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Square root

Index 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. [1]

160 relations: Absolute value, Additive inverse, Algebra, Algebraic number, Apotome (mathematics), Approximation theory, Area, Ars Magna (Gerolamo Cardano), Aryabhata, Aryabhatiya, Baudhayana sutras, Berlin Papyrus 6619, Book on Numbers and Computation, Branch point, C (programming language), C++, Calculator, Cartesian coordinate system, Characteristic (algebra), Christoph Rudolff, Common logarithm, Commutative ring, Complex logarithm, Complex number, Computational complexity theory, Continued fraction, Continuous function, Cube root, David Eugene Smith, De Moivre's formula, Decimal representation, Derivative, Diagonal, Difference of two squares, Division algebra, Electric current, Endomorphism ring, Euclid, Euclid's Elements, Euclidean distance, Exponentiation, Field (mathematics), Finite field, Floruit, Function (mathematics), Geometric mean, Geometry, Gerolamo Cardano, Greek mathematics, Group (mathematics), ..., Han dynasty, Hero of Alexandria, Hilbert space, Hippasus, History of India, Holomorphic function, Hypotenuse, Ibn al-Yasamin, Identity matrix, If and only if, Imaginary unit, Inequality of arithmetic and geometric means, Integer, Integer square root, Integral domain, Inverter (logic gate), Irrational number, Iterative method, JavaScript, Joseph-Louis Lagrange, Kahun Papyri, La Géométrie, Limit of a sequence, List of square roots, Logic gate, Mathematical fallacy, Mathematical induction, Mathematics, Matrix (mathematics), Methods of computing square roots, Modular arithmetic, Natural logarithm, Natural number, Nested radical, Newton's method, Norm (mathematics), Nothing up my sleeve number, Nth root, Number theory, Penrose method, Periodic continued fraction, PHP, Physics, Piecewise linear function, Pietro di Giacomo Cataneo, Plus-minus sign, Polar coordinate system, Polynomial, Positional notation, Positive-definite matrix, Prime number, Principal value, Product (mathematics), Programming language, Pythagoreanism, Python (programming language), Quadratic equation, Quadratic field, Quadratic integer, Quadratic irrational number, Quadratic residue, Quantum computing, Quaternion, Radical symbol, Rate of convergence, Ratio, Rational number, Real number, Regiomontanus, René Descartes, Repeating decimal, Rhind Mathematical Papyrus, Riemann surface, Right triangle, Ring (mathematics), Root of unity, Set (mathematics), Sexagesimal, SHA-1, SHA-2, Shifting nth root algorithm, Shulba Sutras, Sign function, Similarity (geometry), Slide rule, Software, Solving quadratic equations with continued fractions, Spiral of Theodorus, Spreadsheet, Square, Square (algebra), Square number, Square root of 2, Square root of 3, Square root of 5, Square-free integer, Standard deviation, Subroutine, Subset, System of equations, Tangent, Taylor series, Thales's theorem, Theaetetus (mathematician), Trigonometric functions, Two-dimensional space, Unit sphere, Unit square, Yale Babylonian Collection, Zero divisor. Expand index (110 more) »

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Additive inverse

In mathematics, the additive inverse of a number is the number that, when added to, yields zero.

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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 number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

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Apotome (mathematics)

In the historical study of mathematics, an apotome is a line segment formed from a longer line segment by breaking it into two parts, one of which is commensurable only in power to the whole; the other part is the apotome.

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Approximation theory

In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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Ars Magna (Gerolamo Cardano)

The Ars Magna ("The Great Art") is an important Latin-language book on algebra written by Girolamo Cardano.

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Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

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Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.

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Baudhayana sutras

The Baudhayana sūtras are a group of Vedic Sanskrit texts which cover dharma, daily ritual, mathematics, etc.

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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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Book on Numbers and Computation

The Book on Numbers and Computation, or the Writings on Reckoning, is one of the earliest known Chinese mathematical treatises.

