Claudius Ptolemy was a Greco-Roman mathematician, astronomer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, wrote in Koine Greek, held Roman citizenship; the 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou in the Thebaid. This attestation is quite late, and, according to Gerald Toomer, the translator of his Almagest into English, there is no reason to suppose he lived anywhere other than Alexandria, he died there around AD 168. Ptolemy wrote several scientific treatises, three of which were of importance to Byzantine and Western European science; the first is the astronomical treatise now known as the Almagest, although it was entitled the Mathematical Treatise and known as the Great Treatise. The second is the Geography, a thorough discussion of the geographic knowledge of the Greco-Roman world; the third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day.
This is sometimes known as the Apotelesmatika but more known as the Tetrabiblos from the Greek meaning "Four Books" or by the Latin Quadripartitum. Ptolemaeus is a Greek name, it occurs once in Greek mythology, is of Homeric form. It was common among the Macedonian upper class at the time of Alexander the Great, there were several of this name among Alexander's army, one of whom made himself pharaoh in 323 BC: Ptolemy I Soter, the first king of the Ptolemaic Kingdom. All male kings of Hellenistic Egypt, until Egypt became a Roman province in 30 BC ending the Macedonian family's rule, were Ptolemies; the name Claudius is a Roman nomen. It would have suited custom if the first of Ptolemy's family to become a citizen took the nomen from a Roman called Claudius, responsible for granting citizenship. If, as was common, this was the emperor, citizenship would have been granted between AD 41 and 68; the astronomer would have had a praenomen, which remains unknown. The ninth-century Persian astronomer Abu Maʿshar presents Ptolemy as a member of Egypt's royal lineage, stating that the descendants of Alexander's general Ptolemy I, who ruled Egypt, were wise "and included Ptolemy the Wise, who composed the book of the Almagest".
Abu Maʿshar recorded a belief that a different member of this royal line "composed the book on astrology and attributed it to Ptolemy". We can evidence historical confusion on this point from Abu Maʿshar's subsequent remark "It is sometimes said that the learned man who wrote the book of astrology wrote the book of the Almagest; the correct answer is not known." There is little evidence on the subject of Ptolemy's ancestry, apart from what can be drawn from the details of his name. Ptolemy can be shown to have utilized Babylonian astronomical data, he was a Roman citizen, but was ethnically either a Greek or a Hellenized Egyptian. He was known in Arabic sources as "the Upper Egyptian", suggesting he may have had origins in southern Egypt. Arabic astronomers and physicists referred to him by his name in Arabic: بَطْلُمْيوس Baṭlumyus. Ptolemy's Almagest is the only surviving comprehensive ancient treatise on astronomy. Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena.
Ptolemy, claimed to have derived his geometrical models from selected astronomical observations by his predecessors spanning more than 800 years, though astronomers have for centuries suspected that his models' parameters were adopted independently of observations. Ptolemy presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets; the Almagest contains a star catalogue, a version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations, but unlike the modern system they did not cover the whole sky. Across Europe, the Middle East and North Africa in the Medieval period, it was the authoritative text on astronomy, with its author becoming an mythical figure, called Ptolemy, King of Alexandria; the Almagest was preserved, in Arabic manuscripts. Because of its reputation, it was sought and was translated twice into Latin in the 12th century, once in Sicily and again in Spain.
Ptolemy's model, like those of his predecessors, was geocentric and was universally accepted until the appearance of simpler heliocentric models during the scientific revolution. His Planetary Hypotheses went beyond the mathematical model of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe, he estimated the Sun was at an average dis
Egypt the Arab Republic of Egypt, is a country spanning the northeast corner of Africa and southwest corner of Asia by a land bridge formed by the Sinai Peninsula. Egypt is a Mediterranean country bordered by the Gaza Strip and Israel to the northeast, the Gulf of Aqaba and the Red Sea to the east, Sudan to the south, Libya to the west. Across the Gulf of Aqaba lies Jordan, across the Red Sea lies Saudi Arabia, across the Mediterranean lie Greece and Cyprus, although none share a land border with Egypt. Egypt has one of the longest histories of any country, tracing its heritage back to the 6th–4th millennia BCE. Considered a cradle of civilisation, Ancient Egypt saw some of the earliest developments of writing, urbanisation, organised religion and central government. Iconic monuments such as the Giza Necropolis and its Great Sphinx, as well the ruins of Memphis, Thebes and the Valley of the Kings, reflect this legacy and remain a significant focus of scientific and popular interest. Egypt's long and rich cultural heritage is an integral part of its national identity, which has endured, assimilated, various foreign influences, including Greek, Roman, Ottoman Turkish, Nubian.
