title: Gangs in Chicago

text: Former Mayor Rahm Emanuel disbanded the Chicago Police Department's anti-gang unit in 2012 in order to focus on beat patrols, which he said would have a more long-term solution to violence than anti-gang units.


title: Gangs in Chicago

text: Most traditional Chicago street gangs, known as "nations," fall under two main factions called the People Nation and the Folks Nation, with the former having most, if not all gangs under the "Almighty" moniker while the latter having most gangs divided into various sub-factions, the majority of which are a part of an alliance called "Latin Folks" which are further divided into groups called "familias". There are also nations that are independent of both the Folks and People Nations, such as the Black Soul Nation. Street gangs that are independent of Folks and People but retain similar identifiers and symbolism as well as maintain a hierarchical structure in membership are known as "war crews" and do not identify as nations though they will engage in traditional gang activity and may conflict with nations as well as other crews. Street gangs that do not retain any semblance of traditional nations or war crews are known simply as "cliques." Each individual gang is divided into "sets" which are territories spanning blocks or neighborhoods that may be divided further into subsets. There are currently at least 70 active Chicago street gangs with 747 factions that have been identified. All currently active street gangs in Chicago are:


title: Gangs in Chicago

text: Hispanic-on-Hispanic homicides increased in the summer of 1971 due to the Latin Kings gang election meetings.


title: Gangs in Chicago

text: In July 2021, federal agents participating in Operation Legend arrested 27 Black Disciples gang members associated with drugs and gun violations in the Englewood neighborhood on the South Side of Chicago.


title: Roman Italy

text: Roman Italy (called in both the Latin and Italian languages referring to the Italian Peninsula) was the homeland of the ancient Romans and of the Roman empire. According to Roman mythology, Italy was the ancestral home promised by Jupiter to Aeneas of Troy and his descendants, Romulus and Remus, who were the founders of Rome. Aside from the legendary accounts, Rome was an Italic city-state that changed its form of government from Kingdom to Republic and then grew within the context of a peninsula dominated by the Gauls, Ligures, Veneti, Camunni and Histri in the North, the Etruscans, Latins, Falisci, Picentes and Umbri tribes (such as the Sabines) in the Centre, and the Iapygian tribes (such as the Messapians), the Oscan tribes (such as the Samnites) and Greek colonies in the South.


title: Roman Italy

text: The consolidation of Italy into a single entity occurred during the Roman expansion in the peninsula, when Rome formed a permanent association with most of the local tribes and cities. The strength of the Italian confederacy was a crucial factor in the rise of Rome, starting with the Punic and Macedonian wars between the 3rd and 2nd century BC. As provinces were being established throughout the Mediterranean, Italy maintained a special status which made it ("Ruler of the Provinces"), and - especially in relation to the first centuries of imperial stability - ("governor of the world") and ("parent of all lands"). Such a status meant that, within Italy in times of peace, Roman magistrates also exercised the (police power) as an alternative to the (military power). Italy's inhabitants had Latin Rights as well as religious and financial privileges.


title: Roman Italy

text: The period between the end of the 2nd century BC and the 1st century BC was turbulent, beginning with the Servile Wars, continuing with the opposition of aristocratic élite to populist reformers and leading to a Social War in the middle of Italy. However, Roman citizenship was recognized to the rest of the Italians by the end of the conflict and then extended to Cisalpine Gaul when Julius Caesar became Roman Dictator. In the context of the transition from Republic to Principate, Italy swore allegiance to Octavian Augustus and was then organized in eleven regions from the Alps to the Ionian Sea.


title: Roman Italy

text: More than two centuries of stability followed. Several emperors made notable accomplishments in this period: Claudius incorporated Britain into the Roman Empire, Vespasian subjugated the Great Revolt of Judea and reformed the financial system, Trajan conquered Dacia and defeated Parthia, and Marcus Aurelius epitomized the ideal of the philosopher king.


title: Roman Italy

text: The crisis of the third century hit Italy particularly hard and left the eastern half of the Empire more prosperous. In 286 AD the Emperor Diocletian moved Imperial residence undertaking the western provinces (the later Western Roman Empire) from Rome to Mediolanum. Meanwhile, the islands of Corsica, Sardinia, Sicily and Malta were added to Italy by Diocletian in 292 AD, and Italian cities such as Mediolanum and Ravenna continued to serve as de facto capitals for the West.


title: Roman Italy

text: The Bishop of Rome had gained importance gradually from the reign of Constantine, and was given religious primacy with the Edict of Thessalonica under Theodosius I. Italy was invaded several times by the wandering Germanic peoples and fell under the control of Odoacer, when Romulus Augustus was deposed in 476 AD. Except for about more than a decade between the end of the Gothic War in mid-550s and Lombard invasion of Italy in 568 when (Eastern) Roman Empire reunited Italy, no single authority was established in Italy as a whole until it was reunited in the 19th century by the House of Savoy in the Kingdom of Italy, which became the present-day Italian Republic in 1946.


title: Roman Italy

text: Following the end of the Social War in 87 BC, Rome had allowed its fellow Italian allies full rights in Roman society and granted Roman citizenship to all fellow Italic peoples.


title: Roman Italy

text: After having been for centuries the heart of the Roman Empire, from the 3rd century the government and the cultural center began to move eastward: first the Edict of Caracalla in 212 AD extended Roman citizenship to all free men within the Imperial boundaries. Then, Christianity began to establish itself as the dominant religion from Constantine's reign (306–337), raising the power of Eastern metropolises, later grouped into Pentarchy. Although not founded as a capital city in 330, Constantinople grew in importance. It finally gained the rank of eastern capital when given an Praefectus Urbi in 359 and the senators who were "clari" became senators of the lowest rank as "clarissimi".


title: Roman Italy

text: As a result, Italy began to decline in favour of the provinces, which resulted in the division of the Empire into two administrative units in 395: the Western Roman Empire, with its capital at Mediolanum (now Milan), and the Eastern Roman Empire, with its capital at Constantinople (now Istanbul). In 402, the Imperial residence was moved to Ravenna from Milan, confirming the decline of the city of Rome (which was sacked in 410 for the first time in almost eight centuries).


title: Roman Italy

text: The name "Italia" covered an area whose borders evolved over time. According to Strabo's "Geographica", before the expansion of the Roman Republic, the name was used by Greeks to indicate the land between the strait of Messina and the line connecting the gulf of Salerno and gulf of Taranto (corresponding roughly to the current region of Calabria); later the term was extended by Romans to include the Italian Peninsula up to the Rubicon, a river located between Northern and Central Italy.


title: Roman Italy

text: In 49 BC, with the "Lex Roscia", Julius Caesar gave Roman citizenship to the people of the Cisalpine Gaul; while in 42 BC the hitherto existing province was abolished, thus extending Italy to the north up to the southern foot of the Alps.


title: Roman Italy

text: Under Augustus, the peoples of today's Aosta Valley and of the western and northern Alps were subjugated (so the western border of Roman Italy was moved to the Varus river), and the Italian eastern border was brought to the Arsia in Istria. Lastly, in the late 3rd century, Italy came to also include the islands of Sicily, Corsica and Sardinia, as well as Raetia and part of Pannonia. The city of Emona (modern Ljubljana, Slovenia) was the easternmost town of Italy.


title: Roman Italy

text: At the beginning of the Roman Imperial era, Italy was a collection of territories with different political statuses. Some cities, called "municipia", had some independence from Rome, while others, the "coloniae", were founded by the Romans themselves. Around 7 BC, Augustus divided Italy into eleven "regiones", as reported by Pliny the Elder in his "Naturalis Historia":


title: Roman Italy

text: Italy was privileged by Augustus and his heirs, with the construction, among other public structures, of a dense network of Roman roads. The Italian economy flourished: agriculture, handicraft and industry had a sensible growth, allowing the export of goods to the provinces. The Italian population may have grown as well: three census were ordered by Augustus, also assuming role of Roman censor, in order to record the number of Roman citizens throughout the empire. The surviving totals were 4,063,000 in 28 BC, 4,233,000 in 8 BC, and 4,937,000 in AD 14, but it is still debated whether these counted all citizens, all adult male citizens, or citizens "sui iuris". Estimates for the population of mainland Italy, including Cisalpine Gaul, at the beginning of the 1st century range from 6,000,000 according to Karl Julius Beloch in 1886, to 14,000,000 according to Elio Lo Cascio in 2009.


title: Roman Italy

text: During the Crisis of the Third Century the Roman Empire was on the verge of disintegration under the combined pressures of invasions, military anarchy and civil wars, and hyperinflation. In 284, Emperor Diocletian restored political stability. He carried out thorough administrative reforms to maintain order. He created the so-called Tetrarchy whereby the empire was ruled by two senior emperors called Augusti and two junior vice-emperors called Caesars. He decreased the size of the Roman provinces by doubling their number to reduce the power of the provincial governors. He grouped the provinces into several dioceses (Latin: diocesis) and put them under the supervision of the Imperial Vicarius (vice, deputy), who was the head of the diocese. During the Crisis of the Third Century the importance of Rome declined because the city was far from the troubled frontiers. Diocletian and his colleagues usually resided in four Imperial seats. The Augusti, Diocletian and Maximian, who were responsible for the East and West respectively, established themselves at Nicomedia, in north-western Anatolia (closer to the Persian frontier in the east) and Milan, in northern Italy (closer to the European frontiers) respectively. The seats of the Caesars were Augusta Treverorum (on the River Rhine frontier) for Constantius Chlorus and Sirmium (on the River Danube frontier) for Galerius who also resided at Thessaloniki.


