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33 relations: Algorithm, Approximations of π, Carl Friedrich Gauss, Elementary function, Elliptic filter, Elliptic integral, Eugene Salamin (mathematician), Exponential function, Gauss's constant, Gauss–Legendre algorithm, Generalized mean, Geometric mean, Geometric–harmonic mean, Harmonic mean, Inequality of arithmetic and geometric means, Jacobi elliptic functions, Joseph-Louis Lagrange, L'Enseignement Mathématique, Limit of a sequence, Mathematical constant, Mathematics, Monotone convergence theorem, Pi, Principal value, Q.E.D., Quarter period, Real number, Richard P. Brent, Sequence, Square root of 2, Time complexity, Transcendental function, Trigonometric functions.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Approximations of π
Approximations for the mathematical constant pi in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes).
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
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Elementary function
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations, exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of ''n''th roots).
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Elliptic filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter with equalized ripple (equiripple) behavior in both the passband and the stopband.
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Elliptic integral
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.
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Eugene Salamin (mathematician)
Eugene Salamin is a mathematician who discovered (independently with Richard Brent) the Salamin–Brent algorithm, used in high-precision calculation of pi.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Gauss's constant
In mathematics, Gauss's constant, denoted by G, is defined as the reciprocal of the arithmetic–geometric mean of 1 and the square root of 2: The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered that so that where Β denotes the beta function.
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Gauss–Legendre algorithm
The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π. However, the drawback is that it is computer memory-intensive and therefore sometimes Machin-like formulas are used instead.
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Generalized mean
In mathematics, generalized means are a family of functions for aggregating sets of numbers, that include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means).
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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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Geometric–harmonic mean
In mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0.
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Harmonic mean
In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.
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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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Jacobi elliptic functions
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance.
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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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L'Enseignement Mathématique
L’Enseignement Mathématique is a journal for mathematics and mathematics education.
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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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Mathematical constant
A mathematical constant is a special number that is "significantly interesting in some way".
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Monotone convergence theorem
In the mathematical field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the convergence of monotonic sequences (sequences that are increasing or decreasing) that are also bounded.
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Pi
The number is a mathematical constant.
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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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Q.E.D.
Q.E.D. (also written QED and QED) is an initialism of the Latin phrase quod erat demonstrandum meaning "what was to be demonstrated" or "what was to be shown." Some may also use a less direct translation instead: "thus it has been demonstrated." Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.
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Quarter period
In mathematics, the quarter periods K(m) and iK ′(m) are special functions that appear in the theory of elliptic functions.
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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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Richard P. Brent
Richard Peirce Brent (born 20 April 1946, Melbourne) is an Australian mathematician and computer scientist.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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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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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Transcendental function
A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
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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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Redirects here:
AGM method, Arithmetic geometric mean, Arithmetic-geometric mean, Arithmetic-geometric mean process, The AGM method of Gauss.
References
[1] https://en.wikipedia.org/wiki/Arithmetic–geometric_mean
