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Rule Of False Position
In mathematics, the ''regula falsi'', method of false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check". Versions of the method predate the advent of algebra and the use of equations. As an example, consider problem 26 in the Rhind papyrus, which asks for a solution of (written in modern notation) the equation . This is solved by false position. First, guess that to obtain, on the left, . This guess is a good choice since it produces an integer value. However, 4 is not the solution of the original equation, as it gives a value which is three times too small. To compensate, multiply (currently set to 4) by 3 and substitute again to get , verifying that the solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Mathematics
Mathematics in China emerged independently by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system ( base 2 and base 10), algebra, geometry, number theory and trigonometry. Since the Han Dynasty, as diophantine approximation being a prominent numerical method, the Chinese made substantial progress on polynomial evaluation. Algorithms like regula falsi and expressions like continued fractions are widely used and have been well-documented ever-since. They deliberately find the principal ''n''th root of positive numbers and the roots of equations. The major texts from the period, '' The Nine Chapters on the Mathematical Art'' and the '' Book on Numbers and Computation'' gave detailed processes for solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they included inverse elements as well as Eucli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Islamic Inheritance Jurisprudence
Islamic Inheritance jurisprudence is a field of Islamic jurisprudence ( ar, فقه) that deals with inheritance, a topic that is prominently dealt with in the Qur'an. It is often called ''Mīrāth'', and its branch of Islamic law is technically known as ''ʿilm al-farāʾiḍ'' ( ar, علم الفرائض, "the science of the ordained quotas"). Inheritance and the Qur'an The Qur'an introduced a number of different rights and restrictions on matters of inheritance, including what were at that time general improvements to the treatment of women and family life. The Qur'an also presented efforts to fix the laws of inheritance, and thus forming a complete legal system. This development was in contrast to pre-Islamic societies where rules of inheritance varied considerably. They do, however, also differ from ongoing secular egalitarian improvements since that time, up to, though principally in, the modern era. Furthermore, the Qur'an introduced additional heirs that were not ent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics In Medieval Islam
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics ( Aryabhata, Brahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry. Arabic works played an important role in the transmission of mathematics to Europe during the 10th—12th centuries. Concepts Algebra The study of algebra, the name of which is derived from the Arabic word meaning completion or "reunion of broken parts", flourished during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a Persian scholar in the House of Wisdom in Baghdad was the founder of algebra, is along with the Greek mathematician Diophantus, known as the father of algebra. In his book '' The Compendious Book on Calculation by Completion and Balancin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logical system in which each result is '' proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebanon
Lebanon ( , ar, لُبْنَان, translit=lubnān, ), officially the Republic of Lebanon () or the Lebanese Republic, is a country in Western Asia. It is located between Syria to Lebanon–Syria border, the north and east and Israel to Blue Line (Lebanon), the south, while Cyprus lies to its west across the Mediterranean Sea; its location at the crossroads of the Mediterranean Basin and the Arabs, Arabian hinterland has contributed to History of Lebanon, its rich history and shaped Culture of Lebanon, a cultural identity of demographics of Lebanon#Religious groups, religious diversity. It is part of the Levant region of the Middle East. Lebanon is home to roughly six million people and covers an area of , making it the List of countries and dependencies by area, second smallest country in continental Asia. The official language of the state is Arabic, while French language, French is also formally recognized; the Lebanese Arabic, Lebanese dialect of Arabic is used alongside Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baalbek
Baalbek (; ar, بَعْلَبَكّ, Baʿlabakk, Syriac-Aramaic: ܒܥܠܒܟ) is a city located east of the Litani River in Lebanon's Beqaa Valley, about northeast of Beirut. It is the capital of Baalbek-Hermel Governorate. In Greek and Roman times Baalbek was also known as Heliopolis (, Greek for "Sun City"). In 1998 Baalbek had a population of 82,608, mostly Shia Muslims, followed by Sunni Muslims and Christians. It is home to the Baalbek temple complex which includes two of the largest and grandest Roman temple ruins: the Temple of Bacchus and the Temple of Jupiter. It was inscribed in 1984 as an UNESCO World Heritage site. Name A few miles from the swamp from which the Litani (the classical Leontes) and the Asi (the upper Orontes) flow, Baalbek may be the same as the ''manbaa al-nahrayn'' ("Source of the Two Rivers"), the abode of El in the Ugaritic Baal Cycle discovered in the 1920s and a separate serpent incantation. Baalbek was called Heliopolis during the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arab