title: Roman Italy

text: Under Diocletian Italy became the Dioecesis Italiciana. It included Raetia. It was subdivided the following provinces:


title: Roman Italy

text: Constantine subdivided the empire into four Praetorian prefectures. The "Diocesis Italiciana" became the Praetorian prefecture of Italy ("praefectura praetoria Italiae"), and was subdivided into two dioceses. It still included Raetia. The two dioceses and their provinces were:


title: Roman Italy

text: Diocesis Italia annonaria (Italy of the annona - its inhabitants had the obligation to provide the court, the administration and the troops, first allocated in Milan and then in Ravenna, supplies, wine and timber)


title: Roman Italy

text: In 330, Constantine completed the rebuilding of Byzantium as Constantinople. He established the Imperial court, a Senate, financial and judicial administrations, as well as the military structures. The new city, however, did not receive an urban prefect until 359 which raised it to the status of eastern capital. After the death of Theodosius in 395 and the subsequent division of the Empire, Italy was home base of the Western Roman Empire. As a result of Alaric's invasion in 402 the western seat was moved from Mediolanum to Ravenna. Alaric, king of Visigoths, sacked Rome itself in 410; something that hadn't happened for eight centuries. Northern Italy was attacked by Attila's Huns in 452. Rome was sacked in 455 again by the Vandals under the command of Genseric.


title: Roman Italy

text: According to "Notitia Dignitatum", one of the very few surviving documents of Roman government updated to the 420s, Roman Italy was governed by a praetorian prefect, "Prefectus praetorio Italiae" (who also governed the Diocese of Africa and the Diocese of Pannonia), one "vicarius", and one "comes rei militaris". The regions of Italy were governed at the end of the fourth century by eight "consulares" ("Venetiae et Histriae", "Aemiliae", "Liguriae", "Flaminiae et Piceni annonarii", "Tusciae et Umbriae", "Piceni suburbicarii", "Campaniae", and "Siciliae"), two "correctores" ("Apuliae et Calabriae" and "Lucaniae et Bruttiorum") and seven "praesides" ("Alpium Cottiarum", "Rhaetia Prima" and "Secunda", "Samnii", "Valeriae", "Sardiniae", and "Corsicae"). In the fifth century, with the Emperors controlled by their barbarian generals, the Western Imperial government maintained weak control over Italy itself, whose coasts were periodically under attack. In 476, with the abdication of Romulus Augustulus, the Western Roman Empire had formally fallen unless one considers Julius Nepos, the legitimate emperor recognized by Constantinople as the last. He was assassinated in 480 and may have been recognized by Odoacer. Italy remained under Odoacer and his Kingdom of Italy, and then under the Ostrogothic Kingdom. The Germanic successor states under Odoacer and Theodoric the Great continued to use the Roman administrative apparatus, as well as being nominal subjects of the Eastern emperor at Constantinople. In 535 Roman Emperor Justinian invaded Italy which suffered twenty years of disastrous war. In August 554, Justinian issued a Pragmatic sanction which maintained most of the organization of Diocletian. The "Prefecture of Italy" thus survived, and was reestablished under Roman control in the course of Justinian's Gothic War.


title: Roman Italy

text: As a result of the Lombard invasion in 568, the Byzantines lost most of Italy, except the territories of the Exarchate of Ravenna - a corridor from Venice to Lazio via Perugia - and footholds in the south Naples and the toe and heel of the peninsula.


title: Bride kidnapping

text: Bride kidnapping, also known as marriage by abduction or marriage by capture, is a practice in which a man abducts the woman he wishes to marry.


title: Bride kidnapping

text: Bride kidnapping (hence the portmanteau bridenapping) has been practiced around the world and throughout prehistory and history, among peoples as diverse as the Hmong in Southeast Asia, the Tzeltal in Mexico, and the Romani in Europe. Bride kidnapping still occurs in various parts of the world, but it is most common in the Caucasus and Central Asia.


title: Bride kidnapping

text: In most nations, bride kidnapping is considered a sex crime because of the implied element of rape, rather than a valid form of marriage. Some types of it may also be seen as falling along the continuum between forced marriage and arranged marriage. The term is sometimes confused with elopements, in which a couple runs away together and seeks the consent of their parents later. In some cases, the woman cooperates with or accedes to the kidnapping, typically in an effort to save face for herself or her parents. In many jurisdictions, this used to be encouraged by so-called marry-your-rapist laws. Even in countries where the practice is against the law, if judicial enforcement is weak, customary law ("traditional practices") may prevail.


title: Bride kidnapping

text: Bride kidnapping is often (but not always) a form of child marriage. It may be connected to the practice of bride price, wealth paid by the groom and his family to the bride's parents, and the inability or unwillingness to pay it.


title: Bride kidnapping

text: Bride kidnapping is distinguished from "raptio" in that the former refers to the abduction of one woman by one man (and his friends and relatives), and is still a widespread practice, whereas the latter refers to the large scale abduction of women by groups of men, possibly in a time of war. "Raptio" was assumed to be a historical practice, hence the Latin term, but the 21st century has seen a resurgence of war rape, some of which has elements of bride kidnapping; for example, women and girls abducted by Boko Haram in Nigeria, the Lord's Resistance Army in Uganda and ISIS in the Middle East have been taken as wives by their abductors.


title: Bride kidnapping

text: Rituals indicating a symbolic bride kidnapping still exist in some cultures (such as Circassians), as part of traditions surrounding a wedding. According to some sources, the honeymoon is a relic of marriage by capture, based on the practice of the husband going into hiding with his wife to avoid reprisals from her relatives, with the intention that the woman would be pregnant by the end of the month.


title: Bride kidnapping

text: Though the motivations behind bride kidnapping vary by region, the cultures with traditions of marriage by abduction are generally patriarchal with a strong social stigma on sex or pregnancy outside marriage and illegitimate births.


title: Bride kidnapping

text: In some modern cases, the couple colluded to elope under the guise of a bride kidnapping, presenting their parents with a "fait accompli". In most cases, however, the men who resort to capturing a wife are often of lower social status, because of poverty, disease, poor character or criminality. They are sometimes deterred from legitimately seeking a wife because of the payment the woman's family expects, the bride price (not to be confused with a dowry, paid by the "woman's" family).


title: Bride kidnapping

text: In agricultural and patriarchal societies, where bride kidnapping is most common, children work for their families. A woman leaves her birth family, geographically and economically, when she marries, becoming instead a member of the groom's family. (See patrilocality for an anthropological explanation.) Due to this loss of labour, the women's families do not want their daughters to marry young, and demand economic compensation (the aforementioned bride price) when they do leave them. This conflicts with the interests of men, who want to marry early, as marriage means an increase in social status, and the interests of the groom's family, who will gain another pair of hands for the family farm, business or home. Depending on the legal system under which she lives, the consent of the woman may not be a factor in judging the validity of the marriage.


title: Bride kidnapping

text: In addition to the issue of forced marriage, bride kidnapping may have other negative effects on young women and their society. For example, fear of kidnap is cited as a reason for the lower participation of girls in the education system.


title: Bride kidnapping

text: The mechanism of marriage by abduction varies by location. This article surveys the phenomenon by region, drawing on common cultural factors for patterns, but noting country-level distinctions.


title: Bride kidnapping

text: There have been cases of Coptic Christian women and girls abducted, forced to convert to Islam and then married to Muslim men. The practice has increased with the rise of Salafist networks under president Abdel Fattah Saeed Hussein Khalil el-Sisi, who pay as much as $3000 for every Coptic Christian woman kidnapped, raped and married to a Muslim man.


title: Bride kidnapping

text: Bride kidnapping is prevalent in many regions of Ethiopia. According to surveys conducted in 2003 by the National Committee on Traditional Practices in Ethiopia, the custom's prevalence rate was estimated at 69 percent nationally, and highest in the Southern Nations, Nationalities and People's Region at 92 percent. A man working in co-ordination with his friends may kidnap a girl or woman, sometimes using a horse to ease the escape. The abductor will then hide his intended bride or bring her to his family and rape her, sometimes in front of his family, until she becomes pregnant. As the father of the woman's child, the man can claim her as his wife. Subsequently, the kidnapper may try to negotiate a bride price with the village elders to legitimize the marriage. Girls as young as eleven years old are reported to have been kidnapped for the purpose of marriage. Though Ethiopia criminalised such abductions and raised the marriageable age to 18 in 2004, the law has not been well implemented. A 2016 UNICEF evidence review (based on data from 2010 and 2013) estimated that 10 to 13 percent of marriages in the highest risk areas involved abduction, with rates of 1.4 percent to 2.4 percent in lower risk areas of the country.


title: Bride kidnapping

text: The bride of the forced marriage may suffer from the psychological and physical consequences of forced sexual activity and early pregnancy and the early end to her education. Women and girls who are kidnapped may also be exposed to sexually transmitted diseases such as HIV/AIDS.


title: Bride kidnapping

text: Forced marriages continue to be a problem for young girls in Kenya. The United States Department of State reports that children and young teenaged girls (aged ten and up) are sometimes married to men two decades older.


title: Bride kidnapping

text: Marriage by abduction used to be, and to some extent still is, a customary practice for the Kisii ethnic group. In their practice, the abductor kidnaps the woman forcibly and rapes her in an attempt to impregnate her. The "bride" is then coerced through the stigma of pregnancy and rape to marry her abductor. Though most common in the late 19th century through the 1960s, such marriage abductions still occur occasionally.


title: Bride kidnapping

text: The Turkana tribe also practised marriage by abduction. In this culture, bridal kidnapping ("akomari") occurred before any formal attempts to arrange a marriage with a bride's family. According to one scholar, a successful bridal kidnapping raised the abductor's reputation in his community, and allowed him to negotiate a lower bride price with his wife's family. Should an attempted abductor fail to seize his bride, he was bound to pay a bride price to the woman's family, provide additional gifts and payments to the family, and to have an arranged marriage ("akota").


title: Bride kidnapping

text: Bride-kidnapping is prevalent in areas of Rwanda. Often the abductor kidnaps the woman from her household or follows her outside and abducts her. He and his companions may then rape the woman to ensure that she submits to the marriage. The family of the woman either then feels obliged to consent to the union, or is forced to when the kidnapper impregnates her, as pregnant women are not seen as eligible for marriage. The marriage is confirmed with a ceremony that follows the abduction by several days. In such ceremonies, the abductor asks his bride's parents to forgive him for abducting their daughter. The man may offer a cow, money, or other goods as restitution to his bride's family.


title: Bride kidnapping

text: Bride-kidnap marriages in Rwanda often lead to poor outcomes. Human rights workers report that one third of men who abduct their wives abandon them, leaving the wife without support and impaired in finding a future marriage. Additionally, with the growing frequency of bride-kidnapping, some men choose not to solemnize their marriage at all, keeping their "bride" as a concubine.