Egypt was an early and important centre of Christianity, but was Islamised in the seventh century and remains a predominantly Muslim country, albeit with a significant Christian minority. From the 16th to the beginning of the 20th century, Egypt was ruled by foreign imperial powers: The Ottoman Empire and the British Empire. Modern Egypt dates back to 1922, when it gained nominal independence from the British Empire as a monarchy. However, British military occupation of Egypt continued, many Egyptians believed that the monarchy was an instrument of British colonialism. Following the 1952 revolution, Egypt expelled British soldiers and bureaucrats and ended British occupation, nationalized the British-held Suez Canal, exiled King Farouk and his family, declared itself a republic. In 1958 it merged with Syria to form the United Arab Republic, which dissolved in 1961. Throughout the second half of the 20th century, Egypt endured social and religious strife and political instability, fighting several armed conflicts with Israel in 1948, 1956, 1967 and 1973, occupying the Gaza Strip intermittently until 1967.
In 1978, Egypt signed the Camp David Accords withdrawing from the Gaza Strip and recognising Israel. The country continues to face challenges, from political unrest, including the recent 2011 revolution and its aftermath, to terrorism and economic underdevelopment. Egypt's current government is a presidential republic headed by President Abdel Fattah el-Sisi, described by a number of watchdogs as authoritarian. Islam is the official religion of Egypt and Arabic is its official language. With over 95 million inhabitants, Egypt is the most populous country in North Africa, the Middle East, the Arab world, the third-most populous in Africa, the fifteenth-most populous in the world; the great majority of its people live near the banks of the Nile River, an area of about 40,000 square kilometres, where the only arable land is found. The large regions of the Sahara desert, which constitute most of Egypt's territory, are sparsely inhabited. About half of Egypt's residents live in urban areas, with most spread across the densely populated centres of greater Cairo and other major cities in the Nile Delta.
The sovereign state of Egypt is a transcontinental country considered to be a regional power in North Africa, the Middle East and the Muslim world, a middle power worldwide. Egypt's economy is one of the largest and most diversified in the Middle East, is projected to become one of the largest in the world in the 21st century. In 2016, Egypt became Africa's second largest economy. Egypt is a founding member of the United Nations, Non-Aligned Movement, Arab League, African Union, Organisation of Islamic Cooperation. "Miṣr" is the Classical Quranic Arabic and modern official name of Egypt, while "Maṣr" is the local pronunciation in Egyptian Arabic. The name is of Semitic origin, directly cognate with other Semitic words for Egypt such as the Hebrew "מִצְרַיִם"; the oldest attestation of this name for Egypt is the Akkadian "mi-iṣ-ru" related to miṣru/miṣirru/miṣaru, meaning "border" or "frontier". There is evidence of rock carvings in desert oases. In the 10th millennium BCE, a culture of hunter-gatherers and fishers was replaced by a grain-grinding culture.
