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Algorism

Algorism

Algorism is the name for the Indo-Arabian decimal system of writing and working with numbers, in which symbols (the ten digits 0 through 9) are used to describe values using a place-value system (positional notation), where each symbol has ten times the weight of the one to its right. This system was originally invented in India in the 6th century CE (or earlier), and was soon adopted in the Islamic world. Muslim mathematicians made many contributions (including the concept of the decimal fractions as an extension of the notation, which led to the notion of the decimal point), and the written European forms of the digits called Arabic numerals are derived from the ghubar (sand-table or dust-table) numerals used in north-west Africa and Spain. The word algorism comes from the name al-Khwarizmi ("the one from Khwarizm"), the cognomen (nickname) of an early 9th century Persian mathematician, possibly from what is now Khiva in western Uzbekistan. His name is also the root of the word algorithm. Category:Numeration

Positional notation

Positional notation or place-value notation is a numeral system in which each position is related to the next by a constant multiplier called the base of that numeral system. Each position may be represented by a unique symbol or by a limited set of symbols. The resultant value of each position is the value of its symbol or symbols multiplied by a power of the base. The total value of a positional number is the total of the resultant values of all positions. The decimal system uses ten unique symbols, whereas the sexagesimal system usually uses a pseudo-decimal system for each position and separates each position from the next by punctuation. Modern computers use binary, octal, and hexadecimal numbers, the latter using decimal numerals (0–9) plus the letters A–F to provide the sixteen possible symbols in each position. The idea of indicating magnitude by means of position was embodied long ago by the use of the abacus in all its various forms. With an abacus to perform arithmetic operations, the writing of the starting, intermediate and final values of a calculation could easily be done with a simple additive system such as Roman Numerals. This approach required no memorization of tables (as does positional notation) and could produce results for all practical purposes very quickly. For four centuries (13th - 16th) there was strong disagreement between those who believed in adopting the positional system and those who wanted to stay with the additive-system-plus-abacus. A key argument against the positional system was its susceptibility to easy fraud by simply putting a number at the beginning or end of a quantity, thereby changing (e.g.) 100 into 5100, or 100 into 1000. Modern bank checks require a natural language spelling of an amount, as well as the amount itself, to prevent such fraud. The abacus was in widespread use in Japan and other Asian countries until very recent times, when it was replaced by calculators. The real value of positional notation turned out to be its ability to invite the further study of numbers. Integers, rational numbers, and place-holders (e.g. zero) were long known about, but irrational numbers, infinity, transfinite numbers, and imaginary numbers were all concepts that could only be discovered once the idea of a continuous number line was implied by positional notation.

Decimal system

In the decimal or base 10 number system, each position starting from the right is a higher power of 10. The first position represents 10⁰, the second position 10¹, the third 10², the fourth 10³, and so on. Fractional values are indicated by a separator, which varies by locale. Usually this separator is a period or full stop, or a comma. Digits to the right of it are multiplied by 10 raised to a negative power or exponent. The first position to the right of the separator indicates 10^-1, the second position 10^-2, and so on for each successive position. As an example, the number 2674 in a base 10 number system is : :( 2 × 10³ ) + ( 6 × 10² ) + ( 7 × 10¹ ) + ( 4 × 10⁰ ) or :( 2 × 1000 ) + ( 6 × 100 ) + ( 7 × 10 ) + ( 4 × 1 )

Sexagesimal system

The sexagesimal or base sixty system was used for the integral and fractional portions of Babylonian numerals, by Hellenistic astronomers using Greek numerals for the fractional portion only, and is still used for modern time and angles, but only for minutes and seconds. Modern time separates each position by a colon or point. For example, the time might be 10:25:59 (10 hours 25 minutes 59 seconds). Angles use similar notation. For example, an angle might be 10°25'59" (10 degrees 25 minutes 59 seconds). In both cases, only minutes and seconds use sexagesimal notation — angular degrees can be larger than 59 (one rotation around a circle is 360°, two rotations are 720°, etc.), and both time and angles use decimal fractions of a second. This contrasts with the numbers used by Hellenistic and Renaissance astronomers, who used thirds, fourths, etc. for finer increments. Where we might write 10°25'59.392", they would have written 10°25'592331'12 or 10°25^I59^II23^III31^IV12^V. In the 1930s, Otto Neugebauer introduced a modern notational system for Babylonian and Hellenistic numbers that substitutes modern decimal notation from 0 to 59 in each position, while using a semicolon (;) to separate the integral and fractional portions of the number and using a comma (,) to separate the positions within each portion. For example, the mean synodic month used by both Babylonian and Hellenistic astronomers and still used in the Hebrew calendar is 29;31,50,8,20 days.

Non-positional positions

Each position does not need to be positional itself. Hellenistic astronomers used one or two alphabetic Greek numerals for each position (one chosen from 5 letters representing 10–50 and/or one chosen from 9 letters representing 1–9, or a zero symbol), whereas Babylonian numerals used groups of two kinds of wedges representing ones and tens (a narrow vertical wedge ( | ) and an open left pointing wedge (<)) — up to 14 symbols per position (5 tens (<<<<<) and 9 ones ( ||||||||| ) grouped into one or two near squares containing up to three tiers of symbols, or a place holder (\\) for the lack of a position). A hypothetical Roman numeral positional system would separate each position with punctuation marks but would not necessarily require a symbol for zero. For example, 144 might be I.IV.IV. in decimal notation (medieval Roman numerals were always terminated by a point to show that they were a number). To indicate zero, its position might not be present, for example I.IV.. would mean 140. About 725, Bede or a colleague used N for zero (the initial of the Latin word nulla meaning nothing), so the latter might be I.IV.N.

External links

- [http://www.cut-the-knot.org/binary.shtml Base Converter] at cut-the-knot
- [http://www.cut-the-knot.org/recurrence/conversion.shtml Implementation of Base Conversion] at cut-the-knot
- [http://www.cut-the-knot.org/blue/frac_conv.shtml Conversion of Fractions in Various Bases] at cut-the-knot
- [http://www.cut-the-knot.org/blue/SysTable.shtml Addition and Multiplication Tables in Various Bases] at cut-the-knot

References

- Donald Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms, Third Edition. Addison-Wesley, 1997. ISBN 0-201-89684-2. Section 4.1: Positional Number Systems, pp.195–213. Category:Numeration Category:Mathematical notation

India

The Republic of India is a country in South Asia which comprises of the majority of the Indian subcontinent. India has a coastline which stretches over seven thousand kilometres, and shares its borders with Pakistan to the west, the People's Republic of China, Nepal, and Bhutan to the northeast, and Bangladesh and Myanmar on the east. On the Indian Ocean, it is adjacent to the island nations of the Maldives on the southwest, Sri Lanka on the south, and Indonesia on the southeast. India also claims a border with Afghanistan to the northwest. India is the fourth largest economy in the world in terms of purchasing power parity. It is the second most populous country in the world, with a population of over one billion, and is the seventh largest country by geographical area. It is home to some of the most ancient civilizations, and a centre of important historic trade routes. Four major world religions: Hinduism, Buddhism, Jainism and Sikhism have originated from India. Formerly a major part of the British Empire as the British Raj before gaining independence in 1947, during the past twenty years the country has grown significantly, especially in its economic and military spheres, regionally as well as globally. The name India , is derived from the Old Persian version of Sindhu, the historic local appellation for the river Indus; see Origin of India's name. The Constitution of India and general usage also recognises Bharat ( ), which is derived from the Sanskrit name of an ancient Hindu king, whose story is to be found in the Mahabharata, as an official name of equal status. A third name, Hindustan ( ) , or Land of the Hindus in Persian, has been used since the twelfth century, though its contemporary use is unevenly applied due to domestic disputes over its representiveness as a national signifier.