title: Bride kidnapping

text: Bride kidnapping is not specifically outlawed in Rwanda, though violent abductions are punishable as rape. According to a criminal justice official, bride kidnappers are virtually never tried in court: "When we hear about abduction, we hunt down the kidnappers and arrest them and sometimes the husband, too. But we're forced to let them all go several days later," says an official at the criminal investigation department in Nyagatare, the capital of Umutara. Women's rights groups have attempted to reverse the tradition by conducting awareness raising campaigns and by promoting gender equity, but the progress has been limited so far.


title: Bride kidnapping

text: The practice is known as "ukuthwalwa" or simply "thwala" in the Nguni-speaking tribes. (The Basotho call it "tjhobediso".) Among Zulu people, "thwala" was once an acceptable way for two young people in love to get married when their families opposed the match, and so it was actually a form of elopement. "Thwala" has been abused, however, "to victimize isolated rural women and enrich male relatives."


title: Bride kidnapping

text: In Central Asia, bride kidnapping exists in Kyrgyzstan, Kazakhstan, Turkmenistan, and Karakalpakstan, an autonomous region of Uzbekistan. Though origin of the tradition in the region is disputed, the rate of nonconsensual bride kidnappings appears to be increasing in several countries throughout Central Asia as the political and economic climate changes.


title: Bride kidnapping

text: Despite its illegality, with the practice being subjected to stricter crackdowns in 2013, which punish it by a prison sentences of up to 10 years, in many primarily rural areas, bride kidnapping, known as "ala kachuu" (to take and flee), is an accepted and common way of taking a wife. The matter is somewhat confused by the local use of the term "bride kidnap" to reflect practices along a continuum, from forcible abduction and rape (and then, almost unavoidably, marriage), to something akin to an elopement arranged between the two young people, to which both sets of parents have to consent after the act. Bride kidnappings that involve rape do so to psychologically force the would-be bride to accept her kidnapper and his family's pressure to marry him, since if she then refuses she would never be considered marriageable again. Of 12,000 yearly bride kidnappings, approximately 2,000 women reported that she had been raped by the would-be groom. However, the United Nations Development Programme disputes that bride kidnapping is part of the country's culture or tradition, and considers it a human rights violation.


title: Bride kidnapping

text: Estimates of the prevalence of bride kidnapping vary, sometimes widely. A 2015 crime victimization survey included the kidnapping of young women for marriage. Fourteen percent of married women answered that they had been kidnapped; two-thirds of these cases had been consensual, in that the woman knew the man and had agreed with it up front. This means that about five percent of extant marriages are cases of "Ala Kachuu". A 2007 study published in the "Central Asian Survey" concluded that approximately half of all Kyrgyz marriages included bride kidnapping; of those kidnappings, two-thirds are non-consensual. Research by non-governmental organizations give estimates from a low of 40% to between 68 and 75 percent.


title: Bride kidnapping

text: Although the practice is illegal, bride kidnappers are rarely prosecuted. This reluctance to enforce the code is in part caused by the pluralistic legal system, where many villages are "de facto" ruled by councils of elders and "aqsaqal" courts following customary law, away from the eyes of the state legal system. "Aqsaqal" courts, tasked with adjudicating family law, property and torts, often fail to take bride kidnapping seriously. In many cases, "aqsaqal" members are invited to the kidnapped bride's wedding and encourage the family of the bride to accept the marriage.


title: Bride kidnapping

text: In Kazakhstan, bride kidnapping ("alyp qashu") is divided into non-consensual and consensual abductions, "kelisimsiz alyp qashu" ("to take and run without agreement") and "kelissimmen alyp qashu" ("to take and run with agreement"), respectively. Though some kidnappers are motivated by the wish to avoid a bride price or the expense of hosting wedding celebrations or a feast to celebrate the girl leaving home, other would-be husbands fear the woman's refusal, or that the woman will be kidnapped by another suitor first. Generally, in nonconsensual kidnappings, the abductor uses either deception (such as offering a ride home) or force (such as grabbing the woman, or using a sack to restrain her) to coerce the woman to come with him. Once at the man's house, one of his female relatives offers the woman a kerchief ("oramal") that signals the bride's consent to the marriage. Though in consensual kidnappings, the woman may agree with little hesitation to wear the kerchief, in non-consensual abductions, the woman may resist the kerchief for days. Next, the abductor's family generally asks the "bride" to write a letter to her family, explaining that she had been taken of her own free will. As with the kerchief, the woman may resist this step adamantly. Subsequently, the "groom" and his family generally issues an official apology to the bride's family, including a letter and a delegation from the groom's household. At this time, the groom's family may present a small sum to replace the bride-price. Though some apology delegations are met cordially, others are greeted with anger and violence. Following the apology delegation, the bride's family may send a delegation of "pursuers" ("qughysnshy") either to retrieve the bride or to verify her condition and honour the marriage.


title: Bride kidnapping

text: A recent victimization survey in Kazakhstan (2018) included the crime of kidnapping of young women for marriage. 4% of married women answered that they were kidnapped at the time and that two-thirds of these cases were consensual, the woman knew the man and had agreed with it up front. This means that about 1-1.5% of current marriages in Kazakhstan are the result of non-consensual abductions.


title: Bride kidnapping

text: In Karakalpakstan, an autonomous region in Uzbekistan, nearly one fifth of all marriages are conducted by bride kidnapping. Activist groups in the region tie an increase in kidnappings to economic instability. Whereas weddings can be prohibitively expensive, kidnappings avoid both the cost of the ceremony and any bride price. Other scholars report that less desirable males with inferior educations or drug or alcohol problems are more likely to kidnap their brides. In Karakalpakstan, the bride kidnapping sometimes originates out of a dating relationship and, at other times, happens as an abduction by multiple people.


title: Bride kidnapping

text: There are instances in which Hindu women and some Christian women and minor girls are forced to marry Muslim men. Many of these convert, either willingly or by force.


title: Bride kidnapping

text: Marriage by abduction also occurs in traditional Hmong culture, in which it is known as "zij poj niam". As in some other cultures, bride kidnapping is generally a joint effort between the would-be groom and his friends and family. Generally, the abductor takes the woman while she is alone. The abductor then sends a message to the kidnap victim's family, informing them of the abduction and the abductor's intent to marry their daughter. If the victim's family manage to find the woman and insist on her return, they might be able to free her from the obligation to marry the man. However, if they fail to find the woman, the kidnap victim is forced to marry the man. The abductor still has to pay a bride price for the woman, generally an increased amount because of the kidnapping. Because of this increased cost (and the general unpleasantness of abduction), kidnapping is usually only a practice reserved for a man with an otherwise blemished chance of securing a bride, because of criminal background, illness or poverty.


title: Bride kidnapping

text: Occasionally, members of the Hmong ethnic group have engaged in bride kidnapping in the United States. In some cases, the defendant has been allowed to plead a cultural defense to justify his abduction. This defense has sometimes been successful. In 1985, Kong Moua, a Hmong man, kidnapped and raped a woman from a Californian college. He later claimed that this was an act of "zij poj niam" and was allowed to plead to false imprisonment only, instead of kidnapping and rape. The judge in this case considered cultural testimony as an explanation of the man's crime.


title: Bride kidnapping

text: Until the 1940s, marriage by abduction, known as "qiangqin" (), occurred in rural areas of China. Though illegal in imperial China, for rural areas it often became a local "institution". According to one scholar, marriage by abduction was sometimes a groom's answer to avoid paying a bride price. In other cases, the scholar argues, it was a collusive act between the bride's parents and the groom to circumvent the bride's consent.


title: Bride kidnapping

text: Chinese scholars theorise that this practice of marriage by abduction became the inspiration for a form of institutionalised public expression for women: the bridal lament. In imperial China, a new bride performed a two- to three-day public song, including chanting and sobbing, that listed her woes and complaints. The bridal lament would be witnessed by members of her family and the local community.


title: Bride kidnapping

text: In recent years bride kidnapping has resurfaced in areas of China. In many cases, the women are kidnapped and sold to men in poorer regions of China, or as far abroad as Mongolia. Reports say that buying a kidnapped bride is nearly one tenth of the price of hosting a traditional wedding. The United States Department of State tie this trend of abducting brides to China's one-child policy, and the consequent gender imbalance as more male children are born than female children.


title: Bride kidnapping

text: Bride abduction also occurred in Tibetan history, sometimes involving ceremonial mock abductions or as a bargaining procedure.


title: Bride kidnapping

text: According to a study conducted by Kunio Yanagita, a scholar of Folklore in Japan, three patterns of bride kidnapping are known to have existed in Japan:


title: Bride kidnapping

text: The practice of kidnapping children, teenagers and women from neighbouring tribes and adopting them into the new tribe was common among Indigenous peoples of the Americas. The kidnappings were a way of introducing new blood into the group. Captured European women sometimes settled down as adopted members of the tribe and at least one woman, Mary Jemison, refused rescue when it was offered.


title: Bride kidnapping

text: The trope of the captured Indigenous (great, great) grandmother is a standard origin myth for many white Brazilian families, captured in the widely use phrase "my (great, great) grandmother was an Indian caught in the rope" (the phrase Índia pega no laço). The phrase reflect "in part" the facts of centuries of female abductions by colonialists that continued even into the 20th century. For example, in a paper discussing the phrase, Indigenous academic Mirna P Marinho da Silva Anaquiri reports a quote from a teacher in Goiânia interviewed as part of her fieldwork:


title: Bride kidnapping

text: Helena Valero, a Brazilian woman kidnapped by Amazonian Indians in 1937, dictated her story to an Italian anthropologist, who published it in 1965.


title: Bride kidnapping

text: Cases exist within some Mormon Fundamentalist communities around the Utah-Arizona border; however, accurate information is difficult to obtain from these closed communities. Most of these cases are usually referred to as forced marriages, although they are similar to other bride kidnappings around the world.