The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, North Africa, the Horn of Africa, and the western Indian Ocean islands (including the Comoros). An Arab diaspora is also present around the world in significant numbers, most notably in the Americas, Western Europe, Turkey, Indonesia, and Iran. In modern usage, the term "Arab" tends to refer to those who both carry that ethnic identity and speak Arabic as their native language. This contrasts with the narrower traditional definition, which refers to the descendants of the tribes of Arabia. The religion of Islam was developed in Arabia, and Classical Arabic serves as the language of Islamic literature. 93 percent of Arabs are Muslims (the remainder consisted mostly of Arab Christians), while Arab Muslims are only 20 percent of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qusta Ibn Luqa
Qusta ibn Luqa (820–912) (Costa ben Luca, Constabulus) was a Syrian Melkite Christian physician, philosopher, astronomer, mathematician and translator. He was born in Baalbek. Travelling to parts of the Byzantine Empire, he brought back Greek texts and translated them into Arabic. Personal life Qusta ibn Luqa al-Ba'albakki, i. e. from Baalbek or Heliopolis, modern-day Lebanon, a Melkite Christian, was born in 820 and flourished in Baghdad. He was a philosopher, physician, mathematician and astronomer. He died in Armenia possibly in A.D. 912/913. Translations Translations of Diophantos, Theodosius of Bithynia's ''Sphaerica'', ''On Days and Nights (Περὶ ἡμερῶν καὶ νυκτῶν -De diebus et noctibus)'', ''On the places of habitation'' (''Περὶ οἰκήσεων - De habitationibus''), Autolycus' ''On the moving sphere'' (''Περὶ κινουμένης σφαίρας'' - ''De sphaera quae movetur), On Risings and Settings'' (''Περὶ ἐπιτολ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle East
The Middle East ( ar, الشرق الأوسط, ISO 233: ) is a geopolitical region commonly encompassing Arabia (including the Arabian Peninsula and Bahrain), Asia Minor (Asian part of Turkey except Hatay Province), East Thrace (European part of Turkey), Egypt, Iran, the Levant (including Ash-Shām and Cyprus), Mesopotamia (modern-day Iraq), and the Socotra Archipelago (a part of Yemen). The term came into widespread usage as a replacement of the term Near East (as opposed to the Far East) beginning in the early 20th century. The term "Middle East" has led to some confusion over its changing definitions, and has been viewed by some to be discriminatory or too Eurocentric. The region includes the vast majority of the territories included in the closely associated definition of Western Asia (including Iran), but without the South Caucasus, and additionally includes all of Egypt (not just the Sinai Region) and all of Turkey (not just the part barring East Thrace). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abu Kamil
Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ ( Latinized as Auoquamel, ar, أبو كامل شجاع بن أسلم بن محمد بن شجاع, also known as ''Al-ḥāsib al-miṣrī''—lit. "the Egyptian reckoner") (c. 850 – c. 930) was a prominent Egyptian mathematician during the Islamic Golden Age. He is considered the first mathematician to systematically use and accept irrational numbers as solutions and coefficients to equations. His mathematical techniques were later adopted by Fibonacci, thus allowing Abu Kamil an important part in introducing algebra to Europe. Abu Kamil made important contributions to algebra and geometry. He was the first Islamic mathematician to work easily with algebraic equations with powers higher than x^2 (up to x^8), and solved sets of non-linear simultaneous equations with three unknown variables. He illustrated the rules of signs for expanding the multiplication (a \pm b)(c \pm d). He wrote all problems rhetorically, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egyptians
Egyptians ( arz, المَصرِيُون, translit=al-Maṣriyyūn, ; arz, المَصرِيِين, translit=al-Maṣriyyīn, ; cop, ⲣⲉⲙⲛ̀ⲭⲏⲙⲓ, remenkhēmi) are an ethnic group native to the Nile, Nile Valley in Egypt. Egyptian identity is closely tied to Geography of Egypt, geography. The population is concentrated in the Nile Valley, a small strip of cultivable land stretching from the Cataracts of the Nile, First Cataract to the Mediterranean Basin, Mediterranean and enclosed by desert both to the Eastern Desert, east and to the Western Desert (North Africa), west. This unique geography has been the basis of the DNA history of Egypt, development of Egyptian society since Ancient Egypt, antiquity. The daily language of the Egyptians is a continuum of the local variety of Arabic, varieties of Arabic; the most famous dialect is known as Egyptian Arabic or ''Masri''. Additionally, a sizable minority of Egyptians living in Upper Egypt speak Sa'idi Arabic, a mix bet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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