History

Stone Age rock shelters with paintings at Bhimbetka in Madhya Pradesh are the earliest known traces of human life in India. The first known permanent settlements appeared 9,000 years ago and developed into the Indus Valley Civilisation, which peaked between 2600 BC and 1900 BC. It was followed by the Vedic Civilisation. From around 550 BC onwards, many independent kingdoms came into being. In the north, the Maurya dynasty, which included Ashoka, contributed greatly to India's cultural landscape. From 180 BC, a series of invasions from Central Asia followed, with the successive establishment in the northern Indian Subcontinent of the Indo-Greek, Indo-Scythian and Indo-Parthian kingdoms, and finally the Kushan Empire. From the 3rd century AD onwards the Gupta dynasty oversaw the period referred to as ancient India's "Golden Age". Gupta dynasty built by emperor Ashoka in the 3rd century BC]] In the south, several dynasties including the Chalukyas, Cheras, Cholas, Kadambas, Pallavas and Pandyas prevailed during different periods. Science, art, literature, mathematics, astronomy, engineering, religion and philosophy flourished under the patronage of these kings. Following the Islamic invasions in the beginning of the second millennium, much of north and central India came to be ruled by the Delhi Sultanate, and later, much of the entire subcontinent by the Mughal dynasty. Nevertheless, several indigenous kingdoms remained or rose to power, especially in the relatively sheltered south. Vijayanagara Empire was notable among such kingdoms. During the middle of the second millennium, several European countries, including the Portuguese, Dutch, French and British, who were initially interested in trade with India, took advantage of fractured kingdoms fighting each other to establish colonies in the country. After a failed insurrection in 1857 against the British East India Company, popularly known in India as the First War of Indian Independence and most commonly known in the West as the Indian Mutiny, most of India came under the direct administrative control of the crown of the British Empire. British Empire, Orissa built in the 13th century, is one of the most famous monuments of stone sculpture in the world.]] sculpture in the 10th century AD.]] In the early part of the 20th century, a prolonged and largely non-violent struggle for independence, the Indian independence movement, followed, to be eventually led by Mahatma Gandhi, regarded officially as the Father Of The Nation. The culmination of this path-breaking struggle was reached on 1947-08-15 when India gained full independence from British rule, later becoming a republic on 1950-01-26. As a multi-ethnic and multi-religious country, India has had its share of sectarian violence and insurgencies in different parts of the country. Nonetheless, it has held itself together as a secular, liberal democracy barring a brief period from 1975 to 1977 during which the then Prime Minister Indira Gandhi declared a "state of emergency" with the suspension of civil rights. India has unresolved border disputes with China, which escalated into a brief war in 1962, and Pakistan which resulted in wars in 1947, 1965, and 1971, and a border altercation in the northern state of Kashmir in 1999. India was a founding member of the Non-Aligned Movement and the United Nations. In 1974, India conducted an underground nuclear test, making it an unofficial member of the "nuclear club", which was followed up with a series of five more tests in 1998. Significant economic reforms beginning in 1991 have transformed India into one of the fastest growing economies in the world and added to its global clout.

Government

The Constitution of India states India to be a sovereign, socialist, secular, democratic republic. India is a federal republic, with a bicameral parliament operating under a Westminster-style parliamentary system. It has a three branch system of governance consisting of the legislature, executive and judiciary. The President, who is the head of state, has a largely ceremonial role. His roles include interpreting the constitution, signing laws into action, and issuing pardons. He is also the Commander-in-Chief of the armed forces. The President and Vice-President are elected indirectly by an electoral college for five-year terms. The Prime Minister is the head of government and most executive powers are vested in this office. He (or she) is elected by legislators of the political party, or coalition, commanding a parliamentary majority, and serves a five-year term incumbent upon enjoying this majority. The constitution does not provide for a post of Deputy Prime Minister, but this option has been exercised from time to time. The legislature of India is the bicameral Parliament which consists of the upper house known as the Rajya Sabha, or Council of States, the lower house known as the Lok Sabha, or House of the People, and the President. The 245-member Rajya Sabha is chosen indirectly through an electoral college and has a staggered six year term. The 545-member Lok Sabha is directly elected for a five year term, and is the determinative constituent of political power and government formation. All Indian citizens above the age of eighteen are eligible to vote. The executive arm consists of the President, Vice-President and the Council of Ministers (the Cabinet) headed by the Prime Minister. Any minister holding a portfolio must be a member of either house of parliament. In India's parliamentary system, the executive is subordinate to the legislature. India's independent judiciary consists of the Supreme Court, headed by the Chief Justice of India. The Supreme Court has both original jurisdiction over disputes between states and the Centre, and appellate jurisdiction over the High Courts of India. There are eighteen appellate High Courts, having jurisdiction over a large state or a group of states. Each of these states has a tiered system of lower courts. A conflict between the legislature and the judiciary is referred to the President.

Politics

Chief Justice of India For most of its independent history, India's national government has been controlled by the Indian National Congress Party. Following its position as the largest political organisation in pre-independence India, Congress, usually led by a member of the Nehru-Gandhi family, dominated national politics for over forty years. In 1977, a united opposition, under the banner of the Janata Party, won the election and formed a non-Congress government for a short period after the unpopular 'emergency rule' imposed by Indira Gandhi in the previous Congress regime. In 1996, the Bharatiya Janata Party (BJP), a political party with a right wing nationalist ideology, became the largest single party, and established for the first time a serious opposition to the largely centre-left Congress. But power was held by two successive coalition governments, who stayed on with the support of the Congress. In 1998, the BJP formed the National Democratic Alliance (NDA) along with smaller parties and became the first non-Congress government to sustain the full five year term after it returned to power in 1999. The decade prior to 1999 was marked by short-lasting governments, with seven separate governments formed within that period. One however, a Congress government formed in 1991, lasted the full five years and initiated significant economic reforms. In the 2004 Indian elections the Congress party returned to power after winning the largest number of seats, by a narrow margin. Congress formed a government in alliance with the Communist Party of India (Marxist) and with several mostly-regional parties called the United Progressive Alliance. The NDA, led by the BJP, currently forms the main opposition. All governments formed since 1996 have required party coalitions, with no single majority party, due to the steady rise of regional parties at the national level.

States and union territories

India is divided into twenty-eight states (which are further subdivided into districts), six Union Territories and the National Capital Territory of Delhi. States have their own elected government, whereas Union Territories are governed by an administrator appointed by the union government, though some have elected governments. India has had two scientific bases in Antarctica – the Dakshin Gangotri and Maitri, but has made no territorial claims so far.

Geography

Maitri in the north to Arunachal Pradesh in the far east making up most of India's eastern borders]] India's entire north and northeast states are made up of the Himalayan Range. The rest of northern, central and eastern India consists of the fertile Indo-Gangetic plain. Towards western India, bordering southeast Pakistan, lies the Thar Desert. The southern Indian peninsula is almost entirely composed of the Deccan plateau. The plateau is flanked by two hilly coastal ranges, the Western Ghats and Eastern Ghats. India is home to several major rivers such as the Ganga (Ganges), the Brahmaputra, the Yamuna, the Godavari, and the Krishna. The rivers are responsible for the fertile plains in northern India which are conducive to farming. The Indian climate varies from a tropical climate in the south to a more temperate climate in the north. Parts of India which lie in the Himalaya have a tundra climate. India gets most of its rains through the monsoons.

