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Al-Khwarizmi: The Father of Algebra
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Is Brahmagupta real father of algebra?
https://in.answers.yahoo.com/question/index?qid=20080207201127AAfRtbx
So many people have been proclaimed as father of mathematics as well as father of Algebra . As per the acceptance by most people in the world the father of Algebra is :Muhammad bin Mūsā al-Khwārizmī who wrote the book titled Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations.
The origins of algebra can be traced to the ancient Babylonians,[2] who developed an advanced arithmetical system with which they were able to do calculations in an algebraic fashion. With the use of this system they were able to apply formulas and calculate solutions for unknown values for a class of problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations. By contrast, most Egyptians of this era, and most Indian, Greek and Chinese mathematicians in the first millennium BC, usually solved such equations by geometric methods, such as those described in the Rhind Mathematical Papyrus, Sulba Sutras, Euclid's Elements, and The Nine Chapters on the Mathematical Art. The geometric work of the Greeks, typified in the Elements, provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations.
Later, the Indian mathematicians developed algebraic methods to a high degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Brahmagupta was the first to solve equations using general methods. He solved the linear indeterminate equations, quadratic equations, second order indeterminate equations and equations with multiple variable.
The word "algebra" is named after the Arabic word "al-jabr" from the title of the book al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, meaning The book of Summary Concerning Calculating by Transposition and Reduction, a book written by the Persian mathematician Muhammad ibn Mūsā al-khwārizmī in 820. The word Al-Jabr means "reunion". The Hellenistic mathematician Diophantus has traditionally been known as "the father of algebra" but debate now exists as to whether or not Al-Khwarizmi should take that title.[3] Those who support Al-Khwarizmi point to the fact that much of his work on reduction is still in use today and that he gave an exhaustive explanation of solving quadratic equations. Those who support Diophantus point to the fact that the algebra found in Al-Jabr is more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[4] Another Persian mathematician, Omar Khayyam, developed algebraic geometry and found the general geometric solution of the cubic equation. The Indian mathematicians Mahavira and Bhaskara II, and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quartic, quintic and higher-order polynomial equations.
Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century. Abstract algebra was developed in the 19th century, initially focusing on what is now called Galois theory, and on constructibility issues.
The stages of the development of symbolic algebra are roughly as follows:
Rhetorical algebra, which was developed by the Babylonians and remained dominant up to the 16th century;
Geometric constructive algebra, which was emphasised by the Vedic Indian and classical Greek mathematicians;
Syncopated algebra, as developed by Diophantus, Brahmagupta and the Bakhshali Manuscript; and
Symbolic algebra, which was initiated by Abū al-Hasan ibn Alī al-Qalasādī and sees its culmination in the work of Gottfried Leibniz.
Cover of the 1621 edition of Diophantus's Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.A timeline of key algebraic developments are as follows:
Circa 1800 BC: The Old Babylonian Strassburg tablet seeks the solution of a quadratic elliptic equation.
Circa 1600 BC: The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script.
Circa 800 BC: Indian mathematician Baudhayana, in his Baudhayana Sulba Sutra, discovers Pythagorean triples algebraically, finds geometric solutions of linear equations and quadratic equations of the forms ax2 = c and ax2 + bx = c, and finds two sets of positive integral solutions to a set of simultaneous Diophantine equations.
Circa 600 BC: Indian mathematician Apastamba, in his Apastamba Sulba Sutra, solves the general linear equation and uses simultaneous Diophantine equations with up to five unknowns.
Circa 300 BC: In Book II of his Elements, Euclid gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.
Circa 300 BC: A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using Euclidean tools.
Circa 100 BC: Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations.
Circa 100 BC: The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.
Circa 150 AD: Hero of Alexandria treats algebraic equations in three volumes of mathematics.
Circa 200: Diophantus, who lived in Egypt and is often considered the "father of algebra", writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers.
499: Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation and gives integral solutions of simultaneous indeterminate linear equations.
Circa 625: Chinese mathematician Wang Xiaotong finds numerical solutions of cubic equations.
