāhmasphuṭasiddhānta", which includes, among many other things, a study of equations of the form . In particular he considered what is now called Pell's equation, , and found a method for its solution. In Europe this problem was studied by Brouncker, Euler and Lagrange.


title: Quadratic form

text: In 1801 Gauss published "Disquisitiones Arithmeticae," a major portion of which was devoted to a complete theory of binary quadratic forms over the integers. Since then, the concept has been generalized, and the connections with quadratic number fields, the modular group, and other areas of mathematics have been further elucidated.


title: Quadratic form

text: So, two different matrices define the same quadratic form if and only if they have the same elements on the diagonal and the same values for the sums formula_12 and formula_13 In particular, the quadratic form formula_14 is defined by a unique symmetric matrix


title: Quadratic form

text: the matrix formula_18 is symmetric, defines the same quadratic form as , and is the unique symmetric matrix that defines formula_19


title: Quadratic form

text: So, over the real numbers (and, more generally, over a field of characteristic different from two), there is a one-to-one correspondence between quadratic forms and symmetric matrices that determine them.


title: Quadratic form

text: A fundamental question is the classification of the real quadratic form under linear change of variables.


title: Quadratic form

text: Jacobi proved that, for every real quadratic form, there is an orthogonal diagonalization, that is an orthogonal change of variables that puts the quadratic form in a "diagonal form"


title: Quadratic form

text: where the associated symmetric matrix is diagonal. Moreover, the coefficients are determined uniquely up to a permutation.


title: Quadratic form

text: If the change of variables is given by an invertible matrix, that is not necessarily orthogonal, one can suppose that all coefficients are 0, 1, or −1. Sylvester's law of inertia states that the numbers of each 1 and −1 are invariants of the quadratic form, in the sense that any other diagonalization will contain the same number of each. The signature of the quadratic form is the triple , where "n" is the number of 0s and "n" is the number of ±1s. Sylvester's law of inertia shows that this is a well-defined quantity attached to the quadratic form.


title: Quadratic form

text: The case when all "λ" have the same sign is especially important: in this case the quadratic form is called positive definite (all 1) or negative definite (all −1). If none of the terms are 0, then the form is called ; this includes positive definite, negative definite, and indefinite (a mix of 1 and −1); equivalently, a nondegenerate quadratic form is one whose associated symmetric form is a nondegenerate "bilinear" form. A real vector space with an indefinite nondegenerate quadratic form of index (denoting "p" 1s and "q" −1s) is often denoted as R particularly in the physical theory of spacetime.


title: Quadratic form

text: The discriminant of a quadratic form, concretely the class of the determinant of a representing matrix in "K"/("K") (up to non-zero squares) can also be defined, and for a real quadratic form is a cruder invariant than signature, taking values of only “positive, zero, or negative”. Zero corresponds to degenerate, while for a non-degenerate form it is the parity of the number of negative coefficients, formula_21


title: Quadratic form

text: Let "q" be a quadratic form defined on an "n"-dimensional real vector space. Let "A" be the matrix of the quadratic form "q" in a given basis. This means that "A" is a symmetric matrix such that


title: Quadratic form

text: where "x" is the column vector of coordinates of "v" in the chosen basis. Under a change of basis, the column "x" is multiplied on the left by an invertible matrix "S", and the symmetric square matrix "A" is transformed into another symmetric square matrix "B" of the same size according to the formula


title: Quadratic form

text: by a suitable choice of an orthogonal matrix "S", and the diagonal entries of "B" are uniquely determined – this is Jacobi's theorem. If "S" is allowed to be any invertible matrix then "B" can be made to have only 0,1, and −1 on the diagonal, and the number of the entries of each type ("n" for 0, "n" for 1, and "n" for −1) depends only on "A". This is one of the formulations of Sylvester's law of inertia and the numbers "n" and "n" are called the positive and negative indices of inertia. Although their definition involved a choice of basis and consideration of the corresponding real symmetric matrix "A", Sylvester's law of inertia means that they are invariants of the quadratic form "q".


title: Quadratic form

text: The quadratic form "q" is positive definite (resp., negative definite) if (resp., ) for every nonzero vector "v". When "q"("v") assumes both positive and negative values, "q" is an indefinite quadratic form. The theorems of Jacobi and Sylvester show that any positive definite quadratic form in "n" variables can be brought to the sum of "n" squares by a suitable invertible linear transformation: geometrically, there is only "one" positive definite real quadratic form of every dimension. Its isometry group is a "compact" orthogonal group O("n"). This stands in contrast with the case of indefinite forms, when the corresponding group, the indefinite orthogonal group O("p", "q"), is non-compact. Further, the isometry groups of "Q" and −"Q" are the same (, but the associated Clifford algebras (and hence pin groups) are different.


title: Quadratic form

text: A quadratic form over a field "K" is a map formula_25 from a finite-dimensional "K"-vector space to "K" such that formula_26 for all formula_27 and the function formula_28 is bilinear.