Economy

monsoon India has an economy ranked as the tenth largest in the world in terms of currency conversion and fourth largest in terms of purchasing power parity. It recorded one of the fastest annual growth rates of 6.9% for the year ending March 2005. India's per-capita income by purchasing power parity is US$ 3,262, ranked 125th by the World Bank. India's foreign exchange reserves amount to over US$ 143 billion. Mumbai serves as the nation's financial capital and is also home to both the headquarters of the Reserve Bank of India and the pre-eminent Bombay Stock Exchange. While a quarter of Indians still live below the poverty line, a large middle class has now emerged along with the rapid growth of the IT industry. The Indian economy has shed much of its historical dependence on agriculture, which now contributes to less than 25 % of GDP. Other important industries are mining, petroleum, diamond polishing, films, textiles, information technology services, and handicrafts. Most of India's industrial regions are centred around major cities. In recent years, India has emerged as one of the largest players in software and business process outsourcing services, with revenues of US$ 17.2 billion in 2004 to 2005. Many small-scale industries provide steady employment to workers in small towns and villages. business process outsourcing While India receives only around three million foreign visitors a year, tourism is still an important but under-developed source of national income. Tourism contributes 5.3 % of India's GDP. The actual employment generation, both direct and indirect, is estimated to be 42 million, or about 10 % of India's work force. In monetary terms, it contributes about US$4 billion in foreign exchange. India's major trading partners are the United States, Japan, China and the United Arab Emirates. India's main exports items include agricultural products, textile goods, gems and jewellry, software services and technology, engineering goods, chemicals and leather products while its main import commodities are crude oil, machinery, gems, fertiliser, chemicals. For the year 2004, India's total exports stood at US$ 69.18 billion while the imports were worth at US $89.33 billion.

Demographics

India is the second most populous country in the world, with only China having a larger population. By 2030, India is expected to surpass China with the world's largest population, estimated at 1.6 billion. Language, religion, and caste are major determinants of social and political organisation within the highly diverse Indian population today. Its biggest metropolitan agglomerations are Mumbai (formerly Bombay), Delhi, Kolkata (formerly Calcutta) and Chennai (formerly Madras). Chennai]] India's literacy rate is 64.8 % with 53.7 % of females and 75.3 % of males being literate. The sex ratio is 933 females for every 1000 males. Work Participation Rate (WPR) (the percentage of workers to total population) stands at 39.1 % with male WPR at 51.7 % and female WPR at 25.6 % inote|eu{inote|demostats{inote|religion{ref|languages{inote|tongues{see2|Christianity in India|Jews in India{seealso3|List of Indian languages by total speakers|List of cities in India|Religion in India{main|Culture of India{seealso4|List of World Heritage sites in India|Indian architecture|Indian family name|Cuisine of India{main|Sports in India{main|Holidays in India{Official Holidays of India{Topics related to India{portal{sisterlinks|India{wikitravel{wikicities|india|India{explain-inote{Web reference | title=India facts and figures | work=Embassy of India| URL= http://www.indianembassy.org/dydemo/indiaprofile/profile.htm | date=August 14 | year=2005{Web reference | title= Forex reserves up by $1bn | work=Economic Times| URL= http://economictimes.indiatimes.com/articleshow/1093864.cms | date=August 14 | year=2005{Web reference | title= India Economy | work=Travel Document Systems |URL= http://www.traveldocs.com/in/economy.htm | date=August 14 | year=2005{Web reference | title= Services | work=India in Business| URL= http://www.indiainbusiness.nic.in/india-profile/ser-infotech.htm | date=August 14 | year=2005{Web reference | title= Destination India: An Unpolished Diamond | work=Times of India | URL= http://timesfoundation.indiatimes.com/articleshow/819309.cms | date=August 14 | year=2005{Web reference | title= US, UAE, UK, China, Japan among India's top trade partners | work=Indian Express| URL= http://www.indianexpress.com/news/business/20050102-0.html | date=August 14 | year=2005{Web reference | title= CIA Factbook : India | work=CIA Factbook | URL= http://www.cia.gov/cia/publications/factbook/geos/in.html | date=August 14 | year=2005{Web reference | title= Provisional Population Totals 2001 Census| work=Census of India| URL=http://www.censusindia.net/results/resultsmain.html | date=August 14 | year=2005{Web reference | title= Debating India & India's literacy rate | work=Debating India | URL= http://india.eu.org/1963.html | date=August 14 | year=2005{Web reference | title= India – Country profiles | work=indexmundi.com | URL= http://www.indexmundi.com/India/ India | date=August 14 | year=2005{Web reference | title= Census of India 2001, Data on Religion | work=Census of India | URL= http://www.censusindia.net/results/religion_main.html | date=August 14 | year=2005{Web reference | title= Languages of India | work=India image | URL= http://indiaimage.nic.in/languages.htm| date=August 14 | year=2005{Book reference | Author=K.M. Matthew | Title=Manorama Yearbook 2003 | Publisher= Malaya Manorama | Year=2003 | ID=ISBN 8190046187{mnb|afgh|1{mnb|LoC|2{South Asia{Asia{Commonwealth of Nations{SAARC{Life in India{Link FA|sv{Link FA|sv

Islamic world

The Islamic world is the world-wide community of those who identify with Islam, known as Muslims, and who number approximately one-and-a-half billion people. Many Muslims not only live in, but also have an official status in the following regions: Muslim
- Southwest Asia: Arab nations such as Saudi Arabia, Iraq and non-Arab countries like Turkey, Iran
- Africa: Arab countries like Morocco, Algeria, Tunisia, Libya, Egypt and non-Arab like Mali, Nigeria or Somalia.
- the Balkans: countries like Albania and Bosnia and Herzegovina
- Eastern Europe: parts of Russia and Ukraine (especially in the Crimea).
- Central Asia: Afghanistan, formerly Soviet states like Uzbekistan
- South Asia: Pakistan, Bangladesh, and the Maldives
- Southeast Asia: Indonesia, Brunei and Malaysia The countries of Southwest Asia, and many in Northern Africa are considered part of the Middle East. Also worthy of mention are provinces of Kurdistan, Kosovo and Chechnya, where Muslims are in the majority. Some definitions would also include the sizable Muslim minorities in:
- several countries of the European Union, (especially France)
- several regions of the Russian Federation
- northwestern India,
- People's Republic of China
- Singapore and the Philippines,
- U.S.A. and Canada. Like Christians or Buddhists, there is no single Muslim race; the world's Muslims are connected only by the common heritage of a religion. When believers in Islam cooperate as Muslims, they are known as the "ummah", which means "all of the believers". The faith emphasizes unity and defense of fellow Muslims, so it should be common for Muslim nations to cooperate; however, Muslim politics, particularly Arab politics, has tended to divide rather than unite the Muslim world.

Demographics

One quarter of the world population share Islam as an ethical tradition. Muslims are the majority in 52 nations. They speak about 60 languages and come from diverse ethnic backgrounds.
- 8 million Muslims in Canada and the United States
- 3 million Muslims in Latin and Central America
- 10 million Muslims in Western Europe, mostly in the UK, France, Germany
- 6.8 million Muslims in the Balkans, mostly in Bosnia and Herzegovina, Kosovo, Albania and Republic of Macedonia
- 67 million Muslims in Turkey
- 284.4 million Muslims in the Arab League including Iraq (with about 15 million Shia, 60% of the population in Iraq)
- 254 million Muslims in Sub-Saharan Africa
- 67 million Muslims (90% of them Shia) in Iran
- 48.5 million Muslims in Central Asia - in Azerbaijan, Uzbekistan, Tajikistan, Kazakhstan, Kyrgyzstan, Turkmenistan - formerly republics of the Soviet Union.
- 26 million Muslims in Russia
- 28 million Muslims in Afghanistan
- 260 million Muslims in Pakistan and Bangladesh together
- 120 million Muslims in India - (third largest Muslim population in the world)
- 50 million Muslims in China
- 209 million Muslims in Indonesia(the largest Muslim country in the world, by population)
- 30.0 million Muslims in the rest of South-East Asia, especially Malaysia
- A few in Japan, Mongolia, North Korea or the South Pacific
- close to 1.5 billion in total See: Islam by country

History

Islam spread rapidly into the regions where Muslims are now a majority, until 631 CE - see caliph for the politics that were partially to cease the rapid expansion of Islam at about this time. The spread of Islam was also due particularly to the powerful Ottoman Empire. Nations were conquered, and their inhabitants were given a choice to convert to Islam, or live as dhimmis, protected second class citizens practicing an officially accepted religion. The Ottoman Empire came to an end in 1918 when Turkey lost control of the bulk of the Arab World, which it had ruled for centuries and in which it had suppressed most of the traditional norms of Islam. The United Kingdom and the United States supported Arab independence, but France insisted on retaining control of Lebanon and ultimately Syria. This, plus the status of Kuwait and Palestine, and the later partition of India, remain major sources of global tension to this day. Islam allows oppressed Muslims to practice Jihad, struggle against aggressors. The 20th century also saw a series of defeats for some Islamist movements, Iran and the now-defunct Taliban regime in Afghanistan being notable exceptions. Elsewhere the rule has been for military rulers, e.g. Suharto, Moammar Qaddafi, Zia al-Haq, Saddam Hussein, to cynically exploit Islamic imagery and language without following the rules, sometimes implementing weak but spectacular forms of sharia in rural areas to appease peasant supporters. In Turkey, Pakistan, Algeria and other nations with Islamist parties, these tend to have either no power or they substantially moderate these policies when they participate in government (as in Turkey in 2003 where the government approved a U.S. plan to invade Iraq via Turkey but was over-ruled by the parliament after public pressure from the 94% of Turks opposed to an invasion). Nationalism plays more of a role in decisions to go to war than religious similarities or differences. : See also: History of Islam

Important organizations

The Organization of Petroleum Exporting Countries includes many nations that are also in the Arab League. Although most oil sources on Earth are not in nations with Muslim majorities, the fully developed exporting regions are. A politically motivated oil embargo in 1974 (to support Egypt and Syria in their 1973 war against Israel) had drastic economic and political consequences in the United States and Europe. Although such a move would have less impact today, it demonstrates the power of the Islamic world acting in concert, and the key role of religion and ethnicity in the politics of oil regions, with which the Islamic world intersects. As oil sources in Indonesia, Central Asia and southern regions of Russia become more developed, oil politics may be less dependent on the Arab World but more dependent on the Islamic World as a whole. Activities of Islamists seem destined to play a larger role, as they seek unified policies and support for unified fronts against non-Muslim peoples who control Muslim oil resources. The Organization of the Islamic Conference formed in 1969 lets the Muslim nations work as a group. Russia joined in 2003.

Main denominations of Islam

The two main denominations of Islam are the Sunni and Shia sects. The difference between them is primarily in terms of how the life of the ummah ("faithful") should be governed, and the role of the imam. The overwhelming majority of Muslims in the world are Sunni. The Shi'a are a majority in Iraq (60%) and in Iran (89%). A more strictly traditional Shia regime maintains power in Iran, although a nominally Sunni minority held political power in Iraq up until the 2003 invasion of Iraq. There are other differences in Muslims practice their faith, notably there's the Islamists who are fundamentalist.

Islam in law and ethics

In some nations, Muslim ethnic groups enjoy considerable autonomy. In some places, Muslims implement a form of Islamic law, called shariah in Arabic. The Islamic law exists in many variations, but the main forms are the five (four Sunni and one Shia) schools of jurisprudence (fiqh):
- the Hanafi school in India, Pakistan and Bangladesh, West Africa, Egypt,
- the Maliki in North Africa and West Africa,
- the Shafi'i in Malaysia and Indonesia,
- the Hanbali in Arabia, and
- Jaferi in Iran and Iraq - where the majority is Shia. All five are centuries old and many Muslims feel a new fiqh must be created for modern society. Islam has a method for doing this, al-urf and ijtihad are the words to describe this method, but they have not been used in a long time, and few people are trusted enough to use them to make new laws. So, in most of the Muslim world, people are socially conservative. Muslim women often dress extremely modestly, and many do so by choice. Thus, in some countries an interpretation of the Islamic law requires women to cover either just legs, shoulders and head or the whole body apart from the face. In strictest forms, the face as well must be covered leaving just a mesh to see through. These rules for dressing are one of the things that cause tension between the Western World and that of Muslims, concerning particularly Muslims living in western countries. Islamic economics bans interest but in most Muslim countries Western banking is allowed. This is another issue that many Muslims have with the Western world.

Islam in politics

Many people in Islamic countries also see Islam manifested politically as Islamism. In democratic countries there is usually at least one Islamic party. Political Islam is powerful in all Muslim-majority countries. Islamic parties in Turkey, Pakistan and Algeria have taken power. Many in these movements call themselves Islamists, which also sometimes describes more militant Islamic groups. The relationships between these groups and their views of democracy are complex. Some of these groups practice terrorism. According to US President George W. Bush, they all have a single common agenda: "The militants believe that controlling one country will rally the Muslim masses, enabling them to overthrow all moderate governments in the region, and establish a radical Islamic empire that spans from Spain to Indonesia," Bush asserted in an October 2005 speech.

Conflicts with Israel and the US

Israel is very unpopular in the Muslim world, because of the Israeli-Palestinian conflict and the way that the state of Israel came into being in 1948 which many Arabs thought was unfair. Some Muslims see this as a fight against Judaism or Jews, but not all. In Morocco for instance, the Islamists recently invited Jews to join the party. Jewish groups also cooperate with Arabs in the West Bank, where Neturei Karta (anti-Zionist orthodox Jewish) leader Rabbi Mosche Hirsch served as the Minister for Jewish Affairs in the Fatah before there was a Palestinian Authority. Like the Arabs, this small group of Jews thought the way Israel was created was not right. In 1979 there was a big shift in the way the Muslim world dealt with the rest of the world. In that year, Egypt made peace with Israel, Iran became an Islamic state after a revolution, and there was an invasion of Afghanistan by the Soviet Union. A lot of things changed in that year. By 2001 the Soviet Union was gone, Jordan had also made peace with Israel, and on September 11, 2001 there were major attacks on the U.S. - which most people believe were made to drive the United States out of the Muslim world, especially Saudi Arabia. In many ways the events of 1979 led to the events of 2001. The 2001 invasion of Afghanistan and 2003 invasion of Iraq are called part of a "War on Terrorism" by the United States. Many or most Muslims see it as a War on Islam. After the invasion, the Islamic parties won more seats, and a majority of Muslims polled in many nations expressed support for Osama bin Laden and said he would "do the right thing". Olivier Roy is a French scholar who thinks that this does not express support for Al Qaeda or militant Islam but opposing colonialism and what many Muslims call racism - favourable treatment for Jews especially those living in West Bank settlements, many of whom have American or British passport, and which the United Nations says have no right to live there. The situation is very complicated and there are many different views of it.

