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Quadratic equation

Index Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to. [1]

124 relations: 'Abd al-Hamīd ibn Turk, Abū Kāmil Shujāʿ ibn Aslam, Abraham bar Hiyya, Algebra, Algebraic equation, Algorithm, American Mathematical Monthly, Arithmetica, Artin–Schreier theory, Babylonian mathematics, Bakhshali manuscript, Berlin Papyrus 6619, Bicentric quadrilateral, Brahmagupta, Carlyle circle, Cartesian coordinate system, Celestial mechanics, Chakravala method, Characteristic (algebra), Chinese mathematics, Circle, Circumscribed circle, Clay tablet, Coefficient, Compass-and-straightedge construction, Completing the square, Complex conjugate, Complex number, Conic section, Coordinate system, Cube root, Cubic function, Degree of a polynomial, Delta (letter), Descartes' theorem, Diophantus, Discriminant, Dissection problem, Domain of a function, Ellipse, Euclid, Ex-tangential quadrilateral, Exponentiation, Factorization, Field (mathematics), Field extension, Finite field, First Babylonian dynasty, Floating-point arithmetic, Fundamental theorem of algebra, ..., Gerolamo Cardano, Golden ratio, Graph of a function, Graphing calculator, Greek language, Greek mathematics, Henry Heaton, Hyperbola, Imaginary unit, Incircle and excircles of a triangle, Indeterminate equation, Indeterminate form, Indian mathematics, Iran, Irrational number, Irreducible polynomial, La Géométrie, Latin, Lill's method, Linear equation, Loss of significance, Mathematical proof, Mathematical table, Mathematics in medieval Islam, Middle Kingdom of Egypt, Monic polynomial, Muhammad ibn Musa al-Khwarizmi, Muller's method, Multiplicity (mathematics), Nested radical, Nth root, Numerical analysis, Numerical stability, Order of magnitude, Parabola, Periodic points of complex quadratic mappings, Plus-minus sign, Polynomial expansion, Programming language, Prosthaphaeresis, Pythagoras, Quadratic formula, Quadratic function, Quadratic irrational number, Quadratic residue, Quartic function, Quintic function, Radius, Rational number, Real number, Regular polygon, René Descartes, Round-off error, Simon Stevin, Sine, Solving quadratic equations with continued fractions, Splitting field, Springer Science+Business Media, Square (algebra), Square number, Square root, Sridhara, Step response, The Nine Chapters on the Mathematical Art, Third Dynasty of Ur, Thomas Carlyle, Trigonometric functions, Unit (ring theory), Univariate, Uta Merzbach, Vertex (curve), Vieta's formulas, Yang Hui, Zero of a function. Expand index (74 more) »

'Abd al-Hamīd ibn Turk

(fl. 830), known also as (ابومحمد عبدالحمید بن واسع بن ترک الجیلی) was a ninth-century Muslim mathematician.

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Abū Kāmil Shujāʿ ibn Aslam

(Latinized as Auoquamel, ابو كامل, also known as al-ḥāsib al-miṣrī—lit. "the Egyptian reckoner") (c. 850 – c. 930) was an Egyptian Muslim mathematician during the Islamic Golden Age.

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Abraham bar Hiyya

(1070 Barcelona, Catalonia – 1136 or 1145 Narbonne, France) was a Jewish mathematician, astronomer and philosopher, also known as Savasorda (from the Arabic صاحب الشرطة Ṣāḥib al-Shurṭa "Chief of the Police") or Abraham Judaeus.

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Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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Arithmetica

Arithmetica (Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD.

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Artin–Schreier theory

In mathematics, Artin–Schreier theory is a branch of Galois theory, specifically a positive characteristic analogue of Kummer theory, for Galois extensions of degree equal to the characteristic p. introduced Artin–Schreier theory for extensions of prime degree p, and generalized it to extensions of prime power degree pn.

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Babylonian mathematics

Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC.

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Bakhshali manuscript

The Bakhshali manuscript is a mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan).

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Berlin Papyrus 6619

The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is an ancient Egyptian papyrus document from the Middle Kingdom, second half of the 12th or 13th dynasty.

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Bicentric quadrilateral

In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle.

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Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

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Carlyle circle

In mathematics, a Carlyle circle (named for Thomas Carlyle) is a certain circle in a coordinate plane associated with a quadratic equation.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

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Chakravala method

The chakravala method (चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation.

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Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.

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Chinese mathematics

Mathematics in China emerged independently by the 11th century BC.

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Circle

A circle is a simple closed shape.