title: Bride kidnapping

text: Among the Tzeltal community, a Mayan tribe in Chiapas, Mexico, bride kidnapping has been a recurring method of securing a wife. The Tzeltal people are an indigenous, agricultural tribe that is organised patriarchally. Premarital contact between the sexes is discouraged; unmarried women are supposed to avoid speaking with men outside their families. As with other societies, the grooms that engage in bride kidnapping have generally been the less socially desirable mates.


title: Bride kidnapping

text: In the Tzeltal tradition, a girl is kidnapped by the groom, possibly in concert with his friends. She is generally taken to the mountains and raped. The abductor and his future bride often then stay with a relative until the bride's father's anger is reported to have subsided. At that point, the abductor will return to the bride's house to negotiate a bride-price, bringing with him the bride and traditional gifts such as rum.


title: Bride kidnapping

text: The largest Comanche raids into Mexico took place from 1840 to the mid-1850s, when they declined in size and intensity. The captured Mexican girls often became one of several wives of Comanche men.


title: Bride kidnapping

text: Among the Mapuche of Chile, the practice was known as "casamiento por capto" in Spanish, and "ngapitun" in Mapudungun. Contemporary chronicler Alonso González de Nájera writes that during the Destruction of the Seven Cities in southern Chile Mapuches took over 500 Spanish women as captives. In the case of the women it was, in the words of González de Nájera, "to exploit them". The capture of women initiated a tradition of abductions of Spanish women in the 17th century by Mapuches.


title: Bride kidnapping

text: Bride kidnapping is an increasing trend in the countries and regions of the Caucasus, both in Georgia in the South and in Dagestan, Chechnya and Ingushetia in the North. In the Caucasian versions of bride-kidnapping, the kidnap victim's family may play a role in attempting to convince the woman to stay with her abductor after the kidnapping, because of the shame inherent in the presumed consummation of the marriage.


title: Bride kidnapping

text: The Dagestan, Chechnya and Ingushetia regions in the Northern Caucasus (in Russia) have also witnessed an increase in bride kidnappings since the fall of the Soviet Union. As in other countries, kidnappers sometimes seize acquaintances to be brides and other times abduct strangers. The social stigma of spending a night in a male's house can be a sufficient motivation to force a young woman to marry her captor. Under Russian law, though a kidnapper who refuses to release his bride could be sentenced to eight to ten years, a kidnapper will not be prosecuted if he releases the victim or marries her with her consent. Bride captors in Chechnya are liable, in theory, to receive also a fine of up to 1 million rubles. As in the other regions, authorities often fail to respond to the kidnappings. In Chechnya, the police failure to respond to bridal kidnappings is compounded by a prevalence of abductions in the region. Several such kidnappings have been captured on video.


title: Bride kidnapping

text: Researchers and non-profit organisations describe a rise in bride kidnappings in the North Caucasus in the latter half of the 20th century. In Chechnya, women's rights organisations tie the increase in kidnappings to a deterioration of women's rights under the rule of Chechen president Ramzan Kadyrov.


title: Bride kidnapping

text: In Azerbaijan, both marriage by capture ("qız qaçırmaq") and elopement ("qoşulub qaçmaq") are relatively common practices. In the Azeri kidnap custom, a young woman is taken to the home of the abductor's parents through either deceit or force. Regardless of whether rape occurs or not, the woman is generally regarded as impure by her relatives, and is therefore forced to marry her abductor. Despite a 2005 Azeri law that criminalised bride kidnapping, the practice places women in extremely vulnerable social circumstances, in a country where spousal abuse is rampant and recourse to law enforcement for domestic matters is impossible. In Azerbaijan, women abducted by bride kidnapping sometimes become slaves of the family who kidnap them.


title: Bride kidnapping

text: In Georgia, bride kidnapping occurs in the south of the country mostly concentrated in and around the town of Akhalkalaki ethnic minority areas. Although the extent of the problem is not known, non-governmental activists estimate that hundreds of women are kidnapped and forced to marry each year. In a typical Georgian model of bride kidnapping, the abductor, often accompanied by friends, accosts the intended bride, and coerces her through deception or force to enter a car. Once in the car, the victim may be taken to a remote area or the captor's home. These kidnappings sometimes include rape, and may result in strong stigma to the female victim, who is assumed to have engaged in sexual relations with her captor. Women who have been victims of bride kidnapping are often regarded with shame; the victim's relatives may view it as a disgrace if the woman returns home after a kidnapping. In other cases, the kidnapping is a consensual elopement. Human Rights Watch reports that prosecutors often refuse to bring charges against the kidnappers, urging the kidnap victim to reconcile with her aggressor. Enforcing the appropriate laws in this regard may also be a problem because the kidnapping cases often go unreported as a result of intimidation of victims and their families.


title: Bride kidnapping

text: Bride kidnapping has been documented as a marital practice in some Romani community traditions. In the Romani culture, girls as young as twelve years old may be kidnapped for marriage to teenaged boys. As the Roma population lives throughout Europe, this practice has been seen on multiple occasions in Ireland, England, the Czech Republic, the Netherlands, Bulgaria and Slovakia. The kidnapping has been theorized as a way to avoid a bride price or as a method of ensuring exogamy. The tradition's normalization of kidnapping puts young women at higher risk of becoming victims of human trafficking.


title: Bride kidnapping

text: Marriage by capture was practiced in ancient cultures throughout the Mediterranean area. It is represented in mythology and history by the tribe of Benjamin in the Bible; by the Greek hero Paris stealing the beautiful Helen of Troy from her husband Menelaus, thus triggering the Trojan War; and by the Rape of the Sabine Women by Romulus, the founder of Rome.


title: Bride kidnapping

text: In 326 A.D., the Emperor Constantine issued an edict prohibiting marriage by abduction. The law made kidnapping a public offence; even the kidnapped bride could be punished if she later consented to a marriage with her abductor. Spurned suitors sometimes kidnapped their intended brides as a method of restoring honor. The suitor, in coordination with his friends, generally abducted his bride while she was out of her house in the course of her daily chores. The bride would then be secreted outside the town or village. Though the kidnapped woman was sometimes raped in the course of the abduction, the stain on her honor from a presumptive consummation of the marriage was sufficient to damage her marital prospects irreversibly. Sometimes, the abduction masked an elopement.


title: Bride kidnapping

text: The custom of "fuitina" was widespread in Sicily and continental southern Italy. In 1965, this custom was brought to national attention by the case of Franca Viola, a 17-year-old abducted and raped by a local small-time criminal, with the assistance of a dozen of his friends. When she was returned to her family after a week, she refused to marry her abductor, contrary to local expectation. Her family backed her up, and suffered severe intimidation for their efforts; the kidnappers were arrested and the main perpetrator was sentenced to 11 years in prison.


title: Bride kidnapping

text: The exposure of this "archaic and intransigent system of values and behavioural mores" caused great national debate. In 1968, Franca married her childhood sweetheart, with whom she would later have three children. Conveying clear messages of solidarity, Giuseppe Saragat, then president of Italy, sent the couple a gift on their wedding day, and soon afterwards, Pope Paul VI granted them a private audience. A 1970 film, "La moglie più bella" ("The Most Beautiful Wife") by Damiano Damiani and starring Ornella Muti, is based on the case. Viola never capitalised on her fame and status as a feminist icon, preferring to live a quiet life in Alcamo with her family.


title: Bride kidnapping

text: The law allowing "rehabilitating marriages" (also known as marry-your-rapist law) to protect rapists from criminal proceedings was abolished in 1981.


title: Bride kidnapping

text: The 12th-century Norman invasion of Ireland was invited by an instance of wife-stealing: in 1167, the King of Leinster, Diarmait Mac Murchada, had his lands and kingship revoked by order of the High King of Ireland, Ruaidrí Ua Conchobair, as punishment for abducting the wife of another king in 1152. This led Diarmait to seek the assistance of King Henry II of England in order to reclaim his kingdom.


title: Bride kidnapping

text: The abduction of heiresses was an occasional feature in Ireland until 1800, as illustrated in the film "The Abduction Club".


title: Bride kidnapping

text: In 2015, Malta was criticized by Equality Now, for a law which, in certain circumstances, can extinguish the punishment for a man who abducts a woman if, following the abduction, the man and woman get married. (Article 199 and Article 200 of the Criminal Code of Malta) The article was ultimately abolished by Act XIII of 2018, Article 24.


title: Bride kidnapping

text: East Slavic tribes, predecessor tribes to the Rus state, practiced bride kidnapping in the eleventh century. The traditions were documented by Rus' monk Nestor. According to his "Chronicles", the Drevlian tribe captured wives non-consensually, whereas the Radimich, Viatich, and Severian tribes "captured" their wives after having come to an agreement about marriage with them. The clergy's increase in influence may have helped the custom to abate.


title: Bride kidnapping

text: Marriage by capture occurred among the South Slavs until the beginning of the 1800s. Common in Serbia, Montenegro, Croatia and Bosnia-Herzegovina, the custom was known as "otmitza". The practice was mentioned in a statute in the Politza, the 1605 Croatian legal code. According to Serbian folk-chronicler Vuk Karadzic, a man would dress for "battle" before capturing a woman. Physical force was a frequent element of these kidnappings.


title: Bride kidnapping

text: Bride kidnapping was also a custom in Bulgaria. With the consent of his parents and the aid of his friends, the abductor would accost his bride and take her to a barn away from the home, as superstition held that pre-marital intercourse might bring bad luck to the house. Whether or not the man raped his bride, the abduction would shame the girl and force her to stay with her kidnapper to keep her reputation. As in other cultures, sometimes couples would elope by staging false kidnappings to secure the parents' consent.


title: Bride kidnapping

text: In Catholic canon law, the impediment of "raptus" specifically prohibits marriage between a woman abducted with the intent to force her to marry, and her abductor, as long as the woman remains in the abductor's power. According to the second provision of the law, should the woman decide to accept the abductor as a husband after she is safe, she will be allowed to marry him. The canon defines "raptus" as a "violent" abduction, accompanied by physical violence or threats, or fraud or deceit. The Council of Trent insisted that the abduction in "raptus" must be for the purpose of marriage to count as an impediment to marriage.