Growing polarization

In Pakistan, nominally a US ally, virulently anti-American Islamist won local elections in two out of four of the country's provinces and became in mid-2003 the third largest party in the national parliament, their best showing ever. For the first time, their support comes not just from the areas bordering Afghanistan, but even from urban areas. In Kuwait, elections in July returned Islamic traditionalists and supporters of the royal family, while liberals suffered a severe defeat. In Indonesia, the growth of various groups allied to those seemingly responsible for the Bali bombing most of which have been invisible, has been marked. It is expected that executions of perpetrators of that attack, which hit mostly citizens of Australia, will polarize that nation further.

Future

Some believe that the Islamic World is fated to democratize and replace constitutional monarchy and military dictatorship with representative democracy. G. E. Jansen in 1979, in his book "Militant Islam", proposed that Islamist movements were themselves the most likely path to democratization. Iran, Turkey, Pakistan, Indonesia and Algeria may represent the examples of a movement towards democracy. They enjoy substantial local democracy and have active political life. Many believe that the Islamic World is fated to come into deeper conflict with the western world. At least one Islamic nation, Pakistan, has developed nuclear weapons, and others, e.g. Iraq, have attempted it. Weapons of mass destruction are likely to become easier to construct given the modernizing economies of the Islamic World.

External links

- [http://www.ucalgary.ca/applied_history/tutor/islam/ The Islamic World to 1600] an online tutorial at the University of Calgary, Canada.
- [http://www.msnbc.com/news/969671.asp MSNBC report] citing Wesley Clark that the US planned to invade Iraq, then Syria, Lebanon, Libya, Iran, Somalia, and Sudan - also his own views on Egypt, Pakistan and Saudi Arabia
- [http://www.truthout.org/docs_03/092403D.shtml Al-Jazeera report] saying the same thing Category:Islam ja:イスラム世界 simple:Islamic world

Decimal point

The decimal separator is a symbol used to mark the boundary between the integer and the fractional parts of a decimal numeral. In the Middle Ages, that is, before printing, a bar over the units digit was used. Later, a separator (a short, roughly vertical, ink-stroke) between the units and tenths position became the norm. When type-set, it was convenient to use the existing marks called a comma or a period, which is variously called a stop or a dot, or else a point for this purpose. In France the dot was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries also chose the comma to mark the decimal units position. It has been made standard by the ISO for international blueprints. English-speaking countries, however, took the comma to separate sequences of three digits. In the US, a period (.), which is called a stop in some other countries, was the standard. In the nations of the British Empire, although this could be used as in typewritten material, the point (middle dot: ·), which can also be called an interpunct, was preferred for the decimal separator in those technologies which could accommodate it. This had the advantage of reducing confusion with the countries that used the period to separate groups of digits, but as the middle dot was already in common use in world mathematics to indicate multiplication (for example, in the dot product), the SI rejected this use of this symbol for this purpose. However, the use of the period as decimal point was not banned. British aviation magazines thus switched to the US form in the late twentieth century. When South Africa adopted the metric system, it adopted the , as the decimal marker (See "Countries where a comma is used to mark the radix point include: ......" below). (For numeral systems other than decimal, the analogous point is known as a radix point.) Examples of use:
- In France, the Netherlands, and much of Latin Europe: 1 234 567,89
- In Germany, Italy, Romania and much of Europe: 1 234 567,89 or 1.234.567,89 (in handwriting you may also come across 1^·234^·567,89)
- In Switzerland (mainly German-speaking Switzerland): 1'234'567,89
- In the United Kingdom, United States, and Japan: 1,234,567.89 or 1,234,567·89; the latter is more commonly found in older, and especially handwritten, documents nowadays; many UK schools now teach the SI style, which has become official in Australia.
- SI style: 1 234 567.89 (dot countries) or 1 234 567,89 (comma countries)
- In China, the comma is sometimes used to separate blocks of four digits: 123,4567.89, since in Chinese, there is a word for 10000 (the next new word is for 10⁸, not 10⁶ as in most languages).

Dot countries

Countries where a dot is used to mark the radix point include: : Australia, Botswana, Canada (English-speaking), China, Costa Rica, Dominican Republic, El Salvador, Guatemala, Honduras, Hong Kong of the People's Republic of China, India, Ireland, Israel, Japan, Korea (both North and South), Malaysia, Mexico, Nicaragua, Nigeria, New Zealand, Pakistan, Panama, Philippines, Saudi Arabia, Singapore, Taiwan, Thailand, United Kingdom, United States (including insular area of Puerto Rico),

Comma countries

Countries where a comma is used to mark the radix point include: : Albania, Andorra, Argentina, Austria, Belarus, Belgium, Bolivia, Brazil, Bulgaria, Canada (French-speaking), Croatia, Cuba, Chile, Colombia, Czech Republic, Denmark, Ecuador, Estonia, Faroes, Finland, France, Germany, Greece, Greenland, Hungary, Indonesia, Iceland, Italy, Latvia, Lithuania, Luxembourg, Macedonia, Moldova, Netherlands, Norway, Paraguay, Peru, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia, Spain, South Africa, Sweden, Switzerland, Turkey, Ukraine, Uruguay, Venezuela, Zimbabwe

Al-Khwarizmi

right Al-Khwarizmi was a Persian scientist, mathematician, astronomer/astrologer, and author born around 800 and died around 840. The word Algebra is derived from the title of one of his books Al-Jabr wa-al-Muqabilah and consequently some have considered him the father of Algebra although the subject was in existence long before his time.

Introduction

Khwarizmi was born in the town of Khwarizm (now Khiva), in Khorasan province of Persia (now in Uzbekistan). Some historians argue though that he was born in Qutrubulli, a small town near Baghdad as mentioned in the works of al-Tabari. He accomplished most of his work in the period between 813 and 833. Mathematical historian Gandz gives this opinion of Khwarizmi's algebra: :"Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers." (1) and Mohammad Khan, says: :"In the foremost rank of mathematicians of all time stands Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra ... gave the name to this important branch of mathematics in the European world..."(2)

Contributions

He made major contributions to the fields of algebra, trigonometry, astronomy/astrology, geography and cartography by translating important works from Sanskrit and other languages. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (الكتاب المختصر في حساب الجبر والمقابلة) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the 12th century, from which the title and term Algebra derives. His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. The book was translated into Latin in the 12th century as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm. Much of his contributions were based on the original research of the Hindus in Astronomy and Greek, and other sources. He appropriated the place-marker symbol of zero, which originated in India. Al-Khwarizmi systematized and corrected Ptolemy's data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard ("The Image of the Earth"; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa. He also assisted in the construction of a world map for the caliph al-Ma'mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then "known world".(3) When his work became known in Europe through Latin translations, it made a significant contribution to the advancement of mathematics in Europe. He also wrote on mechanical devices like the clock, astrolabe, and sundial. His other contributions include tables of trigonometric functions, refinements in the geometric representation of conic sections, and aspects of the calculus of two errors.

Alternate spellings of name

Abu Abdullah Muhammad bin Musa al-Khwarizmi (Arabic and Persian: ابو عبدالله محمد ابن موسى الخوارزمي) also spelled Muhammad ibn-Musa al-Khwarizmi, Muhammad ibn-Musa al-Khowarizmi, Mohammad Bin Musa Al-Khawarizmi, and Abu Jaʿfar Muhammad ibn-Musa Al-Khowarizmi

Famous works

- Al-Jabr wa-al-Muqabilah from whose title came the name "Algebra"
- Kitab al-Jam'a wal-Tafreeq bil Hisab al-Hindi (on Arithmetic, which survived in a Latin translation but was lost in the original Arabic)
- Kitab Surat-al-Ard (on geography)
- Istikhraj Tarikh al-Yahud (about the Jewish calendar)
- Kitab al-Tarikh (literally, the book of history)
- Kitab al-Rukhmat (about sun-dials)

References

(1): S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263-77. (2): A A al'Daffa, The Muslim contribution to mathematics (London, 1978). (3): From his biography in Encyclopædia Britannica.