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Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

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Clay tablet

In the Ancient Near East, clay tablets (Akkadian ṭuppu(m) 𒁾) were used as a writing medium, especially for writing in cuneiform, throughout the Bronze Age and well into the Iron Age.

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Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

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Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

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Completing the square

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. Completing the square is used in.

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Complex conjugate

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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Cube root

In mathematics, a cube root of a number x is a number y such that y3.

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Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

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Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

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Delta (letter)

Delta (uppercase Δ, lowercase δ or 𝛿; δέλτα délta) is the fourth letter of the Greek alphabet.

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Descartes' theorem

In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation.

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Diophantus

Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

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Discriminant

In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them.

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Dissection problem

In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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Ellipse

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

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Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Ex-tangential quadrilateral

In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Factorization

In mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Field extension

In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.

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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

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First Babylonian dynasty

The chronology of the first dynasty of Babylonia (also First Babylonian Empire) is debated as there is a Babylonian King List A and a Babylonian King List B. In this chronology, the regnal years of List A are used due to their wide usage.

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Floating-point arithmetic

In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.

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Fundamental theorem of algebra

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

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Gerolamo Cardano

Gerolamo (or Girolamo, or Geronimo) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.

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Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Graphing calculator

A graphing calculator (also graphics / graphic display calculator) is a handheld computer that is capable of plotting graphs, solving simultaneous equations, and performing other tasks with variables.

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Greek language

Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.

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Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

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Henry Heaton

Henry Heaton (or Henry C Heaton) (1846–1927) was a North-American amateur mathematician.

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Hyperbola

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

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Incircle and excircles of a triangle

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

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Indeterminate equation

An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2x.

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Indeterminate form

In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form.

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Indian mathematics

Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.

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Iran

Iran (ایران), also known as Persia, officially the Islamic Republic of Iran (جمهوری اسلامی ایران), is a sovereign state in Western Asia. With over 81 million inhabitants, Iran is the world's 18th-most-populous country. Comprising a land area of, it is the second-largest country in the Middle East and the 17th-largest in the world. Iran is bordered to the northwest by Armenia and the Republic of Azerbaijan, to the north by the Caspian Sea, to the northeast by Turkmenistan, to the east by Afghanistan and Pakistan, to the south by the Persian Gulf and the Gulf of Oman, and to the west by Turkey and Iraq. The country's central location in Eurasia and Western Asia, and its proximity to the Strait of Hormuz, give it geostrategic importance. Tehran is the country's capital and largest city, as well as its leading economic and cultural center. Iran is home to one of the world's oldest civilizations, beginning with the formation of the Elamite kingdoms in the fourth millennium BCE. It was first unified by the Iranian Medes in the seventh century BCE, reaching its greatest territorial size in the sixth century BCE, when Cyrus the Great founded the Achaemenid Empire, which stretched from Eastern Europe to the Indus Valley, becoming one of the largest empires in history. The Iranian realm fell to Alexander the Great in the fourth century BCE and was divided into several Hellenistic states. An Iranian rebellion culminated in the establishment of the Parthian Empire, which was succeeded in the third century CE by the Sasanian Empire, a leading world power for the next four centuries. Arab Muslims conquered the empire in the seventh century CE, displacing the indigenous faiths of Zoroastrianism and Manichaeism with Islam. Iran made major contributions to the Islamic Golden Age that followed, producing many influential figures in art and science. After two centuries, a period of various native Muslim dynasties began, which were later conquered by the Turks and the Mongols. The rise of the Safavids in the 15th century led to the reestablishment of a unified Iranian state and national identity, with the country's conversion to Shia Islam marking a turning point in Iranian and Muslim history. Under Nader Shah, Iran was one of the most powerful states in the 18th century, though by the 19th century, a series of conflicts with the Russian Empire led to significant territorial losses. Popular unrest led to the establishment of a constitutional monarchy and the country's first legislature. A 1953 coup instigated by the United Kingdom and the United States resulted in greater autocracy and growing anti-Western resentment. Subsequent unrest against foreign influence and political repression led to the 1979 Revolution and the establishment of an Islamic republic, a political system that includes elements of a parliamentary democracy vetted and supervised by a theocracy governed by an autocratic "Supreme Leader". During the 1980s, the country was engaged in a war with Iraq, which lasted for almost nine years and resulted in a high number of casualties and economic losses for both sides. According to international reports, Iran's human rights record is exceptionally poor. The regime in Iran is undemocratic, and has frequently persecuted and arrested critics of the government and its Supreme Leader. Women's rights in Iran are described as seriously inadequate, and children's rights have been severely violated, with more child offenders being executed in Iran than in any other country in the world. Since the 2000s, Iran's controversial nuclear program has raised concerns, which is part of the basis of the international sanctions against the country. The Joint Comprehensive Plan of Action, an agreement reached between Iran and the P5+1, was created on 14 July 2015, aimed to loosen the nuclear sanctions in exchange for Iran's restriction in producing enriched uranium. Iran is a founding member of the UN, ECO, NAM, OIC, and OPEC. It is a major regional and middle power, and its large reserves of fossil fuels – which include the world's largest natural gas supply and the fourth-largest proven oil reserves – exert considerable influence in international energy security and the world economy. The country's rich cultural legacy is reflected in part by its 22 UNESCO World Heritage Sites, the third-largest number in Asia and eleventh-largest in the world. Iran is a multicultural country comprising numerous ethnic and linguistic groups, the largest being Persians (61%), Azeris (16%), Kurds (10%), and Lurs (6%).

