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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] |
Abū Al-Ḥasan Ibn ʿAlī Al-Qalaṣādī
Abū'l-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qurashī al-Qalaṣādī ( ar, أبو الحسن علي بن محمد بن علي القرشي البسطي; 1412–1486) was a Muslim Arab mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence. Franz Woepcke stated that al-Qalaṣādī was known as one of the most influential voices in algebraic notation for taking "the first steps toward the introduction of algebraic symbolism''. He wrote numerous books on arithmetic and algebra, including ''al-Tabsira fi'lm al-hisab'' ( ar, التبصير في علم الحساب "''Clarification of the science of arithmetic''"). Early life Al-Qalaṣādī was born in Baza, an outpost of the Emirate of Granada. He received education in Granada, but continued to support his family in Baza. He published many works and eventually retired to his native Baza. His works dealt with Algebra and contained the precise mathematical answers to problems in everyday life ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ibn Al-Banna' Al-Marrakushi
Ibn al‐Bannāʾ al‐Marrākushī ( ar, ابن البناء المراكشي), full name: Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi al-Marrakushi () (29 December 1256 – 31 July 1321), was a Moroccan polymath who was active as a mathematician, astronomer, Islamic scholar, Sufi and astrologer. Biography Ahmad ibn Muhammad ibn Uthman was born in the ''Qa'at Ibn Nahid'' Quarter of Marrakesh on 29 or 30 December 1256. His ''nisba'' al-Marrakushi is in relation to his birth and death in his hometown Marrakesh. His father was a mason thus the '' kunya'' Ibn al-Banna' (lit. the son of the mason). Ibn al-Banna' studied a variety of subjects under at least 17 masters: Quran under the '' Qari's'' Muhammad ibn al-bashir and shaykh al-Ahdab. '' ʻilm al-ḥadīth'' under ''qadi al-Jama'a'' (chief judge) of Fez َAbu al-Hajjaj Yusuf ibn Ahmad ibn Hakam al-Tujibi, Abu Yusuf Ya'qub ibn Abd al-Rahman al-Jazuli and Abu abd allah ibn. ''Fiqh and Usul al-Fiqh'' under Abu Imran Musa ib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduction (mathematics)
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Minimizing the number of radicals that appear underneath other radicals in an expression is called denesting radicals. Algebra In linear algebra, ''reduction'' refers to applying simple rules to a series of equations or matrices to change them into a simpler form. In the case of matrices, the process involves manipulating either the rows or the columns of the matrix and so is usually referred to as ''row-reduction'' or ''column-reduction'', respectively. Often the aim of reduction is to transform a matrix into its "row-reduced echelon form" or "row-echelon form"; this is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Equations
In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field (mathematics), field, often the field of the rational numbers. For many authors, the term ''algebraic equation'' refers only to ''univariate equations'', that is polynomial equations that involve only one variable (mathematics), variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the ''multivariate'' case), the term ''polynomial equation'' is usually preferred to ''algebraic equation''. For example, :x^5-3x+1=0 is an algebraic equation with integer coefficients and :y^4 + \frac - \frac + xy^2 + y^2 + \frac = 0 is a multivariate polynomial equation over the rationals. Some but not all polynomial equations with Rational number, rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Properties Of Polynomial Roots
Property is the ownership of land, resources, improvements or other tangible objects, or intellectual property. Property may also refer to: Mathematics * Property (mathematics) Philosophy and science * Property (philosophy), in philosophy and logic, an abstraction characterizing an object *Material properties, properties by which the benefits of one material versus another can be assessed *Chemical property, a material's properties that becomes evident during a chemical reaction *Physical property, any property that is measurable whose value describes a state of a physical system *Semantic property *Thermodynamic properties, in thermodynamics and materials science, intensive and extensive physical properties of substances *Mental property, a property of the mind studied by many sciences and parasciences Computer science * Property (programming), a type of class member in object-oriented programming * .properties, a Java Properties File to store program settings as name-value p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Number
In mathematics, the sign of a real number is its property of being either positive, negative, or zero. Depending on local conventions, zero may be considered as being neither positive nor negative (having no sign or a unique third sign), or it may be considered both positive and negative (having both signs). Whenever not specifically mentioned, this article adheres to the first convention. In some contexts, it makes sense to consider a signed zero (such as floating-point representations of real numbers within computers). In mathematics and physics, the phrase "change of sign" is associated with the generation of the additive inverse (negation, or multiplication by −1) of any object that allows for this construction, and is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero. The word "sign" is also often used to indicate other binary aspects of mathemat ... [...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] |
Diophantus
Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the author of a series of books called '' Arithmetica'', many of which are now lost. His texts deal with solving algebraic equations. Diophantine equations ("Diophantine geometry") and Diophantine approximations are important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as ''adaequalitas'' in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek People
The Greeks or Hellenes (; el, Έλληνες, ''Éllines'' ) are an ethnic group and nation indigenous to the Eastern Mediterranean and the Black Sea regions, namely Greece, Cyprus, Albania, Italy, Turkey, Egypt, and, to a lesser extent, other countries surrounding the Mediterranean Sea. They also form a significant diaspora (), with Greek communities established around the world.. Greek colonies and communities have been historically established on the shores of the Mediterranean Sea and Black Sea, but the Greek people themselves have always been centered on the Aegean and Ionian seas, where the Greek language has been spoken since the Bronze Age.. Until the early 20th century, Greeks were distributed between the Greek peninsula, the western coast of Asia Minor, the Black Sea coast, Cappadocia in central Anatolia, Egypt, the Balkans, Cyprus, and Constantinople. Many of these regions coincided to a large extent with the borders of the Byzantine Empire of the late 11th century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baghdad
Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon. In 762 CE, Baghdad was chosen as the capital of the Abbasid Caliphate, and became its most notable major development project. Within a short time, the city evolved into a significant cultural, commercial, and intellectual center of the Muslim world. This, in addition to housing several key academic institutions, including the House of Wisdom, as well as a multiethnic and multi-religious environment, garnered it a worldwide reputation as the "Center of Learning". Baghdad was the largest city in the world for much of the Abbasid era during the Islamic Golden Age, peaking at a population of more than a million. The city was largely destroyed at the hands of the Mongol Empire in 1258, resulting in a decline that would linger through many c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