Other sources to use

Books: #Biography in Dictionary of Scientific Biography (New York 1970-1990). #J N Crossley, The emergence of number (Singapore, 1980). #A F Faizullaev, The scientific heritage of Muhammad al-Khwarizmi (Russian) (Tashkent, 1983). #S Gandz (ed.), The geometry of al-Khwarizmi (Berlin, 1932). #E Grant (ed.), A source book in medieval science (Cambridge, 1974). #O Neugebauer, The exact sciences in Antiquity (New York, 1969). #R Rashed, The development of Arabic mathematics : between arithmetic and algebra (London, 1994). #R Rashed, Entre arithmétique et algèbre: Recherches sur l'histoire des mathématiques arabes (Paris, 1984). #F Rosen (trs.), Muhammad ibn Musa Al-Khwarizmi : Algebra (London, 1831). Articles: #K F Abdulla-Zade, al-Khwarizmi and the Baghdad astronomers (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 178-183. #M Abdullaev, al-Khwarizmi and scientific thought in Daghestan (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 228-232. #A Abdurakhmanov, al-Khwarizmi : great mathematician (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 149-151. #M A Akhadova, The mathematics of India and al-Khwarizmi (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 238-240. #S al-Khalidi, al-Khwarizmi : scholar of astronomical and mathematical geography (Arabic), in Proceedings of the Seventh Annual Conference on the History of Arabic Science (Arabic) (Aleppo, 1986), 55-63. #A Allard, La diffusion en occident des premières oeuvres latines issues de l'arithmétique perdue d'al-Khwarizmi, J. Hist. Arabic Sci. 9 (1-2) (1991), 101-105. #P G Bulgakov, al-Biruni and al-Khwarizmi (Russian), in Mathematics and astronomy in the works of scientists of the medieval East (Tashkent, 1977), 117-122, 140. #J N Crossley and A S Henry, Thus spake al-Khwarizmi : a translation of the text of Cambridge University Library ms. Ii.vi.5, Historia Math. 17 (2) (1990), 103-131. #Y Dold-Samplonius, Developments in the solution to the equation cxÛ + bx = a from al-Khwarizmi to Fibonacci, in From deferent to equant (New York, 1987), 71-87. #R Z Du, al-Khwarizmi and his algebraic treatise (Chinese), Math. Practice Theory (1) (1987), 79-85. #K Fogel, How al-Khwarizmi became known in Germany (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 85-91. #J P Hogendijk, al-Khwarizmi's table of the "sine of the hours" and the underlying sine table, Historia Sci. 42 (1991), 1-12. #B B Hughes, Robert of Chester's Latin translation of al-Khwarizmi's 'al-Jabr', Boethius : Texts and Essays on the History of the Exact Sciences XIV (Stuttgart, 1989). #D K Ibadov, The work of al-Khwarizmi in the estimation of Eastern encyclopedic scholars of the 10th - 16th centuries (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 265-268. #W Kaunzner, Über eine frühe lateinische Bearbeitung der Algebra al-Khwarizmis in MS Lyell 52 der Bodleian Library Oxford, Arch. Hist. Exact Sci. 32 (1) (1985), 1-16. #E S Kennedy, Al-Khwarizmi on the Jewish calendar, Scripta Math. 27 (1964), 55-59. #A S Kennedy and W Ukashah, al-Khwarizmi's planetary latitude tables, Centaurus 14 (1969), 86-96. #M M Khairullaev, al-Khwarizmi and his era (Russian), Voprosy Istor. Estestvoznan. i Tekhn. (3) (1983), 121-127. #P Kunitzsch, al-Khwarizmi as a source for the 'Sententie astrolabii', in From deferent to equant (New York, 1987), 227-236. #G P Matvievskaya, The algebraic treatise of al-Khwarizmi (Russian), in On the history of medieval Eastern mathematics and astronomy (Tashkent, 1983), 3-22. #G P Matvievskaya, History of the study of the scientific work of al-Khwarizmi (Russian),, in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 72-82. #C A Nallino, Al'Khuwarizimi e il suo rifacimento della Geografia di Tolomeo, Raccolta di scritti editie inediti V (Rome, 1944), 458-532. #K H Parshall, The art of algebra from al-Khwarizmi to Viète : a study in the natural selection of ideas, Hist. of Sci. 26 (72, 2) (1988), 129-164. #M A Pathan, Al-Khwarizmi, Math. Ed. 6 (2) (1989), 92-94. #D Pingree, al-Khwarizmi in Samaria, Arch. Internat. Hist. Sci. 33 (110) (1983), 15-21. #B A Rosenfeld, 'Geometric trigonometry' in treatises of al-Khwarizmi, al-Mahani and ibn al-Haytham, in Vestigia mathematica (Amsterdam, 1993), 305-308. #B A Rozenfeld, al-Khwarizmi's spherical trigonometry (Russian), Istor.-Mat. Issled. 32-33 (1990), 325-339. #B A Rozenfeld, Number theory, geometry and astronomy in al-Khwarizmi's 'Book of Indian arithmetic' (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 66-72. #B A Rozenfeld and N D Sergeeva, The astronomical treatises of al-Khwarizmi (Russian), Istor.-Astronom. Issled. 13 (1977), 201-218. #M M Rozhanskaya, The historical-astronomical value of al-Khwarizmi's "zij" (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 158-165. #A S Sadykov, al-Khwarizmi : his era, life and work (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 8-13. #M Sani, The life and work of al-Khwarizmi, Menemui Mat. 4 (1) (1982), 1-9. #K S Siddikov, Muhammad al-Khwarizmi : creator of algebra (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 152-154. #S Kh Sirazhdinov and G P Matvievskaya, Muhammad ibn Musa al-Khwarizmi and his contribution to the history of science (Russian), Voprosy Istor. Estestvoznan. i Tekhn. (1) (1983), 108-119. #Z K Sokolovskaya, The "pretelescopic" period of the history of astronomical instruments. al-Khwarizmi in the development of precision instruments in the Near and Middle East (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 165-178. #B van Dalen, Al'Khwarizmi's astronomical tables revisited : analysis of the equation of time, in From Baghdad to Barcelona (Barcelona, 1996), 195-252. #K Vogel, Wie wurden al-Khwarizmi s mathematische Schriften in Deutschland bekannt?, Sudhoffs Arch. 68 (2) (1984), 230-234. #A I Volodarskii, al-Khwarizmi and Indian mathematics (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 232-238. #E Yu Yusupov and M M Kharullaev, The creative legacy of al-Khwarizmi and his place in the history of science (Russian), Voprosy Filos. (8) (1983), 140-146, 174. #Kh Zemanek, Manuscripts of al-Khwarizmi's works (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 115-121. #V K Zharov, Instrumental counting in al-Khwarizmi's arithmetical treatise (Russian), in The great medieval scientist al-Khwarizmi (Tashkent, 1985), 154-157.