Climate changes or overgrazing around 8000 BCE began to desiccate the pastoral lands of Egypt, forming the Sahara. Early tribal peoples migrated to the Nile River where they developed a settled agricultural economy and more centralised society. By about 6000 BCE, a Neolithic culture rooted in the Nile Valley. During the Neolithic era, several predynastic cultures developed independently in Upper and Lower Egypt; the Badarian culture and the successor Naqada series are regarded as precursors to dynastic Egypt. The earliest known Lower Egyptian site, predates the Badarian by about seven hundred years. Contemporaneous Lower Egyptian communities coexisted with their southern counterparts for more than two thousand years, remaining culturally distinct, but maintaining frequent contact through trade; the earliest known evidence of Egyptian hieroglyphic inscriptions appeared during the predynastic period on Naqada III pottery vessels, dated to about 3200 BCE. A unified kingdom was founded c. 3150 BCE
Al-Andalus known as Muslim Spain, Muslim Iberia, or Islamic Iberia, was a medieval Muslim territory and cultural domain that in its early period occupied most of Iberia, today's Portugal and Spain. At its greatest geographical extent, it occupied the northwest of the Iberian peninsula and a part of present day southern France Septimania and for nearly a century extended its control from Fraxinet over the Alpine passes which connect Italy with the remainder of Western Europe; the name more describes the parts of the peninsula governed by Muslims at various times between 711 and 1492, though the boundaries changed as the Christian Reconquista progressed shrinking to the south around modern-day Andalusia and to the Emirate of Granada. Following the Umayyad conquest of Hispania, al-Andalus at its greatest extent, was divided into five administrative units, corresponding to modern Andalusia and Galicia, Castile and León, Aragon, the County of Barcelona, Septimania; as a political domain, it successively constituted a province of the Umayyad Caliphate, initiated by the Caliph Al-Walid I.
Rule under these kingdoms led to a rise in cultural exchange and cooperation between Muslims and Christians. Christians and Jews were subject to a special tax called Jizya, to the state, which in return provided internal autonomy in practicing their religion and offered the same level of protections by the Muslim rulers. Under the Caliphate of Córdoba, al-Andalus was a beacon of learning, the city of Córdoba, the largest in Europe, became one of the leading cultural and economic centres throughout the Mediterranean Basin and the Islamic world. Achievements that advanced Islamic and Western science came from al-Andalus, including major advances in trigonometry, surgery, pharmacology and other fields. Al-Andalus became a major educational center for Europe and the lands around the Mediterranean Sea as well as a conduit for cultural and scientific exchange between the Islamic and Christian worlds. For much of its history, al-Andalus existed in conflict with Christian kingdoms to the north. After the fall of the Umayyad caliphate, al-Andalus was fragmented into minor states and principalities.
Attacks from the Christians intensified, led by the Castilians under Alfonso VI. The Almoravid empire intervened and repelled the Christian attacks on the region, deposing the weak Andalusi Muslim princes and included al-Andalus under direct Berber rule. In the next century and a half, al-Andalus became a province of the Berber Muslim empires of the Almoravids and Almohads, both based in Marrakesh; the Christian kingdoms in the north of the Iberian Peninsula overpowered the Muslim states to the south. In 1085, Alfonso VI captured Toledo. With the fall of Córdoba in 1236, most of the south fell under Christian rule and the Emirate of Granada became a tributary state of the Kingdom of Castile two years later. In 1249, the Portuguese Reconquista culminated with the conquest of the Algarve by Afonso III, leaving Granada as the last Muslim state on the Iberian Peninsula. On January 2, 1492, Emir Muhammad XII surrendered the Emirate of Granada to Queen Isabella I of Castile, completing the Christian Reconquista of the peninsula.
Although al-Andalus ended as a political entity, the nearly eight centuries of Islamic rule which preceded and accompanied the early formation of the Spanish nation-state and identity has left a profound effect on the country's culture and language in Andalusia. The toponym al-Andalus is first attested by inscriptions on coins minted in 716 by the new Muslim government of Iberia; these coins, called dinars, were inscribed in both Arabic. The etymology of the name "al-Andalus" has traditionally been derived from the name of the Vandals. In 1986, Joaquín Vallvé proposed that "al-Andalus" was a corruption of the name Atlantis, Halm in 1989 derived the name from a Gothic term, *landahlauts, in 2002, Georg Bossong suggested its derivation from a pre-Roman substrate. During the caliphate of the Umayyad Caliph Al-Walid I, the commander Tariq ibn-Ziyad led a small force that landed at Gibraltar on April 30, 711, ostensibly to intervene in a Visigothic civil war. After a decisive victory over King Roderic at the Battle of Guadalete on July 19, 711, Tariq ibn-Ziyad, joined by Arab governor Musa ibn Nusayr of Ifriqiya, brought most of the Visigothic Kingdom under Muslim occupation in a seven-year campaign.