title: Bride kidnapping

text: Bride capture has been reflected in feature films from many cultures, sometimes humorously, sometimes as social commentary.


title: Bride kidnapping

text: Bride kidnapping is depicted as an American frontier solution in the 1954 Hollywood musical "Seven Brides for Seven Brothers". Stephen Vincent Benét wrote a short story called "The Sobbin' Women" that parodied the legend of the rape of the Sabine women. The short story, and then the film, focus on seven gauche but sincere backwoodsmen, one of whom gets married and encourages the others to seek partners. After a social where they meet girls they are attracted to, they are denied the chance to pursue their courtship by the latter's menfolk. Following the Roman example, they abduct the girls. As in the original tale, the women are at first indignant but are eventually won over.


title: Bride kidnapping

text: The 1960 Hong Kong film "Qiangpin" ("The Bride Hunter") portrays the custom in the format of an all-female Yue opera comedy, in which Xia Meng plays a gender-bending role as a man masquerading as a woman. Bride kidnapping is displayed somewhat humorously in Pedro Almodóvar's 1990 Spanish hit "¡Átame!" ("Tie Me Up! Tie Me Down!"), starring Antonio Banderas and Victoria Abril. It is the underlying theme behind the 2005 Korean movie "The Bow". In the 2006 comedy "", the eponymous fictional reporter Borat, played by British comedian/satirist Sacha Baron Cohen, attempts to kidnap Canadian actress Pamela Anderson in order to take her as his wife. He brings a "wedding sack" which he has made for the occasion, suggesting that such kidnappings are a tradition in his parody of Kazakhstan.


title: Bride kidnapping

text: On a more serious note, a 1970 Italian film, "La moglie più bella" ("The Most Beautiful Wife") by Damiano Damiani and starring Ornella Muti, is based on the story of Franca Viola, described above. However, before the national debate caused by the Viola case, a 1964 satire directed by Pietro Germi, "Seduced and Abandoned" ("Sedotta e abbandonata"), treated the Sicilian custom as a dark comedy. The 2009 film "Baarìa - la porta del vento" shows a consensual "fuitina" in 20th-century Sicily (atypically having the couple enclosed in the girl's house) as the only way the lovers can avoid the girl's arranged marriage to a richer man.


title: Bride kidnapping

text: Some Russian films and literature depict bride kidnapping in the Caucasus. There is a Soviet comedy entitled "Kidnapping, Caucasian Style" (, literally translated as "The Girl Prisoner of the Caucasus"), where a bride kidnapping occurs in an unidentified Caucasian country. The 2007 Kyrgyz film "Pure Coolness" also revolves around the bride kidnapping custom, mistaken identity, and the clash between modern urban expectations and the more traditional countryside.


title: Bride kidnapping

text: In 2005, a documentary film entitled "Bride Kidnapping in Kyrgyzstan" made by Petr Lom was presented at the United Nations Association Film Festival, and subsequently on PBS and Investigation Discovery (ID) in the United States. The film met controversy in Kyrgyzstan because of ethical concerns about the filming of real kidnappings.


title: Bride kidnapping

text: The millennia-old Srimad Bhavata Purana refers to "riksasa", the ritual kidnapping of the bride: Young Rukmini, "beautiful-eyed" and "with an exquisite waist", did not want the marriage arranged for her to Sisupala, the king of the Cedis, so she arranged to be abducted by Krishna. After he carried her away Krishna married Rukmini "according to the appropriate rights" amid the great joy of the citizens of Dvaraka. [144]


title: Bride kidnapping

text: In Frances Burney's novel, "Camilla" (1796), the heroine's sister, Eugenia, is kidnapped by an adventurer called Alphonso Bellamy. Eugenia decides to stay with her husband on the grounds that she believes her word is a solemn oath. Eugenia is fifteen years old, and so underage, and is coerced into the marriage—both were grounds for treating the marriage as illegal.


title: Bride kidnapping

text: A Sherlock Holmes story features bride kidnapping. In "The Adventure of the Solitary Cyclist" (1903), a woman is employed as a governess by a man who knows that she will soon inherit a fortune, with the intent of a confederate marrying her. The ceremony does eventually occur, but is void.


title: Bride kidnapping

text: The manga Otoyomegatari "A Bride's Story" takes place in central Asia. The heroine is married to a boy in an outside clan, but regrets regarding this decision occur when her original clan has problems bearing heirs. Her birth family comes to retrieve her with the intention of marrying her to someone else, but without success. Her new family tells the invaders that the girl has been impregnated, which would be the last seal on the marriage. They doubt this has occurred as the groom is very young and, desperate, they resort to a kidnap attempt, but again fail.


title: Bride kidnapping

text: The fantasy novel "A Storm of Swords" features marriage by capture (or "stealing a woman") as the traditional form of marriage north of the Wall. The Free Folk consider it a test for a man to "steal" a wife and outwit her attempts on his life long enough for her to respect his strength and come to love him. More often, though, marriages by capture are conducted between a couple already in love, an elopement without the extra element of attempted murder. Jon Snow and Ygritte have such a marriage by capture, although at the time Jon was ignorant of the custom and thought he was merely taking her prisoner. The Ironborn are also known to practice this custom, taking secondary wives while reaving the mainland, which they refer to as "salt wives".


title: Bride kidnapping

text: The Tamora Pierce fantasy novel "The Will of the Empress" includes bride kidnapping as a major plot point and has extensive discussions of the morality of bride kidnapping. Multiple characters are kidnapped for the purpose of marriage during the novel, which is used as a warning against it (in keeping with the women's rights focus of her series), particularly in the case of poor women or those without social support systems.


title: Bride kidnapping

text: In the BBC radio and television comedy series "The League of Gentlemen", the character Papa Lazarou comes to the fictional town of Royston Vasey under the guise of a peg-seller. He seeks to kidnap women by entering their homes, talking gibberish to them (Gippog) and persuading them to hand over their wedding rings. He 'names' them all 'Dave', and, after obtaining their rings, proclaims; "you're my wife now".


title: Preadolescence

text: Preadolescence is a stage of human development following middle childhood and preceding adolescence. It commonly ends with the beginning of puberty. Preadolescence is commonly defined as ages 9–12 ending with the major onset of puberty. It may also be defined as simply the 2-year period before the major onset of puberty. Preadolescence can bring its own challenges and anxieties.


title: Preadolescence

text: A term used to refer to the preadolescent stage in everyday speech is tween and its perhaps older variants tweenie, tweeny, tweenager, and tweener. It's a blend (portmanteau) of the words "teen" and "between" in the sense of "between childhood and adolescence" and refers to 8-, 9-, or 10- to 12-year-olds. Sometimes the terms "tweenie" and "tweenager" are used to differentiate between older (10 to 15) and younger (7 to 11) age groups, respectively.


title: Preadolescence

text: While known as "preadolescent" in psychology, the terms "preteen" or "tween" are common in everyday use. A preteen or preteenager is a person ages 12 and under. Generally, the term is restricted to those close to reaching age 13, especially ages 9 to 12. "Tween" is an American neologism and marketing term for "preteen", which is a blend of "between" and "teen". People within this age range are variously described as tweens, preadolescents, tweenies, preteens, pubescents, middle schoolers, or tweenagers.


title: Preadolescence

text: A junior high school can sometimes be confused with a middle school. Though serving a similar purpose in bridging a gap between elementary school and high school, a junior high school typically serves 7th to 9th grade students, whereas a middle school serves 6th to 8th grade students. Therefore, middle schools serve a slightly younger demographic, more befitting of preadolescents, while junior high schools typically serve young adolescents.


title: Preadolescence

text: Being prepubescent is not the same thing as being preadolescent. Instead, "prepubescent" (and sometimes "child") is a term for boys and girls who have not developed secondary sex characteristics, while "preadolescent" is generally defined as those ranging from age 9 to 12 years.


title: Preadolescence

text: The point at which a child becomes an adolescent is defined by the major onset of puberty. However, in some individuals (particularly females), puberty begins in the preadolescence years. Studies indicate that the onset of puberty has been one year earlier with each generation since the 1950s.


title: Preadolescence

text: One can also distinguish middle childhood and preadolescence – middle childhood from approximately 5–8 years, as opposed to the time children are generally considered to reach preadolescence. There is no exact agreement as to when preadolescence starts and ends.


title: Preadolescence

text: Early puberty begins as the result of the initiation of the pulsatile gonadotropin-releasing hormone (GnRH) secretion by the hypothalamus; the exact mechanism of this initiation is currently unknown and remains under investigation. Pulsatile GnRH secretion results in the pulsatile secretions of gonadotropins Luteinizing Hormone (LH) and Follicle Stimulating Hormone (FSH), which act on the gonads (ovaries in females or testicles in males) to cause increase secretion of sex steroids. In females, the predominant sex steroid released is estrogen and in individuals with testicles, the predominant sex steroid released is testosterone. These sex hormones then lead to the development of secondary sex characteristics.


title: Preadolescence

text: The stages of puberty can be described with the Tanner scale, also known as the Sexual Maturity Rating, which incorporates measurements and characteristics of primary and secondary sex characteristics. For example, genital and breast development, as well as pubic hair growth. Pubertal development is regulated by the hypothalamic-pituitary-gonadal (HPG) axis. Tanner staging ranges from 1 through 5 (with 5 being the most developed).


title: Preadolescence

text: With regards to pubic hair development, the scale goes as follows: Stage 1-no hair; 2-downy hair; 3-scant terminal hair; 4-terminal hair overlying the pubic triangle; 5-terminal hair extending to the thigh. With regards to male genitalia development, the scale goes as follows: 1-testes at the same size and proportion of early childhood; 2-enlargement of the scrotum/change in texture of scrotal skin; 3-growth of the penis length-wise; 4-growth of the penis in terms of length and circumference; 5-adult-sized genitalia.


title: Preadolescence

text: With regards to female breast development, the scale is as follows: 1-no palpable gland tissue; 2-palpable breast bud under areola; 3-breast tissue palpable outside of areola; 4-areola elevated above breast contour; 5-areolar mound recedes into single breast contour. The average age in which both males and females reach Tanner stage 5 of pubertal development is around 15–16.