External links

- [http://members.aol.com/bbyars1/algebra.html al'Khwarizmi & algebra]
- [http://members.tripod.com/~wzzz/KHAWARIZ.html Mohammad Bin Musa Al-Khawarizmi]
- [http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Al-Khwarizmi.html Abu Ja'far Muhammad ibn Musa Al-Khwarizmi] in the MacTutor archive Khwarizmi Khwarizmi Khwarizmi Khwarizmi Kkwarizmi Kkwarizmi ko:알 콰리즈미 ms:Abu Abdullah Mohammad Ibn Musa al-Khawarizmi ja:フワーリズミー simple:Al-Khwarizmi th:อัลคอวาริซมีย์

Cognomen

The cognomen ("name known by" in English) was originally the third name of a Roman in the Roman naming convention. The term is also occasionally seen in modern times as an obscure synonym for nickname or epithet. Because of the limited nature of Roman names, the cognomen developed to distinguish branches of the family from one another, and occasionally, to highlight an individual's achievement, typically in warfare. Some Romans – notably general Gaius Marius – had no cognomen at all. By the Late Roman Republic, however, the use of cognomen even in daily conversation had become typical. In contrast to the honorary cognomen adopted by successful generals, most cognomen were based on a physical or personality quirk; for example, 'Rufus' meaning red-headed or 'Scaevola' meaning left-handed. Today, we refer to many prominent ancient Romans by only their cognomen; for example, 'Cicero' serves as a shorthand for Marcus Tullius Cicero and Caesar for Gaius Julius Caesar.

9th century

. It is housed in the Smithsonian Institute in Washington, D.C.]]

Events

- An unknown event causes the decline of the Maya Classical Era
- Beowulf might have been written down in this century, though it could also have been in the 8th century
- Reign of Charlemagne, and concurrent (and controversially labeled) Carolingian Renaissance in western Europe
- Large-scale Viking attacks on Europe begin, devestating countless numbers of people
- Oseberg ship burial
- The Magyars arrive in what is now Hungary, forcing the Serbs and Bulgars south of the Danube.
- The Tukolor settle in the Senegal river valley.
- Muslim traders settle in the north-west and south-east of Madagascar.
- around 813-around 915 - period of serious Arab naval raids on shores of Tyrrhenian and Adriatic seas
- 870 - Prague Castle founded
- 800-909 - rule of Aghlabids as independent dynasty in North Africa
- 850-875 - The first Norse settlers arrive on Iceland.
- 863-879 - period of schism between eastern and western churches
- Late 9th century: Bulgaria stretches from the mouth of the Danube to Epirus and Bosnia.
- In Italy, some cities became free republics: for instance Forlì, in the 889.
- The Christian Nubian kingdom reaches its peak of prosperity and military power. (Early history of Sudan)
- Harald Fairhair was victorious at the battle of Hafrsfjord, and Norway was unified into one kingdom.

Significant people

- Alfred the Great
- Arnulf of Carinthia
- Charlemagne
- Louis the Pious
- Adi Sankara
- Harald I of Norway

Inventions, discoveries, introductions

- Vulgar Latin begins to devolve into various Romance languages
- First image of a rotary grindstone in a European source - illustration shows crank, first known use of a crank in the West (Utrecht Psalter, A.D. 843)
- Invention of gunpowder by Chinese Taoist Alchemists

Decades and years

Category:9th century 09th century ko:9세기 ja:9世紀 nb:9. århundre th:คริสต์ศตวรรษที่ 9

Khiva

Khiva (alternative names include Khorasam, Khoresm, Khwarezm, Khwarizm, Khwarazm, Chiwa and Chorezm) is the former capital of Khwarezmia, which lies in the present-day Khorezm Province of Uzbekistan. Itchan Kala in Khiva was the first site in Uzbekistan to be inscribed in the World Heritage List (1991).World Heritage List

History

The district of Khwarazm, centred on the formerly rich and fertile delta of the Oxus or Amu-Darya, was an ancient centre of Iranic culture and Iranian architecture. In the very early part of its history, the inhabitants of the area were from Iranian stock, belonging to the Khwarazmian branch. They spoke an eastern Iranian language called Khwarezmian. As a consequence of the constant Turkic attack and migration, the Khiva area now has a mixed population of Karakalpaks, Uzbeks and Kazakhs, and has lost its Iranian language. Historically the main centre of population was Konya-Urgench or 'Old Urgench', but the city was abandoned owing to the depredations of the Mongols and Tamerlane, together with a shift in the course of the Amu-Darya. The city of Khiva was first recorded by Arabic travellers in the 10th century, although the archaeologists assert that the city existed since the 6th century. By the early 17th century Khiva had become the capital of a Khanate of the same name, ruled over by a branch of the Ghengissid Astrakhanid dynasty. The discovery of gold on the banks of the Oxus during the reign of Peter the Great, together with the desire of Russia to open a trade route to India, prompted an armed trade expedition to the region, led by Prince Alexander Bekovich-Cherkassky, and consisting of 4,000 men. Upon receiving the men the Khan set up camp under the pretense of goodwill, then ambushed and slaughtered the envoys, leaving ten alive to send back. Peter the Great, indebted after wars with the Ottoman Empire and Sweden, did nothing. Tsar Paul I also attempted to conquer the city, but his expedition was woefully undermanned and undersupplied, and was recalled en route due to his assassination. Tsar Alexander I had no such ambitions, and it is under Tsars Alexander II and Alexander III that serious efforts to annex the city started. A curious episode during The Great Game involved a Russian expedition, in name to free the slaves captured and sold by Turcoman raiders from the Russian frontiers on the Caspian Sea, but also as an attempt to extend its borders while Great Britain entangled itself in the First Anglo-Afghan War in 1839. The expedition, led by General Perovsky, the commander of the Orenburg garrison, consisted of 5,200 infantry, and 10,000 camels. Due to poor planning and a bit of bad luck, they set off in November, 1839, into one of the worst winters in memory, and was forced to turn back on February 1, 1840, arriving back into Orenburg in May, suffering over 1,000 casualties without firing a single shot. Orenburg At the same time, the British, anxious to remove the pretext for the Russian attempt to annex Khiva, launched its own effort to free the slaves - a lone officer stationed in Herat. Captain James Abbott, disguised as an Afghan, set off on Christmas Eve, 1839, for Khiva. He arrived in late January, 1840, and although the Khan was suspicious of his identity, he succeeded in talking the Khan into allowing him to carry a letter for the Tsar regarding the slave issue. He left on March 7, 1840, for Fort Alexandrovsk, and was subsequently betrayed by his guide, robbed, then released when the bandits realized the origin and destination of his letter. Yet his superiors in Herat, not knowing of his fate, sent another officer, Lieutenant Richmond Shakespear, after him. Shakespear was evidently more successful than Abbott in that he somehow talked the Khan into not only freeing all Russian subjects under his control, but also making the ownership of Russian slaves a crime punishable by death. The freed slaves and Shakespear arrived in Fort Alexandrovsk on August 15, 1840, and Russia lost its primary motive for the conquest of Khiva, for now. It was in 1873, after Russia conquered the neighbouring cities of Tashkent and Samarkand, when General Von Kaufman launched an attack consisting of 13,000 infantry and cavalry. The city fell on May 28, 1873, and although Russia now controlled the Khanate, it nominally allowed it to remain as a quasi-independent vassal nation, or Protectorate. Once the Bolsheviks took power after the October revolution, a short lived People's Republic of Khorezm was created out of the territory of the old Khanate of Khiva, before in 1924 it was finally incorporated into the USSR, divided between the new Turkmen SSR and Uzbek SSR.

Sights

Khiva is split into two parts. The outer town, called Dichan Kala, was formerly protected by a wall with 11 gates. The inner town, or Itchan Kala, is encircled by brick walls, whose foundations are believed to have been laid in the 10th century. Present-day crenellated walls date back to the late 17th century and attain the height of 10 meters. The old town retains more than 50 historic monuments and 250 old houses, mostly dating from the 18th or the 19th centuries. Djuma Mosque, for instance, was established in the 10th century and rebuilt in 1788-89, although its celebrated hypostyle hall still retains 112 columns taken from ancient structures.

