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https://en.wikipedia.org/wiki/Inverse | Inverse or invert may refer to:
Science and mathematics
Inverse (logic), a type of conditional sentence which is an immediate inference made from another conditional sentence
Additive inverse (negation), the inverse of a number that, when added to the original number, yields zero
Compositional inverse, a function t... |
https://en.wikipedia.org/wiki/Cohomology | In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homo... |
https://en.wikipedia.org/wiki/Solitary%20wave | In mathematics and physics, a solitary wave can refer to
The solitary wave (water waves) or wave of translation, as observed by John Scott Russell in 1834, the prototype for a soliton.
A soliton, a generalization of the wave of translation to general systems of partial differential equations
A topological defect, ... |
https://en.wikipedia.org/wiki/Heron%27s%20formula | In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . If is the semiperimeter of the triangle, the area is,
It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work Metrica, though it was probably known centuries... |
https://en.wikipedia.org/wiki/Brahmagupta%27s%20formula | In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, Bretschneider's formula, can be used with non-cyclic quadrilateral.
Heron'... |
https://en.wikipedia.org/wiki/Cyclic%20quadrilateral | In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the ci... |
https://en.wikipedia.org/wiki/Completeness%20%28statistics%29 | In statistics, completeness is a property of a statistic in relation to a parameterised model for a set of observed data.
A complete statistic T is one for which any proposed distribution on the domain of T is predicted by one or more prior distributions on the model parameter space. In other words, the model space is... |
https://en.wikipedia.org/wiki/Moment-generating%20function | In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative... |
https://en.wikipedia.org/wiki/Orthonormality | In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal unit vectors. A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all v... |
https://en.wikipedia.org/wiki/Main%20diagonal | In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix is the list of entries where . All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones:
An... |
https://en.wikipedia.org/wiki/Orthonormal%20basis | In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the ... |
https://en.wikipedia.org/wiki/Negligible%20set | In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose.
As common examples, finite sets can be ignored when studying the limit of a sequence, and null sets can be ignored when studying the integral of a measurable function.
Negligible sets define several useful concepts ... |
https://en.wikipedia.org/wiki/Riemannian%20geometry | Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in particular, local notions of angle, length of curves, surface ... |
https://en.wikipedia.org/wiki/Jacobian%20matrix%20and%20determinant | In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is ... |
https://en.wikipedia.org/wiki/Einstein%20notation | In mathematics, especially the usage of linear algebra in mathematical physics, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity. As part of mathematics i... |
https://en.wikipedia.org/wiki/Metric%20tensor | In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there. More precisely, a metric tensor at a... |
https://en.wikipedia.org/wiki/Function%20composition | In mathematics, function composition is an operation that takes two functions and , and produces a function such that . In this operation, the function is applied to the result of applying the function to . That is, the functions and are composed to yield a function that maps in domain to in codomain .
Intuit... |
https://en.wikipedia.org/wiki/Levi-Civita%20symbol | In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers , for some positive integer . It is named after the Italian mathematician and physic... |
https://en.wikipedia.org/wiki/Hermite%20polynomials | In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.
The polynomials arise in:
signal processing as Hermitian wavelets for wavelet transform analysis
probability, such as the Edgeworth series, as well as in connection with Brownian motion;
combinatorics, as an example of an Appell... |
https://en.wikipedia.org/wiki/Polynomial%20sequence | In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics, as well as applied m... |
https://en.wikipedia.org/wiki/Discrete%20sine%20transform | In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real ... |
https://en.wikipedia.org/wiki/Legendre%20function | In physical science and mathematics, the Legendre functions , and associated Legendre functions , , and Legendre functions of the second kind, , are all solutions of Legendre's differential equation. The Legendre polynomials and the associated Legendre polynomials are also solutions of the differential equation in spe... |
https://en.wikipedia.org/wiki/Nicholas%20Saunderson | Nicholas Saunderson (20 January 1682 – 19 April 1739) was a blind English scientist and mathematician. According to one historian of statistics, he may have been the earliest discoverer of Bayes' theorem. He worked as Lucasian Professor of Mathematics at Cambridge University, a post also held by Isaac Newton, Charle... |
https://en.wikipedia.org/wiki/Heptadecagon | In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon.
Regular heptadecagon
A regular heptadecagon is represented by the Schläfli symbol {17}.
Construction
As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass an... |
https://en.wikipedia.org/wiki/Long%20line | Long line or longline may refer to:
Long Line, an album by Peter Wolf
Long line (topology), or Alexandroff line, a topological space
Long line (telecommunications), a transmission line in a long-distance communications network
Longline fishing, a commercial fishing technique
AT&T Long Lines, a telecommunications netwo... |
https://en.wikipedia.org/wiki/Hyperspace%20%28disambiguation%29 | Hyperspace is a faster-than-light method of traveling used in science fiction.
