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74 relations: Approximations of π, Archimedes's cattle problem, Bhāskara I, Bhāskara II, Binary quadratic form, Brahmagupta, Brahmagupta's identity, Brahmagupta's problem, Brahmagupta–Fibonacci identity, Carl Ferdinand Degen, Carl Størmer, Chakravala method, Chebyshev polynomials, Class number formula, Continued fraction, Cube (algebra), Culture of Sussex, Daniel Shanks, Diophantine equation, Diophantine set, Dirichlet's approximation theorem, Dirichlet's unit theorem, Fundamental unit (number theory), Generalized continued fraction, Graciano Ricalde Gamboa, Heronian triangle, History of algebra, History of science and technology in the Indian subcontinent, Indeterminate equation, Indian mathematics, Johann Rahn, John Pell, Joseph-Louis Lagrange, Juan de Ortega (mathematician), List of algorithms, List of equations, List of examples of Stigler's law, List of Indian inventions and discoveries, List of misnamed theorems, List of number theory topics, List of scientific equations named after people, Lucas sequence, Möbius transformation, Measurement of a Circle, Methods of computing square roots, Modular group, Narayana Pandit, Norm form, Number theory, Pell, ..., Pell (disambiguation), Pell number, Pierre de Fermat, Polygonal number, Powerful number, Pythagorean triple, Quadratic form, Quadratic integer, Quantum algorithm, Quantum computing, Recurrence relation, Solving quadratic equations with continued fractions, Special right triangle, Square triangular number, Størmer's theorem, Steyning Grammar School, Stigler's law of eponymy, Sudhakara Dvivedi, Sussex, Timeline of calculus and mathematical analysis, Timeline of mathematics, Timeline of number theory, Werner Weber (mathematician), William Brouncker, 2nd Viscount Brouncker. Expand index (24 more) »
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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Archimedes's cattle problem
Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions.
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Bhāskara I
Bhāskara (c. 600 – c. 680) (commonly called Bhaskara I to avoid confusion with the 12th century mathematician Bhāskara II) was a 7th-century mathematician, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.
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Bhāskara II
Bhāskara (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhaskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer.
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Binary quadratic form
In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables where a, b, c are the coefficients.
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Brahmagupta
Brahmagupta (born, died) was an Indian mathematician and astronomer.
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Brahmagupta's identity
In algebra, Brahmagupta's identity says that the product of two numbers of the form a^2+nb^2 is itself a number of that form.
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Brahmagupta's problem
This problem was given in India by the mathematician Brahmagupta in 628 AD in his treatise Brahma Sputa Siddhanta: solve the Pell equation Brahmagupta gave the smallest solution as.
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Brahmagupta–Fibonacci identity
In algebra, the Brahmagupta–Fibonacci identity expresses the product of two sums of two squares as a sum of two squares in two different ways.
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Carl Ferdinand Degen
Carl Ferdinand Degen (1 November 1766 – 8 April 1825) was a Danish mathematician.
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Carl Størmer
Fredrik Carl Mülertz Størmer (3 September 1874 – 13 August 1957) was a Norwegian mathematician and astrophysicist.
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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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Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
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Class number formula
In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function.
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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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Cube (algebra)
In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name.
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Culture of Sussex
The culture of Sussex refers to the pattern of human activity and symbolism associated with Sussex and its people.
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Daniel Shanks
Daniel Shanks (January 17, 1917 – September 6, 1996) was an American mathematician who worked primarily in numerical analysis and number theory.
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Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
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Diophantine set
In mathematics, a Diophantine equation is an equation of the form P(x1,..., xj, y1,..., yk).
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Dirichlet's approximation theorem
In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real number α and any positive integer N, there exists integers p and q such that 1 ≤ q ≤ N and This is a fundamental result in Diophantine approximation, showing that any real number has a sequence of good rational approximations: in fact an immediate consequence is that for a given irrational α, the inequality is satisfied by infinitely many integers p and q. This corollary also shows that the Thue–Siegel–Roth theorem, a result in the other direction, provides essentially the tightest possible bound, in the sense that the bound on rational approximation of algebraic numbers cannot be improved by increasing the exponent beyond 2.
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Dirichlet's unit theorem
In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet.
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Fundamental unit (number theory)
In algebraic number theory, a fundamental unit is a generator (modulo the roots of unity) for the unit group of the ring of integers of a number field, when that group has rank 1 (i.e. when the unit group modulo its torsion subgroup is infinite cyclic).
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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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Graciano Ricalde Gamboa
Mauro Graciano Ricalde Gamboa (November 21, 1873 – November 9, 1942) was a notable Mexican mathematician.