628: Indian mathematician Brahmagupta, in his treatise Brahma Sputa Siddhanta, invents the chakravala method of solving indeterminate quadratic equations, including Pell's equation, and gives rules for solving linear and quadratic equations.
820: The word algebra is derived from operations described in the treatise written by the Persian mathematician Muḥammad ibn Mūsā al-Ḵwārizmī titled Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of linear and quadratic equations. Al-Khwarizmi is often considered as the "father of algebra", much of whose works on reduction was included in the book and added to many methods we have in algebra now.
Circa 850: Persian mathematician al-Mahani conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.
Circa 850: Indian mathematician Mahavira solves various quadratic, cubic, quartic, quintic and higher-order equations, as well as indeterminate quadratic, cubic and higher-order equations.
Circa 990: Persian Abu Bakr al-Karaji, in his treatise al-Fakhri, further develops algebra by extending Al-Khwarizmi's methodology to incorporate integral powers and integral roots of unknown quantities. He replaces geometrical operations of algebra with modern arithmetical operations, and defines the monomials x, x2, x3, ... and 1/x, 1/x2, 1/x3, ... and gives rules for the products of any two of these.
Circa 1050: Chinese mathematician Jia Xian finds numerical solutions of polynomial equations.
1072: Persian mathematician Omar Khayyam develops algebraic geometry and, in the Treatise on Demonstration of Problems of Algebra, gives a complete classification of cubic equations with general geometric solutions found by means of intersecting conic sections.
1114: Indian mathematician Bhaskara, in his Bijaganita (Algebra), recognizes that a positive number has both a positive and negative square root, and solves various cubic, quartic and higher-order polynomial equations, as well as the general quadratic indeterminant equation.
1202: Algebra is introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci.
Circa 1300: Chinese mathematician Zhu Shijie deals with polynomial algebra, solves quadratic equations, simultaneous equations and equations with up to four unknowns, and numerically solves some quartic, quintic and higher-order polynomial equations.
Circa 1400: Indian mathematician Madhava of Sangamagramma finds iterative methods for approximate solution of non-linear equations.
Circa 1450: Arab mathematician Abū al-Hasan ibn Alī al-Qalasādī took "the first steps toward the introduction of algebraic symbolism." He represented mathematical symbols using characters from the Arabic alphabet.[5]
1535: Nicolo Fonta
https://in.answers.yahoo.com/question/index?qid=20080207201127AAfRtbx
So many people have been proclaimed as father of mathematics as well as father of Algebra . As per the acceptance by most people in the world the father of Algebra is :Muhammad bin Mūsā al-Khwārizmī who wrote the book titled Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations.
The origins of algebra can be traced to the ancient Babylonians,[2] who developed an advanced arithmetical system with which they were able to do calculations in an algebraic fashion. With the use of this system they were able to apply formulas and calculate solutions for unknown values for a class of problems typically solved today by using linear equations, quadratic equations, and indeterminate linear equations. By contrast, most Egyptians of this era, and most Indian, Greek and Chinese mathematicians in the first millennium BC, usually solved such equations by geometric methods, such as those described in the Rhind Mathematical Papyrus, Sulba Sutras, Euclid's Elements, and The Nine Chapters on the Mathematical Art. The geometric work of the Greeks, typified in the Elements, provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations.
Later, the Indian mathematicians developed algebraic methods to a high degree of sophistication. Although Diophantus and the Babylonians used mostly special ad hoc methods to solve equations, Brahmagupta was the first to solve equations using general methods. He solved the linear indeterminate equations, quadratic equations, second order indeterminate equations and equations with multiple variable.
The word "algebra" is named after the Arabic word "al-jabr" from the title of the book al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, meaning The book of Summary Concerning Calculating by Transposition and Reduction, a book written by the Persian mathematician Muhammad ibn Mūsā al-khwārizmī in 820. The word Al-Jabr means "reunion". The Hellenistic mathematician Diophantus has traditionally been known as "the father of algebra" but debate now exists as to whether or not Al-Khwarizmi should take that title.[3] Those who support Al-Khwarizmi point to the fact that much of his work on reduction is still in use today and that he gave an exhaustive explanation of solving quadratic equations. Those who support Diophantus point to the fact that the algebra found in Al-Jabr is more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[4] Another Persian mathematician, Omar Khayyam, developed algebraic geometry and found the general geometric solution of the cubic equation. The Indian mathematicians Mahavira and Bhaskara II, and the Chinese mathematician Zhu Shijie, solved various cases of cubic, quartic, quintic and higher-order polynomial equations.
Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century. Abstract algebra was developed in the 19th century, initially focusing on what is now called Galois theory, and on constructibility issues.
The stages of the development of symbolic algebra are roughly as follows:
Rhetorical algebra, which was developed by the Babylonians and remained dominant up to the 16th century;
Geometric constructive algebra, which was emphasised by the Vedic Indian and classical Greek mathematicians;
Syncopated algebra, as developed by Diophantus, Brahmagupta and the Bakhshali Manuscript; and
Symbolic algebra, which was initiated by Abū al-Hasan ibn Alī al-Qalasādī and sees its culmination in the work of Gottfried Leibniz.
Cover of the 1621 edition of Diophantus's Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.A timeline of key algebraic developments are as follows:
Circa 1800 BC: The Old Babylonian Strassburg tablet seeks the solution of a quadratic elliptic equation.
Circa 1600 BC: The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script.
Circa 800 BC: Indian mathematician Baudhayana, in his Baudhayana Sulba Sutra, discovers Pythagorean triples algebraically, finds geometric solutions of linear equations and quadratic equations of the forms ax2 = c and ax2 + bx = c, and finds two sets of positive integral solutions to a set of simultaneous Diophantine equations.
Circa 600 BC: Indian mathematician Apastamba, in his Apastamba Sulba Sutra, solves the general linear equation and uses simultaneous Diophantine equations with up to five unknowns.
Circa 300 BC: In Book II of his Elements, Euclid gives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School of geometry.
Circa 300 BC: A geometric construction for the solution of the cubic is sought (doubling the cube problem). It is now well known that the general cubic has no such solution using Euclidean tools.
Circa 100 BC: Algebraic equations are treated in the Chinese mathematics book Jiuzhang suanshu (The Nine Chapters on the Mathematical Art), which contains solutions of linear equations solved using the rule of double false position, geometric solutions of quadratic equations, and the solutions of matrices equivalent to the modern method, to solve systems of simultaneous linear equations.
Circa 100 BC: The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.
Circa 150 AD: Hero of Alexandria treats algebraic equations in three volumes of mathematics.
Circa 200: Diophantus, who lived in Egypt and is often considered the "father of algebra", writes his famous Arithmetica, a work featuring solutions of algebraic equations and on the theory of numbers.
499: Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation and gives integral solutions of simultaneous indeterminate linear equations.
Circa 625: Chinese mathematician Wang Xiaotong finds numerical solutions of cubic equations.
628: Indian mathematician Brahmagupta, in his treatise Brahma Sputa Siddhanta, invents the chakravala method of solving indeterminate quadratic equations, including Pell's equation, and gives rules for solving linear and quadratic equations.
820: The word algebra is derived from operations described in the treatise written by the Persian mathematician Muḥammad ibn Mūsā al-Ḵwārizmī titled Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing") on the systematic solution of linear and quadratic equations. Al-Khwarizmi is often considered as the "father of algebra", much of whose works on reduction was included in the book and added to many methods we have in algebra now.
Circa 850: Persian mathematician al-Mahani conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.
Circa 850: Indian mathematician Mahavira solves various quadratic, cubic, quartic, quintic and higher-order equations, as well as indeterminate quadratic, cubic and higher-order equations.
Circa 990: Persian Abu Bakr al-Karaji, in his treatise al-Fakhri, further develops algebra by extending Al-Khwarizmi's methodology to incorporate integral powers and integral roots of unknown quantities. He replaces geometrical operations of algebra with modern arithmetical operations, and defines the monomials x, x2, x3, ... and 1/x, 1/x2, 1/x3, ... and gives rules for the products of any two of these.
Circa 1050: Chinese mathematician Jia Xian finds numerical solutions of polynomial equations.