title: Preadolescence

text: There are significant neurological changes that are expressed during preadolescence. White matter refers to the region of the nervous system corresponding to neuronal axons, which form fibers that convey information across different regions of the brain. In contrast, grey matter refers to the region of the nervous system corresponding to neuronal cell bodies, which process and relay neuronal signals. White matter volume increases at a relatively linear rate of about 12% from ages 4 through 22, specifically focused in the frontal, parietal, and occipital lobes. Increases in white matter volume may be correlated to improvements of fine motor performance, auditory processing, as well as sensory information transfer between language areas of the brain. In contrast, cortical gray matter increases in early life, peaks in preadolescence, and declines through adulthood, with the exception of occipital lobe gray matter. For example, parietal lobe gray matter peaks at age 10 in girls and 12 in boys, while frontal lobe gray matter peaks at age 11 in girls and 12 in boys. Such changes might reflect overproduction of synapses in the preadolescent years; in subsequent years, there seems to be pruning dependent on environmental context, corresponding to increased synchronicity of neuron firing. A key caveat from these imaging studies, however, is that there exists significant variability in the timing and characteristics of neurological change in preadolescents. Neurological changes, particularly in the prefrontal cortex, appear to be highly dependent on environmental input. Toxins, hormones, and lifestyle factors including stress and nutrition impact neurological maturation, demonstrating the importance of early lifestyle health interventions in preadolescence with regards to neurological and psychological development.


title: Preadolescence

text: Of the 'two major socializing agents in children's lives: the family environment...and formal educational institutions,' it is 'the family in its function a primary socializer of the child' that predominates in the first five years of life: middle childhood by contrast is characterized by 'a child's readiness for school...being self-assured and interested; knowing what kind of behavior is expected...being able to wait, to follow directions, and getting along with other children.'


title: Preadolescence

text: Preadolescent children have a different view of the world from younger children in many significant ways. Typically, theirs is a more realistic view of life than the intense, fantasy-oriented world of earliest childhood. Preadolescents have more mature, sensible, realistic thoughts and actions: 'the most "sensible" stage of development...the child is a much "less emotional being" now.' They will often have developed a sense of ' "intentionality". The wish and capacity to have an impact, and to act upon that with persistence'; and will have a more developed sense of looking into the future and seeing effects of their actions (as opposed to early childhood where children often do not worry about their future). This can include more realistic job expectations ("I want to be an engineer when I grow up", as opposed to "I want to be a wizard"). Middle children generally show more investment 'in "control over external reality" through the acquisition of knowledge and competence': where they do have worries, these may be more a fear of kidnappings, rapes, and scary media events, as opposed to fantasy things (e.g., witches, monsters, ghosts).


title: Preadolescence

text: Preadolescents may well view human relationships differently (e.g. they may notice the flawed, human side of authority figures). Alongside that, they may begin to develop a sense of self-identity, and to have increased feelings of independence: 'may feel an individual, no longer "just one of the family."' A different view on morality can emerge; and the middle child will also show more "cooperativeness". The ability to balance one's own needs with those of others in group activities'. Many preadolescents will often start to question their home life and surroundings around this time and they may also start to form opinions that may differ from their upbringing in regards to issues such as politics, religion, sexuality, and gender roles.


title: Preadolescence

text: Greater responsibility within the family can also appear, as middle children become responsible for younger siblings and relatives, as with babysitting; while preadolescents may start caring about what they look like and what they are wearing.


title: Preadolescence

text: Prior to adolescence, children may have a dependence on their family as their main agent of socialization. This helps the child establish their attitudes, viewpoints, social norms, and societal roles.


title: Preadolescence

text: Among these changes is the shift from elementary to middle (or junior high) school. In this unfamiliar environment, the child may find the pressure to rapidly adapt and fit in. Children start to spend less time with family and more time with friends. At this time, socialization by the school and peer environment can become more predominant, as the preadolescent starts to learn more about how they would wish to hold themselves during interpersonal relationships.


title: Preadolescence

text: While children find this need to fit in, preadolescents have a conflicting desire to establish their own individualism. As the child grows into the transitionary period of preadolescence, the child often starts to develop a sense of autonomy as the child is exposed to a larger world around them full of sudden and unfamiliar changes. Compounded with a sense of self-consciousness, the preadolescent starts to explore their own self-identity and their role in society further.


title: Preadolescence

text: During preadolescence (early adolescence), individuals may become more preoccupied with body image and privacy, corresponding to physical changes seen during adrenarche and puberty. Early adolescents may become aware of their sexuality for the first time, and experience attraction towards others. Homosexual and heterosexual experimentation is not uncommon, although it is important to note that many teens who eventually identify as LGBT do not always do so during adolescence. On average, gay, lesbian, and bisexual individuals report experiencing same-sex attraction in early adolescence, at age 12. About 4 in 10 gay men, and 2 in 10 lesbian women report experiencing same-sex attraction before age 10. For individuals who begin to experience same-sex attraction, familial support and acceptance consistently predicts positive outcomes. Parents and guardians can support preadolescents, regardless of sexual orientation, by having honest conversations about sex. Specifically, parents can talk and listen in a way that invites preadolescents to have an open discussion about sexual orientation.


title: Preadolescence

text: Where development has been optimal, preadolescents 'come to school for something to be added to their lives; they want to learn lessons...which can lead to their eventually working in a job like their parents.' When earlier developmental stages have gone astray, however, then, on the principle that 'if you miss a stage, you can always go through it later,' some middle children 'come to school for another purpose...[not] to learn but to find a home from home...a stable emotional situation in which they can exercise their own emotional liability, a group of which they can gradually become a part.'


title: Preadolescence

text: Children at the threshold of adolescence in the nine-to-twelve-year-old group would seem to have particular vulnerabilities to parental separation. Among such problems were the very "eagerness of these youngsters to be co-opted into the parental battling; their willingness to take sides...and the intense, compassionate, caretaking relations which led these youngsters to attempt to rescue a distressed parent often to their own detriment".


title: Preadolescence

text: Preadolescents may well be more exposed to popular culture than younger children and have interests based on internet trends, television shows and movies (no longer just cartoons), fashion, technology, music and social media. Preadolescents generally prefer certain brands, and are a heavily targeted market of many advertisers. Their tendency to buy brand-name items may be due to a desire to fit in, although the desire is not as strong as it is with teenagers.


title: Preadolescence

text: Some scholars suggest that 'pre-adolescents ... reported frequent encounters with sexual material in the media, valued the information received from it, and used it as a learning resource ... and evaluated such content through what they perceived to be sexual morality.' However, other research has suggested that sexual media influences on preadolescent and adolescent sexual behavior is minimal.


title: Preadolescence

text: Freud called this stage the "latency" period to indicate that sexual feelings and interest went underground. Erik H. Erikson noted that latency period children in middle childhood can then direct more of their energy into asexual pursuits such as school, athletics, and same-sex friendships. Nevertheless, recent research contradicts these notions—suggesting that sexual development, interest, and behavior among latent period children does not cease. Instead, the apparent lack of sexual interest is due to children not sharing their sexual interests/emotions with adults.


title: Mezmerize (album)

text: Mezmerize is the fourth studio album by Armenian-American heavy metal band System of a Down, released on May 17, 2005, by American Recordings and Columbia Records. Upon its release, the album received acclaim from critics.


title: Mezmerize (album)

text: Despite the time difference between releases, "Mezmerize" and "Hypnotize" were recorded within the same time frame. The album features guitarist Daron Malakian sharing most of the vocal work with vocalist Serj Tankian, splitting the vocals at least halfway on many of the tracks. In 2018, Malakian and Tankian both independently revealed that at the time of recording the two albums, Tankian was almost out of the band. According to Tankian, this was because of differences in creative input and financial revenue split.


title: Mezmerize (album)

text: Malakian wrote "Old School Hollywood" after playing in a celebrity baseball game for charity. The song mentions Tony Danza and Frankie Avalon, who also played in the game.


title: Mezmerize (album)

text: In "Radio/Video", there are lines referring to two people named Danny and Lisa. Malakian commented on the song to "Revolver" magazine:


title: Mezmerize (album)

text: The Japanese version of the album contains alternate mixes of "Soldier Side (Intro)" and "Lost in Hollywood", the former with additional strings and the latter containing slightly different background vocals, while the leaked MP3 version of "Cigaro" contains a 4-stick hit intro not present in the retail version. The album artwork is done by Vartan Malakian, the father of Daron Malakian.


title: Mezmerize (album)

text: "Mezmerize" was acclaimed by critics, scoring 85 at Metacritic based on 19 reviews, indicating "universal acclaim". The album debuted at number one in at least 12 countries, including the US "Billboard" 200, with 453,000 copies, and has since been certified Platinum by the RIAA. It was chosen as one of Amazon.com's Top 100 Editor's Picks of 2005. The hit single "B.Y.O.B." won a Grammy Award in 2006 for Best Hard Rock Performance.


title: Mezmerize (album)

text: All lyrics written by Daron Malakian and Serj Tankian, except where noted. All music written by Malakian, except "Question!", written by Malakian and Tankian.


title: Gala Dalí

text: Gala Dalí (born Elena Ivanovna Diakonova, Елéна Ивáновна Дья́конова; – 10 June 1982), usually known simply as Gala, was the wife of poet Paul Éluard and later of artist Salvador Dalí, who were both prominent in surrealism. She also inspired many other writers and artists.


title: Gala Dalí

text: Gala was born as Elena Ivanovna Diakonova (Russian: Елена Ивановна Дьяконова) in Kazan, Russian Empire, to a family of intellectuals. Among her childhood friends was the poet Marina Tsvetaeva. She began working as a school-teacher in 1915, at which time she was living in Moscow.


title: Gala Dalí

text: In 1912, she was sent to a sanatorium at Clavadel, near Davos in Switzerland for the treatment of tuberculosis. She met Paul Éluard while in Switzerland and fell in love with him. They were both seventeen. In 1916, during World War I, she traveled from Russia to Paris to reunite with him; they were married one year later. They had one child, daughter Cécile (11 May 1918 — 10 August 2016). Gala detested motherhood, mistreating and ignoring her child.