They occupied Visigothic Septimania in southern France. Most of the Iberian peninsula became part of the expanding Umayyad Empire, under the name of al-Andalus, it was organized as a province subordinate to Ifriqiya, so, for the first few decades, the governors of al-Andalus were appointed by the emir of Kairouan, rather than the Caliph in Damascus. The regional capital was set at Córdoba, the first influx of Muslim settlers was distributed; the small army Tariq led in the initial conquest consisted of Berbers, while Musa's Arab force of over 12,000 soldiers was accompanied by a group of mawālī, that is, non-Arab Muslims, who were clients of the
Mercury is the smallest and innermost planet in the Solar System. Its orbital period around the Sun of 87.97 days is the shortest of all the planets in the Solar System. It is named after the messenger of the gods. Like Venus, Mercury orbits the Sun within Earth's orbit as an inferior planet, never exceeds 28° away from the Sun when viewed from Earth; this proximity to the Sun means the planet can only be seen near the western or eastern horizon during the early evening or early morning. At this time it may appear as a bright star-like object, but is far more difficult to observe than Venus; the planet telescopically displays the complete range of phases, similar to Venus and the Moon, as it moves in its inner orbit relative to Earth, which reoccurs over the so-called synodic period every 116 days. Mercury is tidally locked with the Sun in a 3:2 spin-orbit resonance, rotates in a way, unique in the Solar System; as seen relative to the fixed stars, it rotates on its axis three times for every two revolutions it makes around the Sun.
As seen from the Sun, in a frame of reference that rotates with the orbital motion, it appears to rotate only once every two Mercurian years. An observer on Mercury would therefore see only one day every two Mercurian years. Mercury's axis has the smallest tilt of any of the Solar System's planets, its orbital eccentricity is the largest of all known planets in the Solar System. Mercury's surface appears cratered and is similar in appearance to the Moon's, indicating that it has been geologically inactive for billions of years. Having no atmosphere to retain heat, it has surface temperatures that vary diurnally more than on any other planet in the Solar System, ranging from 100 K at night to 700 K during the day across the equatorial regions; the polar regions are below 180 K. The planet has no known natural satellites. Two spacecraft have visited Mercury: Mariner 10 flew by in 1974 and 1975; the BepiColombo spacecraft is planned to arrive at Mercury in 2025. Mercury appears to have a solid silicate crust and mantle overlying a solid, iron sulfide outer core layer, a deeper liquid core layer, a solid inner core.
Mercury is one of four terrestrial planets in the Solar System, is a rocky body like Earth. It is the smallest planet in the Solar System, with an equatorial radius of 2,439.7 kilometres. Mercury is smaller—albeit more massive—than the largest natural satellites in the Solar System and Titan. Mercury consists of 70% metallic and 30% silicate material. Mercury's density is the second highest in the Solar System at 5.427 g/cm3, only less than Earth's density of 5.515 g/cm3. If the effect of gravitational compression were to be factored out from both planets, the materials of which Mercury is made would be denser than those of Earth, with an uncompressed density of 5.3 g/cm3 versus Earth's 4.4 g/cm3. Mercury's density can be used to infer details of its inner structure. Although Earth's high density results appreciably from gravitational compression at the core, Mercury is much smaller and its inner regions are not as compressed. Therefore, for it to have such a high density, its core must be rich in iron.
Geologists estimate. Research published in 2007 suggests. Surrounding the core is a 500–700 km mantle consisting of silicates. Based on data from the Mariner 10 mission and Earth-based observation, Mercury's crust is estimated to be 35 km thick.. One distinctive feature of Mercury's surface is the presence of numerous narrow ridges, extending up to several hundred kilometers in length, it is thought that these were formed as Mercury's core and mantle cooled and contracted at a time when the crust had solidified. Mercury's core has a higher iron content than that of any other major planet in the Solar System, several theories have been proposed to explain this; the most accepted theory is that Mercury had a metal–silicate ratio similar to common chondrite meteorites, thought to be typical of the Solar System's rocky matter, a mass 2.25 times its current mass. Early in the Solar System's history, Mercury may have been struck by a planetesimal of 1/6 that mass and several thousand kilometers across.