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Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.

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La Géométrie

La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes.

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Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

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Lill's method

In mathematics, Lill's method is a visual method of finding the real roots of polynomials of any degree.

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Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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Loss of significance

Loss of significance is an undesirable effect in calculations using finite-precision arithmetic such as floating-point arithmetic.

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Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

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Mathematical table

Mathematical tables are lists of numbers showing the results of calculation with varying arguments.

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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) and Indian mathematics (Aryabhata, Brahmagupta).

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Middle Kingdom of Egypt

The Middle Kingdom of Egypt (also known as The Period of Reunification) is the period in the history of ancient Egypt between circa 2050 BC and 1710 BC, stretching from the reunification of Egypt under the impulse of Mentuhotep II of the Eleventh Dynasty to the end of the Twelfth Dynasty.

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Monic polynomial

In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

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Muhammad ibn Musa al-Khwarizmi

There is some confusion in the literature on whether al-Khwārizmī's full name is ابو عبد الله محمد بن موسى الخوارزمي or ابو جعفر محمد بن موسی الخوارزمی.

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Muller's method

Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x).

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Multiplicity (mathematics)

In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.

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Nested radical

In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression.

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Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms.

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Order of magnitude

An order of magnitude is an approximate measure of the number of digits that a number has in the commonly-used base-ten number system.

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Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

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Periodic points of complex quadratic mappings

This article describes periodic points of some complex quadratic maps.

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Plus-minus sign

The plus-minus sign (±) is a mathematical symbol with multiple meanings.

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Polynomial expansion

In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition.

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Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

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Prosthaphaeresis

Prosthaphaeresis (from the Greek προσθαφαίρεσις) was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry.

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Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

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Quadratic formula

In elementary algebra, the quadratic formula is the solution of the quadratic equation.

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Quadratic function

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

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Quadratic irrational number

In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the set of rational numbers.

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Quadratic residue

In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.

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Quartic function

In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

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Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

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Radius

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

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Simon Stevin

Simon Stevin (1548–1620), sometimes called Stevinus, was a Flemish mathematician, physicist and military engineer.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Solving quadratic equations with continued fractions

In mathematics, a quadratic equation is a polynomial equation of the second degree.

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Splitting field

In abstract algebra, a splitting field of a polynomial with coefficients in a field is a smallest field extension of that field over which the polynomial splits or decomposes into linear factors.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

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Square number

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Sridhara

Sridharacharya (শ্রীধর আচার্য; c. 750 CE – c. 930 CE) was an Indian mathematician, Sanskrit pandit and philosopher.

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Step response

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions.

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The Nine Chapters on the Mathematical Art

The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE.

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Third Dynasty of Ur

The terms "Third Dynasty of Ur" and "Neo-Sumerian Empire" refer to both a 22nd to 21st century BC (middle chronology) Sumerian ruling dynasty based in the city of Ur and a short-lived territorial-political state which some historians consider to have been a nascent empire.

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Thomas Carlyle

Thomas Carlyle (4 December 17955 February 1881) was a Scottish philosopher, satirical writer, essayist, translator, historian, mathematician, and teacher.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Unit (ring theory)

In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.

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Univariate

In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable.

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Uta Merzbach

Uta Caecilia Merzbach (February 9, 1933 – June 27, 2017) was a German-American historian of mathematics who became the first curator of mathematical instruments at the Smithsonian Institution.

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Vertex (curve)

In the geometry of planar curves, a vertex is a point of where the first derivative of curvature is zero.

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Vieta's formulas

In mathematics, Vieta's formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.

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Yang Hui

Yang Hui (ca. 1238–1298), courtesy name Qianguang (謙光), was a late-Song dynasty Chinese mathematician from Qiantang (modern Hangzhou, Zhejiang).

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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References

[1] https://en.wikipedia.org/wiki/Quadratic_equation

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