Publications

:Campaigning on the Oxus, and the Fall of Khiva, MacGahan, (London, 1874). :Russian Central Asia, Lansdell, (London, 1885). :A travers l'Asie Central, Moser, (Paris, 1886). :Russia against India, Colquhoun, (New York, 1900). :Khiva, in Russian, S. Goulichambaroff, (Askhabad, 1913). Category:Cities in Uzbekistan

Algorithm

In mathematics and computer science an algorithm (the word is derived from the name of the Persian mathematician Al-Khwarizmi) is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a corresponding recognizable end-state (contrast with heuristic). Algorithms can be implemented by computer programs, although often in restricted forms; mistakes in implementation and limitations of the computer can prevent a computer program from correctly executing its intended algorithm. The concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). Correctly performing an algorithm will not solve a problem if the algorithm is flawed or not appropriate to the problem. For example, a hypothetical algorithm for making a potato salad will fail if there are no potatoes present, even if all the motions of preparing the salad are performed as if the potatoes were there. Different algorithms may complete the same task with a different set of instructions in more or less time, space, or effort than others. For example, given two different recipes for making potato salad, one may have peel the potato before boil the potato while the other presents the steps in the reverse order, yet they both call for these steps to be repeated for all potatoes and end when the potato salad is ready to be eaten. Certain countries, such as the USA, controversially allow some algorithms to be patented, provided a physical embodiment is possible (for example, a multiplication algorithm may be embodied in the arithmetic unit of a microprocessor).

Formalized algorithms

Algorithms are essential to the way computers process information, because a computer program is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees’ paychecks or printing students’ report cards. Thus, an algorithm can be considered to be any sequence of operations which can be performed by a Turing-complete system. Typically, when an algorithm is associated with processing information, data is read from an input source or device, written to an output sink or device, and/or stored for further use. Stored data is regarded as part of the internal state of the entity performing the algorithm. For any such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable). Because an algorithm is a precise list of precise steps, the order of computation will almost always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting 'from the top' and going 'down to the bottom', an idea that is described more formally by flow of control. So far, this discussion of the formalisation of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, 'mechanical' means. Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of 'memory' as a scratchpad. There is an example below of such an assignment. See functional programming and logic programming for alternate conceptions of what constitutes an algorithm.

Implementation

Algorithms are not only implemented as computer programs, but often also by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect relocating food), or in electric circuits or in a mechanical device. The analysis and study of algorithms is one discipline of computer science, and is often practiced abstractly (without the use of a specific programming language or other implementation). In this sense, it resembles other mathematical disciplines in that the analysis focuses on the underlying principles of the algorithm, and not on any particular implementation. One way to embody (or sometimes codify) an algorithm is the writing of pseudocode. Some writers restrict the definition of algorithm to procedures that eventually finish. Others include procedures that could run forever without stopping, arguing that some entity may be required to carry out such permanent tasks. In the latter case, success can no longer be defined in terms of halting with a meaningful output. Instead, terms of success that allow for unbounded output sequences must be defined. For example, an algorithm that verifies if there are more zeros than ones in an infinite random binary sequence must run forever to be effective. If it is implemented correctly, however, the algorithm's output will be useful: for as long as it examines the sequence, the algorithm will give a positive response while the number of examined zeros outnumber the ones, and a negative response otherwise. Success for this algorithm could then be defined as eventually outputting only positive responses if there are actually more zeros than ones in the sequence, and in any other case outputting any mixture of positive and negative responses.

Example

One of the simplest algorithms is to find the largest number in an (unsorted) list of numbers. The solution necessarily requires looking at every number in the list, but only once at each. From this follows a simple algorithm: # Look at each item in the list. If it is larger than any that has been seen so far, make a note of it. # The latest noted item is the largest in the list when the process is complete. And here is a more formal coding of the algorithm in pseudocode: Algorithm LargestNumber Input: A non-empty list of numbers L. Output: The largest number in the list L. largest ← -∞ for each item in list L, do if the item > largest, then largest ← the item return largest Notes on notation:
- "←" is a loose shorthand for "changes to". For instance, with "largest ← the item", it means that the largest number found so far changes to this item.
- "return" terminates the algorithm and outputs the value listed behind it. As it happens, most people who implement algorithms want to know how much of a particular resource (such as time or storage) a given algorithm requires. Methods have been developed for the analysis of algorithms to obtain such quantitative answers; for example, the algorithm above has a time requirement of O(n), using the big O notation with n as the length of the list. At all times the algorithm only needs to remember a single value; the largest number found so far. Therefore this algorithm has a space requirement of O(1). (Note that the size of the inputs is not counted as space used by the algorithm.) For a more complex example see Euclid's algorithm.

History

Euclid's algorithm The word algorithm comes from the name of the 9th century Persian mathematician Abu Abdullah Muhammad bin Musa al-Khwarizmi. The word algorism originally referred only to the rules of performing arithmetic using Hindu-Arabic numerals but evolved into algorithm by the 18th century. The word has now evolved to include all definite procedures for solving problems or performing tasks. The first case of an algorithm written for a computer was Ada Byron's notes on the analytical engine written in 1842, for which she is considered by many to be the world's first programmer. However, since Charles Babbage never completed his analytical engine the algorithm was never implemented on it. The lack of mathematical rigor in the "well-defined procedure" definition of algorithms posed some difficulties for mathematicians and logicians of the 19th and early 20th centuries. This problem was largely solved with the description of the Turing machine, an abstract model of a computer formulated by Alan Turing, and the demonstration that every method yet found for describing "well-defined procedures" advanced by other mathematicians could be emulated on a Turing machine (a statement known as the Church-Turing thesis). Nowadays, a formal criterion for an algorithm is that it is a procedure that can be implemented on a completely-specified Turing machine or one of the equivalent formalisms. Turing's initial interest was in the halting problem: deciding when an algorithm describes a terminating procedure. In practical terms computational complexity theory matters more: it includes the problems called NP-complete, which are generally presumed to take more than polynomial time for any (deterministic) algorithm. NP denotes the class of decision problems that can be solved by a non-deterministic Turing machine in polynomial time.

Classes

There are many ways to classify algorithms, and the merits of each classification have been the subject of ongoing debate. One way of classifying algorithms is by their design methodology or paradigm. There is a certain number of paradigms, each different from the other. Furthermore, each of these categories will include many different types of algorithms. Some commonly found paradigms include:
- Divide and conquer. A divide and conquer algorithm repeatedly reduces an instance of a problem to one or more smaller instances of the same problem (usually recursively), until the instances are small enough to solve easily.
- Dynamic programming. When a problem shows optimal substructure, meaning the optimal solution to a problem can be constructed from optimal solutions to subproblems, and overlapping subproblems, meaning the same subproblems are used to solve many different problem instances, we can often solve the problem quickly using dynamic programming, an approach that avoids recomputing solutions that have already been computed. For example, the shortest path to a goal from a vertex in a weighted graph can be found by using the shortest path to the goal from all adjacent vertices.
- The greedy method. A greedy algorithm is similar to a dynamic programming algorithm, but the difference is that solutions to the subproblems do not have to be known at each stage; instead a "greedy" choice can be made of what looks best for the moment.
- Linear programming. When solving a problem using linear programming, the program is put into a number of linear inequalities and then an attempt is made to maximize (or minimize) the inputs. Many problems (such as the maximum flow for directed graphs) can be stated in a linear programming way, and then be solved by a 'generic' algorithm such as the Simplex algorithm.
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