title: Gala Dalí

text: With Éluard, Gala became involved in the Surrealist movement. She was an inspiration for many artists including Éluard, Louis Aragon, Max Ernst, and André Breton. Breton later despised her, claiming she was a destructive influence on the artists she befriended. She, Éluard, and Ernst spent three years in a "ménage à trois", from 1924 to 1927. In early August 1929, Éluard and Gala visited a young Surrealist painter in Spain, the emerging Salvador Dalí. An affair quickly developed between Gala and Dalí, who was about 10 years younger than she. Nevertheless, even after the breakup of their marriage, Éluard and Gala continued to be close.


title: Gala Dalí

text: After living together since 1929, Dalí and Gala married in a civil ceremony in 1934, and remarried in a Catholic ceremony in 1958 in the Pyrenean hamlet of Montrejic. They needed to receive a special dispensation by the Pope because Gala had been previously married and she was a believer (not Catholic, but was an Orthodox Christian). Due to his purported phobia of female genitalia, Dalí was said to have been a virgin when they met on the Costa Brava in 1929. Around that time she was found to have uterine fibroids, for which she underwent a hysterectomy in 1936. She was Dalí's muse, directly inspiring and appearing in many of his works.


title: Gala Dalí

text: In the early 1930s, Dalí started to sign his paintings with his and her name as "(i)t is mostly with your blood, Gala, that I paint my pictures". He stated that Gala acted as his agent, and aided in redirecting his focus. According to most accounts, Gala had a strong libido and throughout her life had numerous extramarital affairs (among them with her former husband Paul Éluard), which Dalí encouraged, since he was a practitioner of candaulism. She had a fondness for young artists, and in her old age she often gave expensive gifts to those who associated with her.


title: Gala Dalí

text: In 1968, Dalí bought Gala the Castle of Púbol, Girona, where she would spend time every summer from 1971 to 1980. He also agreed not to visit there without getting advance permission from her in writing.


title: Gala Dalí

text: Gala died in Port Lligat in Catalonia, Spain, early in the morning of 10 June 1982, at the age of 87. In the months before her death, Gala had battled a severe case of influenza, after which she began to exhibit signs of dementia. She was interred in the Castle of Púbol, which her husband had purchased for her in 1968, in a crypt with a chessboard style pattern.


title: Gala Dalí

text: Gala is a frequent model in Dalí's work, often in religious roles such as the Blessed Virgin Mary in the 1949 painting "The Madonna of Port Lligat". His paintings of her show his great love for her, and some are perhaps the most affectionate and sensual depictions of a middle-aged woman in Western art. Among the paintings she served as a model for are: "Imperial Monument to the Child-Woman, Gala" (1929); "Memory of the Child-Woman" (1932); "The Angelus of Gala" (1935); "Gala and "The Angelus" of Millet before the Imminent Arrival of the Conical Anamorphoses" (1933); "William Tell and Gradiva" (1931); "The Old Age of William Tell" (1931); "The Discovery of America by Christopher Columbus" (1958–59); "The Ecumenical Council" (1960); "Corpus Hypercubus" (1954); and "Galatea of the Spheres" (1952).


title: Gala Dalí

text: In "Portrait of Galarina" (1940–1945), Gala's face is shown severe and confrontational, her bared breast meant to depict bread, and the snake on the arm a gift of Dalí's sponsor Edward James.


title: Continued fraction

text: In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression. In either case, all integers in the sequence, other than the first, must be positive. The integers formula_3 are called the coefficients or terms of the continued fraction.


title: Continued fraction

text: It is generally assumed that the numerator of all of the fractions is 1. If arbitrary values and/or functions are used in place of one or more of the numerators or the integers in the denominators, the resulting expression is a generalized continued fraction. When it is necessary to distinguish the first form from generalized continued fractions, the former may be called a simple or regular continued fraction, or said to be in canonical form.


title: Continued fraction

text: Continued fractions have a number of remarkable properties related to the Euclidean algorithm for integers or real numbers. Every rational number has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to formula_6. The numerical value of an infinite continued fraction is irrational; it is defined from its infinite sequence of integers as the limit of a sequence of values for finite continued fractions. Each finite continued fraction of the sequence is obtained by using a finite prefix of the infinite continued fraction's defining sequence of integers. Moreover, every irrational number formula_7 is the value of a "unique" infinite regular continued fraction, whose coefficients can be found using the non-terminating version of the Euclidean algorithm applied to the incommensurable values formula_7 and 1. This way of expressing real numbers (rational and irrational) is called their "continued fraction representation".


title: Continued fraction

text: The term "continued fraction" may also refer to representations of rational functions, arising in their analytic theory. For this use of the term, see Padé approximation and Chebyshev rational functions.


title: Continued fraction

text: Consider, for example, the rational number , which is around 4.4624. As a first approximation, start with 4, which is the integer part; . The fractional part is the reciprocal of which is about 2.1628. Use the integer part, 2, as an approximation for the reciprocal to obtain a second approximation of .


title: Continued fraction

text: The remaining fractional part, , is the reciprocal of , and is around 6.1429. Use 6 as an approximation for this to obtain as an approximation for and , about 4.4615, as the third approximation; . Finally, the fractional part, , is the reciprocal of 7, so its approximation in this scheme, 7, is exact () and produces the exact expression for .


title: Continued fraction

text: The expression is called the continued fraction representation of . This can be represented by the abbreviated notation = [4; 2, 6, 7]. (It is customary to replace only the "first" comma by a semicolon.) Some older textbooks use all commas in the -tuple, for example, [4, 2, 6, 7].


title: Continued fraction

text: If the starting number is rational, then this process exactly parallels the Euclidean algorithm applied to the numerator and denominator of the number. In particular, it must terminate and produce a finite continued fraction representation of the number. The sequence of integers that occur in this representation is the sequence of successive quotients computed by the Euclidean algorithm. If the starting number is irrational, then the process continues indefinitely. This produces a sequence of approximations, all of which are rational numbers, and these converge to the starting number as a limit. This is the (infinite) continued fraction representation of the number. Examples of continued fraction representations of irrational numbers are:


title: Continued fraction

text: Continued fractions are, in some ways, more "mathematically natural" representations of a real number than other representations such as decimal representations, and they have several desirable properties:


title: Continued fraction

text: When the terms eventually repeat from some point onwards, the expression is called a periodic continued fraction.


title: Continued fraction

text: To calculate a continued fraction representation of a number , write down the integer part (technically the floor) of . Subtract this integer part from . If the difference is 0, stop; otherwise find the reciprocal of the difference and repeat. The procedure will halt if and only if is rational. This process can be efficiently implemented using the Euclidean algorithm when the number is rational. The table below shows an implementation of this procedure for the number 3.245, resulting in the continued fraction expansion [3; 4,12,4].


title: Continued fraction

text: The integers formula_2, formula_23 etc., are called the "coefficients" or "terms" of the continued fraction. One can abbreviate the continued fraction


title: Continued fraction

text: Every finite continued fraction represents a rational number, and every rational number can be represented in precisely two different ways as a finite continued fraction, with the conditions that the first coefficient is an integer and the other coefficients are positive integers. These two representations agree except in their final terms. In the longer representation the final term in the continued fraction is 1; the shorter representation drops the final 1, but increases the new final term by 1. The final element in the short representation is therefore always greater than 1, if present. In symbols:


title: Continued fraction

text: The continued fraction representations of a positive rational number and its reciprocal are identical except for a shift one place left or right depending on whether the number is less than or greater than one respectively. In other words, the numbers represented by


title: Continued fraction

text: The last number that generates the remainder of the continued fraction is the same for both formula_42 and its reciprocal.


title: Continued fraction

text: Every infinite continued fraction is irrational, and every irrational number can be represented in precisely one way as an infinite continued fraction.


title: Continued fraction

text: An infinite continued fraction representation for an irrational number is useful because its initial segments provide rational approximations to the number. These rational numbers are called the convergents of the continued fraction. The larger a term is in the continued fraction, the closer the corresponding convergent is to the irrational number being approximated. Numbers like π have occasional large terms in their continued fraction, which makes them easy to approximate with rational numbers. Other numbers like "e" have only small terms early in their continued fraction, which makes them more difficult to approximate rationally. The golden ratio Φ has terms equal to 1 everywhere—the smallest values possible—which makes Φ the most difficult number to approximate rationally. In this sense, therefore, it is the "most irrational" of all irrational numbers. Even-numbered convergents are smaller than the original number, while odd-numbered ones are larger.


title: Continued fraction

text: The numerator of the third convergent is formed by multiplying the numerator of the second convergent by the third coefficient, and adding the numerator of the first convergent. The denominators are formed similarly. Therefore, each convergent can be expressed explicitly in terms of the continued fraction as the ratio of certain multivariate polynomials called "continuants".


title: Continued fraction

text: If successive convergents are found, with numerators , , ... and denominators , , ... then the relevant recursive relation is:


title: Continued fraction

text: Thus to incorporate a new term into a rational approximation, only the two previous convergents are necessary. The initial "convergents" (required for the first two terms) are ⁄ and ⁄. For example, here are the convergents for [0;1,5,2,2].


title: Continued fraction

text: When using the Babylonian method to generate successive approximations to the square root of an integer, if one starts with the lowest integer as first approximant, the rationals generated all appear in the list of convergents for the continued fraction. Specifically, the approximants will appear on the convergents list in positions 0, 1, 3, 7, 15, ... , , ... For example, the continued fraction expansion for is [1;1,2,1,2,1,2,1,2...]. Comparing the convergents with the approximants derived from the Babylonian method:


title: Continued fraction

text: A Baire space is a topological space on infinite sequences of natural numbers. The infinite continued fraction provides a homeomorphism from the Baire space to the space of irrational real numbers (with the subspace topology inherited from the usual topology on the reals). The infinite continued fraction also provides a map between the quadratic irrationals and the dyadic rationals, and from other irrationals to the set of infinite strings of binary numbers (i.e. the Cantor set); this map is called the Minkowski question mark function. The mapping has interesting self-similar fractal properties; these are given by the modular group, which is the subgroup of Möbius transformations having integer values in the transform. Roughly speaking, continued fraction convergents can be taken to be Möbius transformations acting on the (hyperbolic) upper half-plane; this is what leads to the fractal self-symmetry.


