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42 relations: Approximations of π, Arithmetic–geometric mean, Bailey–Borwein–Plouffe formula, Basel problem, Bernoulli number, Buckling, Carl Benjamin Boyer, Cauchy's integral formula, Chudnovsky algorithm, Circle, Continued fraction, Cosmological constant, Coulomb's law, Double factorial, Einstein field equations, Euler's continued fraction formula, Euler's identity, Euler's totient function, Falling and rising factorials, Fibonacci number, Gamma function, Gaussian integral, General relativity, Generalized continued fraction, Inverse trigonometric functions, John Machin, Leibniz formula for π, Leonhard Euler, List of topics related to π, Mathematical constant, Pendulum, Permeability (electromagnetism), Pi, Proof that 22/7 exceeds π, Ramanujan–Sato series, Riemann sum, Riemann zeta function, Sphere, Stirling's approximation, Uncertainty principle, Viète's formula, Wallis product.
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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Arithmetic–geometric mean
In mathematics, the arithmetic–geometric mean (AGM) of two positive real numbers and is defined as follows: Call and and: \end Then define the two interdependent sequences and as \end where the square root takes the principal value.
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Bailey–Borwein–Plouffe formula
The Bailey–Borwein–Plouffe formula (BBP formula) is a spigot algorithm for computing the nth binary digit of the mathematical constant pi using base-16 representation.
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Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1734 and read on 5 December 1735 in ''The Saint Petersburg Academy of Sciences''.
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Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
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Buckling
In science, buckling is a mathematical instability that leads to a failure mode.
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Carl Benjamin Boyer
Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was an American historian of sciences, and especially mathematics.
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Cauchy's integral formula
In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis.
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Chudnovsky algorithm
The Chudnovsky algorithm is a fast method for calculating the digits of pi.
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Circle
A circle is a simple closed shape.
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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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Cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Double factorial
In mathematics, the double factorial or semifactorial of a number (denoted by) is the product of all the integers from 1 up to that have the same parity (odd or even) as.
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Einstein field equations
The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.
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Euler's continued fraction formula
In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction.
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Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality where Euler's identity is named after the Swiss mathematician Leonhard Euler.
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Euler's totient function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.
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Falling and rising factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.
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Fibonacci number
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: Often, especially in modern usage, the sequence is extended by one more initial term: By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.
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Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
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Gaussian integral
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line.
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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Generalized continued fraction
In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.
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Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
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John Machin
John Machin (bapt. c. 1686 – June 9, 1751), a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.
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Leibniz formula for π
In mathematics, the Leibniz formula for pi, named after Gottfried Leibniz, states that It is also called Madhava–Leibniz series as it is a special case of a more general series expansion for the inverse tangent function, first discovered by the Indian mathematician Madhava of Sangamagrama in the 14th century, the specific case first published by Leibniz around 1676.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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List of topics related to π
This is a list of topics related to pi, the fundamental mathematical constant.
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Mathematical constant
A mathematical constant is a special number that is "significantly interesting in some way".
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Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely.
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Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself.
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Pi
The number is a mathematical constant.
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Proof that 22/7 exceeds π
Proofs of the famous mathematical result that the rational number is greater than pi (pi) date back to antiquity.
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Ramanujan–Sato series
In mathematics, a Ramanujan–Sato seriesHeng Huat Chan, Song Heng Chan, and Zhiguo Liu, "Domb's numbers and Ramanujan–Sato type series for 1/Pi" (2004)Gert Almkvist and Jesus Guillera, Ramanujan–Sato Like Series (2012) generalizes Ramanujan’s pi formulas such as, to the form by using other well-defined sequences of integers s(k) obeying a certain recurrence relation, sequences which may be expressed in terms of binomial coefficients \tbinom, and A,B,C employing modular forms of higher levels.
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Riemann sum
In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum.
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Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Stirling's approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.
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Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.
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Viète's formula
In mathematics, Viète's formula is the following infinite product of nested radicals representing the mathematical constant pi: It is named after François Viète (1540–1603), who published it in 1593 in his work Variorum de rebus mathematicis responsorum, liber VIII.
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Wallis product
In mathematics, Wallis' product for pi, written down in 1655 by John Wallis, states that \prod_^ \left(\frac \cdot \frac\right).
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References
[1] https://en.wikipedia.org/wiki/List_of_formulae_involving_π