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Branch point

In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.

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C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

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C++ ("see plus plus") is a general-purpose programming language.

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An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.

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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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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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Christoph Rudolff

Christoph Rudolff (born 1499 in Jawor, Silesia, died 1545 in Vienna) was the author of the first German textbook on algebra.

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Common logarithm

In mathematics, the common logarithm is the logarithm with base 10.

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Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

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Complex logarithm

In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which.

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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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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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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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David Eugene Smith

David Eugene Smith (January 21, 1860 – July 29, 1944) was an American mathematician, educator, and editor.

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De Moivre's formula

In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) and integer it holds that where is the imaginary unit.

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Decimal representation

A decimal representation of a non-negative real number r is an expression in the form of a series, traditionally written as a sum where a0 is a nonnegative integer, and a1, a2,...

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The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

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Difference of two squares

In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.

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Division algebra

In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.

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Electric current

An electric current is a flow of electric charge.

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Endomorphism ring

In abstract algebra, the endomorphism ring of an abelian group X, denoted by End(X), is the set of all endomorphisms of X (i.e., the set of all homomorphisms of X into itself) endowed with an addition operation defined by pointwise addition of functions and a multiplication operation defined by function composition.

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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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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.

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

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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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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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Floruit, abbreviated fl. (or occasionally, flor.), Latin for "he/she flourished", denotes a date or period during which a person was known to have been alive or active.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Geometric mean

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

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Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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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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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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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Han dynasty

The Han dynasty was the second imperial dynasty of China (206 BC–220 AD), preceded by the Qin dynasty (221–206 BC) and succeeded by the Three Kingdoms period (220–280 AD). Spanning over four centuries, the Han period is considered a golden age in Chinese history. To this day, China's majority ethnic group refers to themselves as the "Han Chinese" and the Chinese script is referred to as "Han characters". It was founded by the rebel leader Liu Bang, known posthumously as Emperor Gaozu of Han, and briefly interrupted by the Xin dynasty (9–23 AD) of the former regent Wang Mang. This interregnum separates the Han dynasty into two periods: the Western Han or Former Han (206 BC–9 AD) and the Eastern Han or Later Han (25–220 AD). The emperor was at the pinnacle of Han society. He presided over the Han government but shared power with both the nobility and appointed ministers who came largely from the scholarly gentry class. The Han Empire was divided into areas directly controlled by the central government using an innovation inherited from the Qin known as commanderies, and a number of semi-autonomous kingdoms. These kingdoms gradually lost all vestiges of their independence, particularly following the Rebellion of the Seven States. From the reign of Emperor Wu (r. 141–87 BC) onward, the Chinese court officially sponsored Confucianism in education and court politics, synthesized with the cosmology of later scholars such as Dong Zhongshu. This policy endured until the fall of the Qing dynasty in 1911 AD. The Han dynasty saw an age of economic prosperity and witnessed a significant growth of the money economy first established during the Zhou dynasty (c. 1050–256 BC). The coinage issued by the central government mint in 119 BC remained the standard coinage of China until the Tang dynasty (618–907 AD). The period saw a number of limited institutional innovations. To finance its military campaigns and the settlement of newly conquered frontier territories, the Han government nationalized the private salt and iron industries in 117 BC, but these government monopolies were repealed during the Eastern Han dynasty. Science and technology during the Han period saw significant advances, including the process of papermaking, the nautical steering ship rudder, the use of negative numbers in mathematics, the raised-relief map, the hydraulic-powered armillary sphere for astronomy, and a seismometer for measuring earthquakes employing an inverted pendulum. The Xiongnu, a nomadic steppe confederation, defeated the Han in 200 BC and forced the Han to submit as a de facto inferior partner, but continued their raids on the Han borders. Emperor Wu launched several military campaigns against them. The ultimate Han victory in these wars eventually forced the Xiongnu to accept vassal status as Han tributaries. These campaigns expanded Han sovereignty into the Tarim Basin of Central Asia, divided the Xiongnu into two separate confederations, and helped establish the vast trade network known as the Silk Road, which reached as far as the Mediterranean world. The territories north of Han's borders were quickly overrun by the nomadic Xianbei confederation. Emperor Wu also launched successful military expeditions in the south, annexing Nanyue in 111 BC and Dian in 109 BC, and in the Korean Peninsula where the Xuantu and Lelang Commanderies were established in 108 BC. After 92 AD, the palace eunuchs increasingly involved themselves in court politics, engaging in violent power struggles between the various consort clans of the empresses and empresses dowager, causing the Han's ultimate downfall. Imperial authority was also seriously challenged by large Daoist religious societies which instigated the Yellow Turban Rebellion and the Five Pecks of Rice Rebellion. Following the death of Emperor Ling (r. 168–189 AD), the palace eunuchs suffered wholesale massacre by military officers, allowing members of the aristocracy and military governors to become warlords and divide the empire. When Cao Pi, King of Wei, usurped the throne from Emperor Xian, the Han dynasty would eventually collapse and ceased to exist.