The impact would have stripped away much of the original crust and mantle, leaving the core behind as a major component. A similar process, known as the giant impact hypothesis, has been proposed to explain the formation of the Moon. Alternatively, Mercury may have formed from the solar nebula before the Sun's energy output had stabilized, it would have had twice its present mass, but as the protosun contracted, temperatures near Mercury could have been between 2,500 and 3,500 K and even as high as 10,000 K. Much of Mercury's surface rock could have been vaporized at such temperatures, forming an atmosphere of "rock vapor" that could have been carried away by the solar wind. A third hypothesis proposes that the solar nebula caused drag on the particles from which Mercury was accreting, which meant that lighter particles were lost from the accreting material and not gathered by Mercury; each hypothesis predicts a different surface composition, there are two space missions set to make observations.
Muslims are people who follow or practice Islam, a monotheistic Abrahamic religion. Muslims consider the Quran, their holy book, to be the verbatim word of God as revealed to the Islamic prophet and messenger Muhammad; the majority of Muslims follow the teachings and practices of Muhammad as recorded in traditional accounts. "Muslim" is an Arabic word meaning "submitter". The largest denomination of Islam are Sunni Muslims who constitute 85-90% of the total Muslim population, followed by the Shia who make up most of the remainder of Muslims; the beliefs of Muslims include: that God is eternal and one. The religious practices of Muslims are enumerated in the Five Pillars of Islam: the declaration of faith, daily prayers, fasting during the month of Ramadan and the pilgrimage to Mecca at least once in a lifetime. To become a Muslim and to convert to Islam, it is essential to utter the Shahada, one of the Five Pillars of Islam, a declaration of faith and trust that professes that there is only one God and that Muhammad is God's messenger.
It is a set statement recited in Arabic: lā ʾilāha ʾillā-llāhu muḥammadun rasūlu-llāh "There is no god but Allah, Muhammad is the messenger of God."In Sunni Islam, the shahada has two parts: la ilaha illa'llah, Muhammadun rasul Allah, which are sometimes referred to as the first shahada and the second shahada. The first statement of the shahada is known as the tahlīl. In Shia Islam, the shahada has a third part, a phrase concerning Ali, the first Shia Imam and the fourth Rashid caliph of Sunni Islam: وعليٌ وليُّ الله, which translates to "Ali is the wali of God; the word muslim is the active participle of the same verb of which islām is a verbal noun, based on the triliteral S-L-M "to be whole, intact". A female adherent is a muslima; the plural form in Arabic is muslimūn or muslimīn, its feminine equivalent is muslimāt. The ordinary word in English is "Muslim", it is sometimes transliterated as "Moslem", an older spelling. The word Mosalman is a common equivalent for Muslim used in South Asia.
Until at least the mid-1960s, many English-language writers used the term Mahometans. Although such terms were not intended to be pejorative, Muslims argue that the terms are offensive because they imply that Muslims worship Muhammad rather than God. Other obsolete terms include Muslimist. Musulmán/Mosalmán is modified from Arabic, it is the origin of the Spanish word musulmán, the German Muselmann, the French word musulman, the Polish words muzułmanin and muzułmański, the Portuguese word muçulmano, the Italian word mussulmano or musulmano, the Romanian word musulman and the Greek word μουσουλμάνος. In English it has become archaic in usage. Apart from Persian, Polish, Portuguese and Greek, the term could be found, with obvious local differences, in Armenian, Pashto, Hindi, Marathi, Turkish, Uzbek, Azeri, Hungarian, Bosnian, Russian, Ukrainian, Romanian and Sanskrit; the Muslim philosopher Ibn Arabi said: A Muslim is a person who has dedicated his worship to God... Islam means making one's religion and faith God's alone.
The Qur'an describes many prophets and messengers within Judaism and Christianity, their respective followers, as Muslim: Adam, Abraham, Jacob and Jesus and his apostles are all considered to be Muslims in the Qur'an. The Qur'an states that these men were Muslims because they submitted to God, preached His message and upheld His values, which included praying, charity and pilgrimage. Thus, in Surah 3:52 of the Qur'an, Jesus' disciples tell him, "We believe in God. In Muslim belief, before the Qur'an, God had given the Tawrat to Moses, the Zabur to David and the Injil to Jesus, who are all considered important Muslim prophets; the most populous Muslim-majority country is Indonesia, home to 12.7% of the world's Muslims, followed by Pakistan and Egypt. About 20 % of the world's Muslims lives in the Middle North Africa. Sizable minorities are found in India, Russia, the Americas and parts of Europe; the country with the highest proportion of self-described Muslims as a proportion of its total population is Morocco.
