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Animation depicting the process of completing the square. (Details, animated GIF version)In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1]
Solomon Gandz has described Al-Khwarizmi as the father of Algebra: Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake ...
By the 10th century AD, in the work of Abū al-Wafā' al-Būzjānī, all six trigonometric functions were used. [44] Abu al-Wafa had sine tables in 0.25° increments, to 8 decimal places of accuracy, and accurate tables of tangent values. [44] He also developed the following trigonometric formula: [45]
Al-Khwarizmi is often considered the "father of algebra", for founding algebra as an independent discipline and for introducing the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which was what he ...
Muhammad ibn Musa al-Khwarizmi (9th century) developed a set of formulas that worked for positive solutions. Al-Khwarizmi goes further in providing a full solution to the general quadratic equation, accepting one or two numerical answers for every quadratic equation, while providing geometric proofs in the process. [27]
Al-Jabr ("forcing", "restoring") operation is moving a deficient quantity from one side of the equation to the other side. In an al-Khwarizmi's example (in modern notation), "x 2 = 40x − 4x 2" is transformed by al-Jabr into "5x 2 = 40x". Repeated application of this rule eliminates negative quantities from calculations.
However, al-Khwarizmi did not use symbolic or syncopated algebra but rather "rhetorical algebra" or ancient Greek "geometric algebra" (the ancient Greeks had expressed and solved some particular instances of algebraic equations in terms of geometric properties such as length and area but they did not solve such problems in general; only ...
This is a timeline of pure and applied mathematics history.It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic ...