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Al-Khwarizmi
Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronomy, and geography. Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.Maher, P. (1998), "From Al-Jabr to Algebra", ''Mathematics in School'', 27(4), 14–15. Al-Khwarizmi's popularizing treatise on algebra (''The Compendious Book on Calculation by Completion and Balancing'', c. 813–833 CEOaks, J. (2009), "Polynomials and Equations in Arabic Algebra", ''Archive for History of Exact Sciences'', 63(2), 169–203.) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the firs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...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 of Perga, 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 language, 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 people, Greek mathematician Diophantus, known as the father of algebra. In his book ''The Compendious Book on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Compendious Book On Calculation By Completion And Balancing
''The Compendious Book on Calculation by Completion and Balancing'' ( ar, كتاب المختصر في حساب الجبر والمقابلة, ; la, Liber Algebræ et Almucabola), also known as ''Al-Jabr'' (), is an Arabic mathematical treatise on algebra written by the Persian polymath Muḥammad ibn Mūsā al-Khwārizmī around 820 CE while he was in the Abbasid capital of Baghdad, modern-day Iraq. ''Al-Jabr'' was a landmark work in the history of mathematics, establishing algebra as an independent discipline, and with the term "algebra" itself derived from ''Al-Jabr''. The ''Compendious Book'' provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree. It was the first text to teach algebra in an elementary form and for its own sake. It also introduced the fundamental concept of "reduction" and "balancing" (which the term ''al-jabr'' originally referred to), the transposition of subtracted terms to the other side o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorism
Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and mathematical table, facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical Magnitude (mathematics), magnitude, such as Roman numerals, and in some cases required a device such as an abacus. Etymology The word ''algorism'' comes from the name Al-Khwārizmī (c. 780–850), a Persians, Persian mathematician, astronomer, geographer and scholarly method, scholar in the House of Wisdom in Baghdad, whose name means "the native of Khwarezm", which is now in modern-day Uzbekistan. He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title ''Algoritmi de numero Indorum''. This title means "Algoritmi on the numbers of the I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the Expression (mathematics), expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex number, c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
House Of Wisdom
The House of Wisdom ( ar, بيت الحكمة, Bayt al-Ḥikmah), also known as the Grand Library of Baghdad, refers to either a major Abbasid public academy and intellectual center in Baghdad or to a large private library belonging to the Abbasid caliphs during the Islamic Golden Age. The House of Wisdom was founded either as a library for the collections of the Caliph Harun al-Rashid in the late 8th century (then later turned into a public academy during the reign of al-Ma'mun) or was a private collection created by al-Mansur (reign 754–775) to house rare books and collections of poetry in Arabic. The House of Wisdom and its contents were destroyed in the Siege of Baghdad in 1258, leaving relatively limited archaeological evidence for the House of Wisdom, such that most knowledge about it is derived from the works of contemporary scholars of the era such as al-Tabari and Ibn al-Nadim. Background The House of Wisdom existed as a part of the major Translation Movement taki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy In The Medieval Islamic World
Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (9th–13th centuries), and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon. Islamic astronomy played a significant role in the revival of Byzantine and EuropeanSaliba (1999). astronomy following the loss of knowledge during the early medieval period, notably with the production of Latin translations of Arabic works during the 12th century. Islamic astronomy also had an influence on Chinese astronomy and Malian a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Islamic Golden Age
The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign of the Abbasid caliph Harun al-Rashid (786 to 809) with the inauguration of the House of Wisdom in Baghdad, the world's largest city by then, where Muslim scholars and polymaths from various parts of the world with different cultural backgrounds were mandated to gather and translate all of the known world's classical knowledge into Aramaic and Arabic. The period is traditionally said to have ended with the collapse of the Abbasid caliphate due to Mongol invasions and the Siege of Baghdad in 1258. A few scholars date the end of the golden age around 1350 linking with the Timurid Renaissance, while several modern historians and scholars place the end of the Islamic Golden Age as late as the end of 15th to 16th centuries meeting with the I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completing The Square
: In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form :ax^2 + bx + c to the form :a(x-h)^2 + k for some values of ''h'' and ''k''. In other words, completing the square places a perfect square trinomial inside of a quadratic expression. Completing the square is used in * solving quadratic equations, * deriving the quadratic formula, * graphing quadratic functions, * evaluating integrals in calculus, such as Gaussian integrals with a linear term in the exponent, * finding Laplace transforms. In mathematics, completing the square is often applied in any computation involving quadratic polynomials. History Completing the square was known in the Old Babylonian Empire. Muhammad ibn Musa Al-Khwarizmi, a famed polymath who wrote the early algebraic treatise Al-Jabr, used the technique of completing the square to solve quadratic equations. Overview Background The formula in elementary algebra for computing the square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geography And Cartography In Medieval Islam
Medieval Islamic geography and cartography refer to the study of geography and cartography in the Muslim world during the Islamic Golden Age (variously dated between the 8th century and 16th century). Muslim scholars made advances to the map-making traditions of earlier cultures, particularly the Hellenistic geography, Hellenistic geographers Ptolemy and Marinus of Tyre, combined with what explorers and merchants learned in their travels across the Old World (Afro-Eurasia). Islamic geography had three major fields: exploration and navigation, physical geography, and cartography and mathematical geography. Islamic geography reached its apex with Muhammad al-Idrisi in the 12th century. History Islamic geography began in the 8th century, influenced by Hellenistic geography, combined with what explorers and merchants learned in their travels across the Old World (Afro-Eurasia). Muslim scholars engaged in extensive exploration and navigation during the 9th-12th centuries, including jou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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