title: Continued fraction

text: The limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1) is the Gauss–Kuzmin distribution.


title: Continued fraction

text: If formula_2, formula_23, formula_47, formula_48 is an infinite sequence of positive integers, define the sequences formula_49 and formula_50 recursively:


title: Continued fraction

text: Corollary 1: Each convergent is in its lowest terms (for if formula_49 and formula_50 had a nontrivial common divisor it would divide formula_64, which is impossible).


title: Continued fraction

text: Theorem 4. Each (formula_70th) convergent is nearer to a subsequent (formula_1th) convergent than any preceding (formula_72th) convergent is. In symbols, if the formula_1th convergent is taken to be formula_74, then


title: Continued fraction

text: Corollary 1: The even convergents (before the formula_1th) continually increase, but are always less than formula_78.


title: Continued fraction

text: Corollary 2: The odd convergents (before the formula_1th) continually decrease, but are always greater than formula_78.


title: Continued fraction

text: Corollary 1: A convergent is nearer to the limit of the continued fraction than any fraction whose denominator is less than that of the convergent.


title: Continued fraction

text: Corollary 2: A convergent obtained by terminating the continued fraction just before a large term is a close approximation to the limit of the continued fraction.


title: Continued fraction

text: where formula_84 is an integer such that formula_85, are called "semiconvergents", "secondary convergents", or "intermediate fractions". The formula_86-st semiconvergent equals the mediant of the formula_84-th one and the convergent formula_88. Sometimes the term is taken to mean that being a semiconvergent excludes the possibility of being a convergent (i.e., formula_89), rather than that a convergent is a kind of semiconvergent.


title: Continued fraction

text: It follows that semiconvergents represent a monotonic sequence of fractions between the convergents formula_90 (corresponding to formula_91) and formula_92 (corresponding to formula_93). The consecutive semiconvergents formula_94 and formula_95 satisfy the property formula_96.


title: Continued fraction

text: If a rational approximation formula_97 to a real number formula_42 is such that the value formula_99 is smaller than that of any approximation with a smaller denominator, then formula_97 is a semiconvergent of the continued fraction expansion of formula_42. The converse is not true, however.


title: Continued fraction

text: One can choose to define a "best rational approximation" to a real number as a rational number , , that is closer to than any approximation with a smaller or equal denominator. The simple continued fraction for can be used to generate "all" of the best rational approximations for by applying these three rules:


title: Continued fraction

text: For example, 0.84375 has continued fraction [0;1,5,2,2]. Here are all of its best rational approximations.


title: Continued fraction

text: The strictly monotonic increase in the denominators as additional terms are included permits an algorithm to impose a limit, either on size of denominator or closeness of approximation.


title: Continued fraction

text: The "half rule" mentioned above requires that when is even, the halved term /2 is admissible if and only if This is equivalent to: .


title: Continued fraction

text: The convergents to are "best approximations" in a much stronger sense than the one defined above. Namely, / is a convergent for if and only if has the smallest value among the analogous expressions for all rational approximations / with ; that is, we have so long as . (Note also that as .)


title: Continued fraction

text: A rational that falls within the interval , for , can be found with the continued fractions for and . When both and are irrational and


title: Continued fraction

text: where and have identical continued fraction expansions up through , a rational that falls within the interval is given by the finite continued fraction,


title: Continued fraction

text: This rational will be best in the sense that no other rational in will have a smaller numerator or a smaller denominator.


title: Continued fraction

text: If is rational, it will have "two" continued fraction representations that are "finite", and , and similarly a rational  will have two representations, and . The coefficients beyond the last in any of these representations should be interpreted as ; and the best rational will be one of , , , or .


title: Continued fraction

text: For example, the decimal representation 3.1416 could be rounded from any number in the interval . The continued fraction representations of 3.14155 and 3.14165 are


title: Continued fraction

text: Thus, is the best rational number corresponding to the rounded decimal number 3.1416, in the sense that no other rational number that would be rounded to 3.1416 will have a smaller numerator or a smaller denominator.


title: Continued fraction

text: will be one of the convergents for the continued fraction expansion of a number, if and only if the number is strictly between (see this proof)


title: Continued fraction

text: The numbers and are formed by incrementing the last coefficient in the two representations for . It is the case that when is even, and when is odd.


title: Continued fraction

text: If there is no such , but one expansion is shorter than the other, say and with for , then if is even and if is odd.


title: Continued fraction

text: To calculate the convergents of we may set , define and , and , . Continuing like this, one can determine the infinite continued fraction of as


title: Continued fraction

text: The fourth convergent of is [3;7,15,1] = = 3.14159292035..., sometimes called Milü, which is fairly close to the true value of .


title: Continued fraction

text: Let us suppose that the quotients found are, as above, [3;7,15,1]. The following is a rule by which we can write down at once the convergent fractions which result from these quotients without developing the continued fraction.


title: Continued fraction

text: The first quotient, supposed divided by unity, will give the first fraction, which will be too small, namely, . Then, multiplying the numerator and denominator of this fraction by the second quotient and adding unity to the numerator, we shall have the second fraction, , which will be too large. Multiplying in like manner the numerator and denominator of this fraction by the third quotient, and adding to the numerator the numerator of the preceding fraction, and to the denominator the denominator of the preceding fraction, we shall have the third fraction, which will be too small. Thus, the third quotient being 15, we have for our numerator , and for our denominator, . The third convergent, therefore, is . We proceed in the same manner for the fourth convergent. The fourth quotient being 1, we say 333 times 1 is 333, and this plus 22, the numerator of the fraction preceding, is 355; similarly, 106 times 1 is 106, and this plus 7 is 113.


title: Continued fraction

text: These convergents are alternately smaller and larger than the true value of , and approach nearer and nearer to . The difference between a given convergent and is less than the reciprocal of the product of the denominators of that convergent and the next convergent. For example, the fraction is greater than , but − is less than  =  (in fact, − is just more than = ).


title: Continued fraction

text: The demonstration of the foregoing properties is deduced from the fact that if we seek the difference between one of the convergent fractions and the next adjacent to it we shall obtain a fraction of which the numerator is always unity and the denominator the product of the two denominators. Thus the difference between and is , in excess; between and , , in deficit; between and , , in excess; and so on. The result being, that by employing this series of differences we can express in another and very simple manner the fractions with which we are here concerned, by means of a second series of fractions of which the numerators are all unity and the denominators successively be the product of every two adjacent denominators. Instead of the fractions written above, we have thus the series:


title: Continued fraction

text: The first term, as we see, is the first fraction; the first and second together give the second fraction, ; the first, the second and the third give the third fraction , and so on with the rest; the result being that the series entire is equivalent to the original value.


title: Continued fraction

text: where the "a" ("n" > 0) are the partial numerators, the "b" are the partial denominators, and the leading term "b" is called the "integer" part of the continued fraction.


title: Continued fraction

text: To illustrate the use of generalized continued fractions, consider the following example. The sequence of partial denominators of the simple continued fraction of does not show any obvious pattern:


title: Continued fraction

text: The first two of these are special cases of the function with = 4 arctan (1) and the fourth and fifth one can be derived using the Wallis product.


title: Continued fraction

text: The continued fraction of formula_109 above consisting of cubes uses the Nilakantha series and an exploit from Leonhard Euler.


title: Continued fraction

text: The numbers with periodic continued fraction expansion are precisely the irrational solutions of quadratic equations with rational coefficients; rational solutions have finite continued fraction expansions as previously stated. The simplest examples are the golden ratio φ = [1;1,1,1,1,1...] and = [1;2,2,2,2...], while = [3;1,2,1,6,1,2,1,6...] and = [6;2,12,2,12,2,12...]. All irrational square roots of integers have a special form for the period; a symmetrical string, like the empty string (for ) or 1,2,1 (for ), followed by the double of the leading integer.


title: Continued fraction

text: Because the continued fraction expansion for φ doesn't use any integers greater than 1, φ is one of the most "difficult" real numbers to approximate with rational numbers. Hurwitz's theorem states that any irrational number can be approximated by infinitely many rational with


title: Continued fraction

text: While virtually all real numbers will eventually have infinitely many convergents whose distance from is significantly smaller than this limit, the convergents for φ (i.e., the numbers , , , , etc.) consistently "toe the boundary", keeping a distance of almost exactly formula_111 away from φ, thus never producing an approximation nearly as impressive as, for example, for . It can also be shown that every real number of the form , where , , , and are integers such that , shares this property with the golden ratio φ; and that all other real numbers can be more closely approximated.


title: Continued fraction

text: While there is no discernible pattern in the simple continued fraction expansion of , there is one for , the base of the natural logarithm:


title: Continued fraction

text: If is the modified, or hyperbolic, Bessel function of the first kind, we may define a function on the rationals by


title: Continued fraction

text: which is defined for all rational numbers, with and in lowest terms. Then for all nonnegative rationals, we have


title: Continued fraction

text: Most irrational numbers do not have any periodic or regular behavior in their continued fraction expansion. Nevertheless, Khinchin proved that for almost all real numbers , the (for ) have an astonishing property: their geometric mean tends to a constant (known as Khinchin's constant, ) independent of the value of . Paul Lévy showed that the th root of the denominator of the th convergent of the continued fraction expansion of almost all real numbers approaches an asymptotic limit, approximately 3.27582, which is known as Lévy's constant. Lochs' theorem states that th convergent of the continued fraction expansion of almost all real numbers determines the number to an average accuracy of just over decimal places.


title: Continued fraction

text: Continued fractions play an essential role in the solution of Pell's equation. For example, for positive integers and , and non-square , it is true that if , then is a convergent of the regular continued fraction for . The converse holds if the period of the regular continued fraction for is 1, and in general the period describes which convergents give solutions to Pell's equation.


title: Continued fraction

text: Continued fractions also play a role in the study of dynamical systems, where they tie together the Farey fractions which are seen in the Mandelbrot set with Minkowski's question mark function and the modular group Gamma.