Converts and immigrant communities are found in every part of the world. Over 75–90% of Muslims are Sunni; the second and third largest sects and Ahmadiyya, make up 10–20%, 1% respectively. With about 1.8 billion followers a quarter of earth's population, Islam is the second-largest and the fastest-growing religion in the world. Due to the young age and high fertilit
A caliphate is an Islamic state under the leadership of an Islamic steward with the title of caliph, a person considered a religious successor to the Islamic prophet Muhammad and a leader of the entire ummah. The caliphates were polities based in Islam which developed into multi-ethnic trans-national empires. During the medieval period, three major caliphates succeeded each other: the Rashidun Caliphate, the Umayyad Caliphate and the Abbasid Caliphate. In the fourth major caliphate, the Ottoman Caliphate, the rulers of the Ottoman Empire claimed caliphal authority from 1517. During the history of Islam, a few other Muslim states all hereditary monarchies, have claimed to be caliphates. Prior to the rise of Muhammad and the unification of the tribes of Arabia under Islam, Arabs followed a pre-Islamic Arab polytheism, lived as self-governing sedentary and nomadic communities, raided their neighbouring tribes. Following the early Muslim conquests of the Arabian Peninsula, the region became unified and most of the tribes adopted Islam.
The first caliphate, the Rashidun Caliphate, was established after Muhammad's death in 632. The four Rashidun caliphs, who directly succeeded Muhammad as leaders of the Muslim community, were chosen through shura, a process of community consultation that some consider to be an early form of Islamic democracy; the fourth caliph, who, unlike the prior three, was from the same clan as Muhammad, is considered by Shia Muslims to be the first rightful caliph and Imam after Muhammad. Ali reigned during the First Fitna, a civil war between supporters of Ali and supporters of the assassinated previous caliph, from Banu Umayya, as well as rebels in Egypt; the second caliphate, the Umayyad Caliphate, was ruled by Banu Umayya, a Meccan clan descended from Umayya ibn Abd Shams. The caliphate continued the Arab conquests, incorporating the Caucasus, Sindh, the Maghreb and the Iberian Peninsula into the Muslim world; the caliphate had considerable acceptance of the Christians within its territory, necessitated by their large numbers in the region of Syria.
Following the Abbasid Revolution from 746–750, which arose from non-Arab Muslim disenfranchisement, the Abbasid Caliphate was established in 750. The third caliphate, the Abbasid Caliphate was ruled by the Abbasids, a dynasty of Meccan origin which descended from Hashim, a great-grandfather of Muhammad, making them part of Banu Hashim, via Abbas, an uncle of Muhammad, hence the name. Caliph al-Mansur founded its second capital of Baghdad in 762 which became a major scientific and art centre, as did the territory as a whole during a period known as the Islamic Golden Age. From the 10th century, Abbasid rule became confined to an area around Baghdad. From 945 to 1157, the Abbasid Caliphate came under Buyid and Seljuq military control. In 1250, a non-Arab army created by the Abbasids called. In 1258, the Mongol Empire sacked Baghdad, ending the Abbasid Caliphate, in 1261 the Mamluks in Egypt re-established the Abbasid Caliphate in Cairo. Though lacking in political power, the Abbasid dynasty continued to claim authority in religious matters until the Ottoman conquest of Mamluk Egypt in 1517.
The fourth major caliphate, the Ottoman Caliphate, was established after their conquest of Mamluk Egypt in 1517. The conquest gave the Ottomans control over the holy cities of Mecca and Medina controlled by the Mamluks; the Ottomans came to be viewed as the de facto leaders and representatives of the Muslim world. In the Indian subcontinent, dominant powers such as the Delhi Sultanate's Alauddin Khilji, Mughal Empire's sixth ruler Aurangzeb, Mysore's kings Hyder Ali and Tipu Sultan have been heralded as few of the Indian caliphs existed, due to their establishments of Islamic laws throughout South Asia. Following their defeat in World War I, their empire was partitioned by the United Kingdom and French Third Republic, on 3 March 1924, the first President of the Turkish Republic, Mustafa Kemal Atatürk, as part of his reforms, constitutionally abolished the institution of the caliphate. A few other states that existed through history have called themselves caliphates, including the Isma'ili Fatimid Caliphate in Northeast Africa, the Umayyad Caliphate of Córdoba in Iberia, the Berber Almohad Caliphate in Morocco and the Fula Sokoto Caliphate in present-day northern Nigeria.