title: Quadratic form

text: More concretely, an "n"-ary quadratic form over a field "K" is a homogeneous polynomial of degree 2 in "n" variables with coefficients in "K":


title: Quadratic form

text: This formula may be rewritten using matrices: let "x" be the column vector with components "x", ..., "x" and be the "n"×"n" matrix over "K" whose entries are the coefficients of "q". Then


title: Quadratic form

text: Two "n"-ary quadratic forms "φ" and "ψ" over "K" are equivalent if there exists a nonsingular linear transformation such that


title: Quadratic form

text: Let the characteristic of "K" be different from 2. The coefficient matrix "A" of "q" may be replaced by the symmetric matrix with the same quadratic form, so it may be assumed from the outset that "A" is symmetric. Moreover, a symmetric matrix "A" is uniquely determined by the corresponding quadratic form. Under an equivalence "C", the symmetric matrix "A" of "φ" and the symmetric matrix "B" of "ψ" are related as follows:


title: Quadratic form

text: Thus, "b" is a symmetric bilinear form over "K" with matrix "A". Conversely, any symmetric bilinear form "b" defines a quadratic form


title: Quadratic form

text: and these two processes are the inverses of each other. As a consequence, over a field of characteristic not equal to 2, the theories of symmetric bilinear forms and of quadratic forms in "n" variables are essentially the same.


title: Quadratic form

text: Given an "n"-dimensional vector space "V" over a field "K", a "quadratic form" on "V" is a function formula_36 that has the following property: for some basis, the function "q" that maps the coordinates of formula_37 to formula_38 is a quadratic form. In particular, if formula_39 with its standard basis, one has


title: Quadratic form

text: The change of basis formulas show that the property of being a quadratic form does not depend on the choice of a specific basis in "V", although the quadratic form "q" depends on the choice of the basis.


title: Quadratic form

text: The map "Q" is a homogeneous function of degree 2, which means that it has the property that, for all "a" in "K" and "v" in "V":


title: Quadratic form

text: This bilinear form "B" is symmetric. That is, for all "x", "y" in "V", and it determines "Q": for all "x" in "V".


title: Quadratic form

text: When the characteristic of "K" is 2, so that 2 is not a unit, it is still possible to use a quadratic form to define a symmetric bilinear form . However, "Q"("x") can no longer be recovered from this "B"′ in the same way, since for all "x" (and is thus alternating). Alternatively, there always exists a bilinear form "B"″ (not in general either unique or symmetric) such that .


title: Quadratic form

text: The pair consisting of a finite-dimensional vector space "V" over "K" and a quadratic map "Q" from "V" to "K" is called a quadratic space, and "B" as defined here is the associated symmetric bilinear form of "Q". The notion of a quadratic space is a coordinate-free version of the notion of quadratic form. Sometimes, "Q" is also called a quadratic form.


title: Quadratic form

text: Two "n"-dimensional quadratic spaces and are isometric if there exists an invertible linear transformation (isometry) such that


title: Quadratic form

text: The isometry classes of "n"-dimensional quadratic spaces over "K" correspond to the equivalence classes of "n"-ary quadratic forms over "K".


title: Quadratic form

text: Let "R" be a commutative ring, "M" be an "R"-module, and be an "R"-bilinear form. A mapping is the "associated quadratic form" of "b", and is the "polar form" of "q".


title: Quadratic form

text: Two elements "v" and "w" of "V" are called orthogonal if . The kernel of a bilinear form "B" consists of the elements that are orthogonal to every element of "V". "Q" is non-singular if the kernel of its associated bilinear form is {0}. If there exists a non-zero "v" in "V" such that , the quadratic form "Q" is isotropic, otherwise it is anisotropic. This terminology also applies to vectors and subspaces of a quadratic space. If the restriction of "Q" to a subspace "U" of "V" is identically zero, then "U" is totally singular.


title: Quadratic form

text: The orthogonal group of a non-singular quadratic form "Q" is the group of the linear automorphisms of "V" that preserve "Q": that is, the group of isometries of into itself.


title: Quadratic form

text: Every quadratic form "q" in "n" variables over a field of characteristic not equal to 2 is equivalent to a diagonal form


title: Quadratic form

text: Classification of all quadratic forms up to equivalence can thus be reduced to the case of diagonal forms.


title: Quadratic form

text: Using Cartesian coordinates in three dimensions, let formula_47, and let formula_48 be a symmetric 3-by-3 matrix. Then the geometric nature of the solution set of the equation formula_49 depends on the eigenvalues of the matrix formula_48.


title: Quadratic form

text: If all eigenvalues of formula_48 are non-zero, then the solution set is an ellipsoid or a hyperboloid. If all the eigenvalues are positive, then it is an ellipsoid; if all the eigenvalues are negative, then it is an "imaginary ellipsoid" (we get the equation of an ellipsoid but with imaginary radii); if some eigenvalues are positive and some are negative, then it is a hyperboloid.


title: Quadratic form

text: If there exist one or more eigenvalues formula_52, then the shape depends on the corresponding formula_53. If the corresponding formula_54, then the solution set is a paraboloid (either elliptic or hyperbolic); if the corresponding formula_55, then the dimension formula_56 degenerates and does not come into play, and the geometric meaning will be determined by other eigenvalues and other components of formula_57. When the solution set is a paraboloid, whether it is elliptic or hyperbolic is determined by whether all other non-zero eigenvalues are of the same sign: if they are, then it is elliptic; otherwise, it is hyperbolic.