1072: Persian mathematician Omar Khayyam develops algebraic geometry and, in the Treatise on Demonstration of Problems of Algebra, gives a complete classification of cubic equations with general geometric solutions found by means of intersecting conic sections.
1114: Indian mathematician Bhaskara, in his Bijaganita (Algebra), recognizes that a positive number has both a positive and negative square root, and solves various cubic, quartic and higher-order polynomial equations, as well as the general quadratic indeterminant equation.
1202: Algebra is introduced to Europe largely through the work of Leonardo Fibonacci of Pisa in his work Liber Abaci.
Circa 1300: Chinese mathematician Zhu Shijie deals with polynomial algebra, solves quadratic equations, simultaneous equations and equations with up to four unknowns, and numerically solves some quartic, quintic and higher-order polynomial equations.
Circa 1400: Indian mathematician Madhava of Sangamagramma finds iterative methods for approximate solution of non-linear equations.
Circa 1450: Arab mathematician Abū al-Hasan ibn Alī al-Qalasādī took "the first steps toward the introduction of algebraic symbolism." He represented mathematical symbols using characters from the Arabic alphabet.[5]
1535: Nicolo Fonta
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PaklovesTurkiye
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KapitaanAli
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India is the term used by Greeks for this landmass and they used it from at least 4th century B.C. They called Indians Indoi.
So there's nothing wrong with saying "Indian mathematician".
It's okay to make fun of Vedic revisionists, but don't be stupid.
Arabian mathematics took a lot from India, especially from the Kerala school of mathematics.
Now you'll tell me the state of Kerala was formed in 1956.
Oops. How dumb of me.
war&peace
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He forgot to mention about the vedic spaceship travelling from one galaxy to another though until recently most of the hindus believed the earth was flat resting on the horns of a very big bull.
wow, I had tough time solving equations with 3 unknowns.
RowdyRathore
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Pakistani are suffering from identity cris since 1947.
Awan68
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Koi sharam hai tum logon men, just keep on pulling history outta ur arse's as u go dont u, the world nor the accepted literary facts give a flying **** what fantasies inferiority complex ridden indians come up with in gao shalas to live with themselves after bieng subjugated by muslims for a thousand years. The simple fact is, u hindus have always been an inferior and nothing culture , always ruled over by other far superior ones through out history. I dont consider u people fit to wash my dogs. Little degenarate slaves of my anscestors. Bloody shameless subhuman gits.
PaklovesTurkiye
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Why argue with him , when the facts supports us.
The Hindu–Arabic numeral system[1] (also called the Arabic numeral system or Hindu numeral system)[2][note 1] is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world. It was an ancient Indian numeral system which was re-introduced in the book On the Calculation with Hindu Numerals written by the medieval-era Iranian mathematician and engineer al-Khwarizmi, whose name was latinized as Algoritmi.[note 2][3] The system later spread to medieval Europe by the High Middle Ages.
If you do have any facts do please do enlighten us. dont derail the thread by unnecessary rubbish trolling. If you think your views are based on fact , write a book , publish it and take it to international conference.
Entire world can get enlightened and applaud you for your deep contribution for progress of mankind. It will also highlight the tremendous education and great thinkers pakistan.
Who knows you might even get the next nobel prize.
Indians only invented zero,oh sorry wicked hindus did it. You can do more than that, dont let your tremendous potential go waste.
any reason why ppl keep asking "pakistan ka matlab kya hai"?
Again this can wash your brain if you have one to start with .
MathFoundations125: Brahmagupta's formula and the Quadruple Quad Formula I
Awan68
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Youtube videos and yahoo forums, i almost feel sorry for u....
PaklovesTurkiye
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Indians invented zero? I can't stans such rubbish...
@Kaptaan Please enlighten us, all if you have time.
Intellectual debate doesn't mean they have inferiority/identity complex...To me, Pakistan means, freedom from hardcore racists/oppressors who were dreaming to rule over us until Jinnah threw them out.
India a term coined by British, used by modern day Indians to take credit from local people/inhabitants. This is all I know.
Since when Greeks used this term?
ok genius, when is your article coming in national geographic or new scientist?
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