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Hero of Alexandria

Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.

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Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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Hippasus of Metapontum (Ἵππασος ὁ Μεταποντῖνος, Híppasos; fl. 5th century BC), was a Pythagorean philosopher.

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History of India

The history of India includes the prehistoric settlements and societies in the Indian subcontinent; the advancement of civilisation from the Indus Valley Civilisation to the eventual blending of the Indo-Aryan culture to form the Vedic Civilisation; the rise of Hinduism, Jainism and Buddhism;Sanderson, Alexis (2009), "The Śaiva Age: The Rise and Dominance of Śaivism during the Early Medieval Period." In: Genesis and Development of Tantrism, edited by Shingo Einoo, Tokyo: Institute of Oriental Culture, University of Tokyo, 2009.

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Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

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In geometry, a hypotenuse (rarely: hypothenuse) is the longest side of a right-angled triangle, the side opposite of the right angle.

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Ibn al-Yasamin

Abu Muhammad 'Abdallah ibn Muhammad ibn Hajjaj ibn al-Yasmin al-Adrini al-Ishbili (died 1204) more commonly known as ibn al-Yasmin, was Berber mathematician.

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Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Imaginary unit

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

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Inequality of arithmetic and geometric means

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

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An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Integer square root

In number theory, the integer square root (isqrt) of a positive integer n is the positive integer m which is the greatest integer less than or equal to the square root of n, For example, \mbox(27).

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Integral domain

In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

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Inverter (logic gate)

In digital logic, an inverter or NOT gate is a logic gate which implements logical negation.

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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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Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

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JavaScript, often abbreviated as JS, is a high-level, interpreted programming language.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Kahun Papyri

The Kahun Papyri (KP) (also Petrie Papyri or Lahun Papyri) are a collection of ancient Egyptian texts discussing administrative, mathematical and medical topics.

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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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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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List of square roots

This is a list of notable square roots.

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Logic gate

In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output.

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Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy.

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Mathematical induction

Mathematical induction is a mathematical proof technique.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Methods of computing square roots

In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a non-negative real number.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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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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Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Nothing up my sleeve number

In cryptography, nothing-up-my-sleeve numbers are any numbers which, by their construction, are above suspicion of hidden properties.