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Heronian triangle
In geometry, a Heronian triangle is a triangle that has side lengths and area that are all integers.
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History of algebra
As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète.
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History of science and technology in the Indian subcontinent
The history of science and technology in the Indian Subcontinent begins with prehistoric human activity in the Indus Valley Civilization to early states and empires.
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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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Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BC until the end of the 18th century.
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Johann Rahn
Johann Rahn (Latinised form Rhonius) (10 March 1622 – 25 May 1676) was a Swiss mathematician who is credited with the first use of the division symbol, ÷ (obelus) and the therefore sign, ∴. The symbols were used in Teutsche Algebra, published in 1659.
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John Pell
John Pell (1 March 1611 – 12 December 1685) was an English mathematician and political agent abroad.
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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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Juan de Ortega (mathematician)
Juan de Ortega (born Palencia, Spain, c. 1480; died c. 1568),M A Catala,, Biography in Dictionary of Scientific Biography (New York 1970-1990).
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List of algorithms
The following is a list of algorithms along with one-line descriptions for each.
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List of equations
This is a list of equations, by Wikipedia page under appropriate bands of maths, science and engineering.
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List of examples of Stigler's law
Stigler's law concerns the supposed tendency of eponymous expressions for scientific discoveries to honor people other than their respective originators.
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List of Indian inventions and discoveries
This list of Indian inventions and discoveries details the inventions, scientific discoveries and contributions of ancient and modern India, including both the ancient and medieval nations in the subcontinent historically referred to as India and the modern Indian state.
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List of misnamed theorems
This is a list of misnamed theorems in mathematics.
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List of number theory topics
This is a list of number theory topics, by Wikipedia page.
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List of scientific equations named after people
This is a list of scientific equations named after people (eponymous equations).
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Lucas sequence
In mathematics, the Lucas sequences U_n(P,Q) and V_n(P, Q) are certain constant-recursive integer sequences that satisfy the recurrence relation where P and Q are fixed integers.
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Möbius transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.
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Measurement of a Circle
Measurement of a Circle or Dimension of the Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) is a treatise that consists of three propositions by Archimedes, ca.
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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 group
In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant.
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Narayana Pandit
Narayana Pandita (নারায়ণ পণ্ডিত; नारायण पण्डित) (1340–1400) was a major mathematician of India.
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Norm form
In mathematics, a norm form is a homogeneous form in n variables constructed from the field norm of a field extension L/K of degree n. That is, writing N for the norm mapping to K, and selecting a basis for L as a vector space over K, the form is given by in variables In number theory norm forms are studied as Diophantine equations, where they generalize, for example, the Pell equation.
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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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Pell
Pell is a surname shared by several notable people, listed below.
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Pell (disambiguation)
Pell may refer to.
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Pell number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2.
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Pierre de Fermat
Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
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Polygonal number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon.
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Powerful number
A powerful number is a positive integer m such that for every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m.
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Pythagorean triple
A Pythagorean triple consists of three positive integers,, and, such that.
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Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
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Quadratic integer
In number theory, quadratic integers are a generalization of the integers to quadratic fields.
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Quantum algorithm
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation.
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Quantum computing
Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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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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Special right triangle
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.
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Square triangular number
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a perfect square.
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Størmer's theorem
In number theory, Størmer's theorem, named after Carl Størmer, gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell equations.
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Steyning Grammar School
Steyning Grammar School is a state comprehensive school in West Sussex, England.
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Stigler's law of eponymy
Stigler's law of eponymy is a process proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication "Stigler’s law of eponymy".
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Sudhakara Dvivedi
Sudhakara Dvivedi (1855–1910) was an Indian scholar in Sanskrit and mathematics.
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Sussex
Sussex, from the Old English Sūþsēaxe (South Saxons), is a historic county in South East England corresponding roughly in area to the ancient Kingdom of Sussex.
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Timeline of calculus and mathematical analysis
A timeline of calculus and mathematical analysis.
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Timeline of mathematics
This is a timeline of pure and applied mathematics history.
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Timeline of number theory
A timeline of number theory.
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Werner Weber (mathematician)
Werner Weber (* January 3, 1906 in Oberstein, near Hamburg, Germany † February 2, 1975) was a German mathematician.
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William Brouncker, 2nd Viscount Brouncker
William Brouncker, 2nd Viscount Brouncker, PRS (1620 – 5 April 1684) was an English mathematician who introduced Brouncker's formula, and was the first President of the Royal Society.
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Redirects here:
Fermat's equation, Pell equation, Pell's equations, Pellian equation, Pells equation.
References
[1] https://en.wikipedia.org/wiki/Pell's_equation