The Sunni branch of Islam stipulates that, as a head of state, a caliph may come to power in one of four ways: either through an election, through nomination, through a selection by a committee, or by force. Followers of Shia Islam, believe a caliph should be an Imam chosen by God from the Ahl al-Bayt. In the early 21st century, following the failure of the Arab Spring and defeat of the self-proclaimed "Islamic State", there has seen "a broad mainstream embrace of a collective Muslim identity" by young Muslims and the appeal of a caliphate as a "idealized future Muslim state" has grown stronger. Before the advent of Islam, Arabian monarchs traditionally used the title malik, or another from the same root; the term caliph, derives from the Arabic word khalīfah, which means "successor", "steward", or "deputy" and has traditionally been considered a shortening of Khalīfat Rasūl Allāh. However, studies of pre-Islamic texts suggest that the original meaning of the phr
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. In particular, 3rd-century astronomers first noted that the ratio of the lengths of two sides of a right-angled triangle depends only of one acute angles of the triangle; these dependencies are now called trigonometric functions. Trigonometry is the foundation of all applied geometry, including geodesy, celestial mechanics, solid mechanics, navigation. Trigonometric functions have been extended as functions of a real or complex variable, which are today pervasive in all mathematics. Sumerian astronomers studied angle measure. They, the Babylonians, studied the ratios of the sides of similar triangles and discovered some properties of these ratios but did not turn that into a systematic method for finding sides and angles of triangles; the ancient Nubians used a similar method.
In the 3rd century BC, Hellenistic mathematicians such as Euclid and Archimedes studied the properties of chords and inscribed angles in circles, they proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. In 140 BC, Hipparchus gave the first tables of chords, analogous to modern tables of sine values, used them to solve problems in trigonometry and spherical trigonometry. In the 2nd century AD, the Greco-Egyptian astronomer Ptolemy constructed detailed trigonometric tables in Book 1, chapter 11 of his Almagest. Ptolemy used chord length to define his trigonometric functions, a minor difference from the sine convention we use today. Centuries passed before more detailed tables were produced, Ptolemy's treatise remained in use for performing trigonometric calculations in astronomy throughout the next 1200 years in the medieval Byzantine and Western European worlds; the modern sine convention is first attested in the Surya Siddhanta, its properties were further documented by the 5th century Indian mathematician and astronomer Aryabhata.
These Greek and Indian works were expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, were applying them to problems in spherical geometry; the Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right. Nasīr al-Dīn al-Tūsī was the first to treat trigonometry as a mathematical discipline independent from astronomy, he developed spherical trigonometry into its present form, he listed the six distinct cases of a right-angled triangle in spherical trigonometry, in his On the Sector Figure, he stated the law of sines for plane and spherical triangles, discovered the law of tangents for spherical triangles, provided proofs for both these laws. Knowledge of trigonometric functions and methods reached Western Europe via Latin translations of Ptolemy's Greek Almagest as well as the works of Persian and Arab astronomers such as Al Battani and Nasir al-Din al-Tusi.
One of the earliest works on trigonometry by a northern European mathematician is De Triangulis by the 15th century German mathematician Regiomontanus, encouraged to write, provided with a copy of the Almagest, by the Byzantine Greek scholar cardinal Basilios Bessarion with whom he lived for several years. At the same time, another translation of the Almagest from Greek into Latin was completed by the Cretan George of Trebizond. Trigonometry was still so little known in 16th-century northern Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts. Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major branch of mathematics. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Gemma Frisius described for the first time the method of triangulation still used today in surveying, it was Leonhard Euler who incorporated complex numbers into trigonometry.
The works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series. In the 18th century, Brook Taylor defined the general Taylor series. If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees; the two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle. If the length of one of the sides is known, the other two are determined; these ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure: Sine function, defined as the ratio of the side opposite the angle to the hypotenuse.
Sin A = opposite hypotenuse = a c. Cosine funct