title: Quadratic form

text: Quadratic forms over the ring of integers are called integral quadratic forms, whereas the corresponding modules are quadratic lattices (sometimes, simply lattices). They play an important role in number theory and topology.


title: Quadratic form

text: An integral quadratic form has integer coefficients, such as ; equivalently, given a lattice Λ in a vector space "V" (over a field with characteristic 0, such as Q or R), a quadratic form "Q" is integral "with respect to" Λ if and only if it is integer-valued on Λ, meaning if .


title: Quadratic form

text: This is the current use of the term; in the past it was sometimes used differently, as detailed below.


title: Quadratic form

text: Historically there was some confusion and controversy over whether the notion of integral quadratic form should mean:


title: Quadratic form

text: This debate was due to the confusion of quadratic forms (represented by polynomials) and symmetric bilinear forms (represented by matrices), and "twos out" is now the accepted convention; "twos in" is instead the theory of integral symmetric bilinear forms (integral symmetric matrices).


title: Quadratic form

text: In "twos out", binary quadratic forms are of the form formula_60, represented by the symmetric matrix


title: Quadratic form

text: Several points of view mean that "twos out" has been adopted as the standard convention. Those include:


title: Quadratic form

text: An integral quadratic form whose image consists of all the positive integers is sometimes called "universal". Lagrange's four-square theorem shows that formula_62 is universal. Ramanujan generalized this to formula_63 and found 54 multisets that can each generate all positive integers, namely,


title: Quadratic form

text: There are also forms whose image consists of all but one of the positive integers. For example, {1,2,5,5} has 15 as the exception. Recently, the 15 and 290 theorems have completely characterized universal integral quadratic forms: if all coefficients are integers, then it represents all positive integers if and only if it represents all integers up through 290; if it has an integral matrix, it represents all positive integers if and only if it represents all integers up through 15.


title: Courland Pocket

text: The Courland Pocket was an area of the Courland Peninsula where Army Group North of Nazi Germany and the Reichskommissariat Ostland were cut off and surrounded by the Red Army for almost a year, lasting from July 1944 until 10 May 1945.


title: Courland Pocket

text: The pocket was created during the Red Army's Baltic Offensive, when forces of the 1st Baltic Front reached the Baltic Sea near Memel (Klaipėda) during its lesser Memel Offensive Operation phases. This action isolated the German Army Group North from the rest of the German forces, having been pushed from the south by the Red Army, standing in a front between Tukums and Libau in Latvia, with the Baltic Sea in the West, the Irbe Strait in the North and the Gulf of Riga in the East behind the Germans. Renamed Army Group Courland on 25 January, the Army Group in the Courland Pocket remained isolated until the end of the war. When they were ordered to surrender to the Soviet command on 8 May, they were in "blackout" and did not get the official order before 10 May, two days after the capitulation of Germany. It was one of the last German groups to surrender in Europe.


title: Courland Pocket

text: Courland, then part of the Latvian SSR, along with the rest of the Baltic eastern coast and islands, was overrun by Army Group North during 1941. Army Group North spent most of the next two years attempting to take Leningrad, without success. In January 1944, the Soviet Army lifted the siege of Leningrad.


title: Courland Pocket

text: On 22 June 1944, the Red Army launched the Belorussian Strategic Offensive, codenamed Operation Bagration. The goal of this offensive was to recapture the Belorussian SSR from the German occupation. Operation Bagration was extremely successful, resulting in the almost complete destruction of Army Group Centre, and ended on 29 August. In its final stages (the Kaunas and Šiauliai Offensives), Operation Bagration saw Soviet forces strike deep towards the Baltic coast, severing communications between the German Army Group North and the remnants of Army Group Centre.


title: Courland Pocket

text: After Operation Bagration ended, the Soviet forces continued the clearing of the Baltic coast, despite German attempts to restore the front in Operation Doppelkopf. The Red Army fought the Memel Offensive Operation with the goal of isolating Army Group North by capturing the city of Memel (Klaipėda).


title: Courland Pocket

text: On 9 October 1944, the Soviet forces reached the Baltic Sea near Memel after over-running the headquarters of the 3rd Panzer Army. As a result, Army Group North was cut off from East Prussia. Hitler's military advisors—notably Heinz Guderian, the Chief of the German General Staff—urged evacuation and utilisation of the troops to stabilise the front in central Europe. However, Hitler refused, and ordered the German forces in Courland and the Estonian islands Hiiumaa (Dagö) and Saaremaa (Ösel) to hold out, believing them necessary to protect German submarine bases along the Baltic coast. Hitler still believed the war could be won, and hoped that Dönitz's new Type XXI U-boat technology could bring victory to Germany in the Battle of the Atlantic, forcing the Allies out of Western Europe. This would allow German forces to focus on the Eastern Front, using the Courland Pocket as a springboard for a new offensive.