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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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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Penrose method

The Penrose method (or square-root method) is a method devised in 1946 by Professor Lionel Penrose for allocating the voting weights of delegations (possibly a single representative) in decision-making bodies proportional to the square root of the population represented by this delegation. This is justified by the fact, that due to the square root law of Penrose, the a priori voting power (as defined by the Penrose–Banzhaf index) of a member of a voting body is inversely proportional to the square root of its size. Under certain conditions, this allocation achieves equal voting powers for all people represented, independent of the size of their constituency. Proportional allocation would result in excessive voting powers for the electorates of larger constituencies. A precondition for the appropriateness of the method is en bloc voting of the delegations in the decision-making body: a delegation cannot split its votes; rather, each delegation has just a single vote to which weights are applied proportional to the square root of the population they represent. Another precondition is that the opinions of the people represented are statistically independent. The representativity of each delegation results from statistical fluctuations within the country, and then, according to Penrose, "small electorate are likely to obtain more representative governments than large electorates." A mathematical formulation of this idea results in the square root rule. The Penrose method is not currently being used for any notable decision-making body, but it has been proposed for apportioning representation in a United Nations Parliamentary Assembly, and for voting in the Council of the European Union. Other bodies where the Penrose method could be appropriate include the US Presidential Electoral College and the Bundesrat of Germany.

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Periodic continued fraction

In mathematics, an infinite periodic continued fraction is a continued fraction that can be placed in the form x.

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PHP: Hypertext Preprocessor (or simply PHP) is a server-side scripting language designed for Web development, but also used as a general-purpose programming language.

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Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Piecewise linear function

In mathematics, a piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.

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Pietro di Giacomo Cataneo

Pietro di Giacomo Cataneo (c. 1510 in Siena-c. 1574) was a 16th-century Italian architect.

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Plus-minus sign

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

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers.

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Positive-definite matrix

In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Principal value

In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.

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Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

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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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Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

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Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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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.

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Quadratic field

In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q, the rational numbers.

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Quadratic integer

In number theory, quadratic integers are a generalization of the integers to quadratic fields.

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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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Quantum computing

Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.

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In mathematics, the quaternions are a number system that extends the complex numbers.

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Radical symbol

In mathematics, the radical sign or radical symbol or root symbol is a symbol for the square root or higher-order root of a number.

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Rate of convergence

In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.

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In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

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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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Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus, was a mathematician and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg.

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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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Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

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Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

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Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Sexagesimal (base 60) is a numeral system with sixty as its base.

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In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographic hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest - typically rendered as a hexadecimal number, 40 digits long.

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SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA).

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Shifting nth root algorithm

The shifting nth root algorithm is an algorithm for extracting the ''n''th root of a positive real number which proceeds iteratively by shifting in n digits of the radicand, starting with the most significant, and produces one digit of the root on each iteration, in a manner similar to long division.

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Shulba Sutras

The Shulba Sutras or Śulbasūtras (Sanskrit: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.

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Sign function

In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

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Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

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Slide rule

The slide rule, also known colloquially in the United States as a slipstick, is a mechanical analog computer.

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Computer software, or simply software, is a generic term that refers to a collection of data or computer instructions that tell the computer how to work, in contrast to the physical hardware from which the system is built, that actually performs the work.

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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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Spiral of Theodorus

In geometry, the spiral of Theodorus (also called square root spiral, Einstein spiral or Pythagorean spiral).

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A spreadsheet is an interactive computer application for organization, analysis and storage of data in tabular form.

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In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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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 of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.

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Square root of 3

The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3.

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Square root of 5

The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5.

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Square-free integer

In mathematics, a square-free integer is an integer which is divisible by no perfect square other than 1.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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In computer programming, a subroutine is a sequence of program instructions that performs a specific task, packaged as a unit.

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In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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System of equations

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

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In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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Thales's theorem

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, then the angle ∠ABC is a right angle.

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Theaetetus (mathematician)

Theaetetus of Athens (Θεαίτητος; c. 417 – 369 BC), possibly the son of Euphronius of the Athenian deme Sunium, was a Greek mathematician.

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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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Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

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Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.

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Unit square

In mathematics, a unit square is a square whose sides have length.

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Yale Babylonian Collection

Comprising some 45,000 items, the Yale Babylonian Collection is an independent branch of the Yale University Library housed on the Yale University campus in Sterling Memorial Library at New Haven, Connecticut, United States.

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Zero divisor

In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.

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

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