Hyperspace or HyperSpace may also refer to:
Mathematics
Hypertopology, a topological space within which some of its elements form another topological space
Higher dimensions, including Kaluza–Klein's 4-dimensional space and Superstring t... |
https://en.wikipedia.org/wiki/Probabilistic%20Turing%20machine | In theoretical computer science, a probabilistic Turing machine is a non-deterministic Turing machine that chooses between the available transitions at each point according to some probability distribution. As a consequence, a probabilistic Turing machine can—unlike a deterministic Turing Machine—have stochastic result... |
https://en.wikipedia.org/wiki/Lagrangian | Lagrangian may refer to:
Mathematics
Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
Lagrangian relaxation, the method of approximating a difficult constrained problem with an easier problem having an enlarged feasible set
Lagrangian dual problem,... |
https://en.wikipedia.org/wiki/Mathematical%20Association%20of%20America | The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many oth... |
https://en.wikipedia.org/wiki/Antisymmetric | Antisymmetric or skew-symmetric may refer to:
Antisymmetry in linguistics
Antisymmetry in physics
Antisymmetric relation in mathematics
Skew-symmetric graph
Self-complementary graph
In mathematics, especially linear algebra, and in theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for m... |
https://en.wikipedia.org/wiki/Erlang%20distribution | The Erlang distribution is a two-parameter family of continuous probability distributions with support . The two parameters are:
a positive integer the "shape", and
a positive real number the "rate". The "scale", the reciprocal of the rate, is sometimes used instead.
The Erlang distribution is the distribution of... |
https://en.wikipedia.org/wiki/Bernoulli%20distribution | In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability . Less formally, it can be thought of as a model for the set of poss... |
https://en.wikipedia.org/wiki/Marko%20Petkov%C5%A1ek | Marko Petkovšek (1955 – 24 March 2023) was a Slovenian mathematician working mainly in symbolic computation.
He was a professor of discrete and computational mathematics at the University of Ljubljana. He is best known for Petkovšek's algorithm, and for the book that he coauthored with Herbert Wilf and Doron Zeilberger... |
https://en.wikipedia.org/wiki/Pierre%20%C3%89mile%20Levasseur | Pierre Émile Levasseur, 3rd Baron Levasseur (8 December 1828 – 10 July 1911), was a French economist, historian, Professor of geography, history and statistics in the Collège de France, at the Conservatoire national des arts et métiers and at the École Libre des Sciences Politiques, known as one of the founders and pro... |
https://en.wikipedia.org/wiki/Binomial%20type | In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities
Many such sequences exist. The set of all such sequences forms a Lie group under t... |
https://en.wikipedia.org/wiki/Quadratic%20residue | 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 ar... |
https://en.wikipedia.org/wiki/Rolle%27s%20theorem | In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the fun... |
https://en.wikipedia.org/wiki/Reflexive%20relation | In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.
An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to po... |
https://en.wikipedia.org/wiki/Transitive%20relation | In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive.
Definition
A homogeneous relation on the set is a transitive relation if,
for all , if and ,... |
https://en.wikipedia.org/wiki/Baire%20space | In mathematics, a topological space is said to be a Baire space if countable unions of closed sets with empty interior also have empty interior.
According to the Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of Baire spaces.
The Baire category theorem combined with the proper... |
https://en.wikipedia.org/wiki/Bell%20number | In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s.... |
https://en.wikipedia.org/wiki/Squaring%20the%20circle | Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidea... |
https://en.wikipedia.org/wiki/Gradient%20descent | In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, b... |
https://en.wikipedia.org/wiki/Orthogonalization | In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ... , vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vec... |
https://en.wikipedia.org/wiki/Principle%20of%20maximum%20entropy | The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information).
Another way of stating this: Take pr... |
https://en.wikipedia.org/wiki/Mean%20squared%20error | In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, correspo... |
https://en.wikipedia.org/wiki/Trapezoid | In geometry, a trapezoid () in North American English, or trapezium () in British English, is a quadrilateral that has at least one pair of parallel sides.
The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the t... |
https://en.wikipedia.org/wiki/MATH-MATIC | MATH-MATIC is the marketing name for the AT-3 (Algebraic Translator 3) compiler, an early programming language for the UNIVAC I and UNIVAC II.
MATH-MATIC was written beginning around 1955 by a team led by Charles Katz under the direction of Grace Hopper. A preliminary manual was produced in 1957 and a final manual the... |
https://en.wikipedia.org/wiki/Standardized%20moment | In probability theory and statistics, a standardized moment of a probability distribution is a moment (often a higher degree central moment) that is normalized, typically by a power of the standard deviation, rendering the moment scale invariant. The shape of different probability distributions can be compared using st... |
https://en.wikipedia.org/wiki/Tensor%20contraction | In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the natural pairing of a finite-dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components of the tensor(s) caused by applying the summation convention to a pair of dummy indice... |
https://en.wikipedia.org/wiki/Adjugate%20matrix | In linear algebra, the adjugate or classical adjoint of a square matrix is the transpose of its cofactor matrix and is denoted by . It is also occasionally known as adjunct matrix, or "adjoint", though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is the conjugat... |
https://en.wikipedia.org/wiki/Covariance%20and%20contravariance%20of%20vectors | In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis. In modern mathematical notation, the role is sometimes swapped.
A simple illustrative case is that of a ve... |
https://en.wikipedia.org/wiki/Spherical%20harmonics | In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields.
Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each f... |
https://en.wikipedia.org/wiki/List%20of%20order%20structures%20in%20mathematics | In mathematics, and more specifically in order theory, several different types of ordered set have been studied.
They include:
Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise
Lattices, partial orders in which each pair of elements has a greatest lower bound and a least u... |
https://en.wikipedia.org/wiki/Predicate | Predicate or predication may refer to:
Predicate (grammar), in linguistics
Predication (philosophy)
several closely related uses in mathematics and formal logic:
Predicate (mathematical logic)
Propositional function
Finitary relation, or n-ary predicate
Boolean-valued function
Syntactic predicate, in formal grammars... |
https://en.wikipedia.org/wiki/Algebraic%20notation | Algebraic notation may refer to:
In mathematics and computers, infix notation, the practice of representing a binary operator and operands with the operator between the two operands (as in "2 + 2")
Algebraic notation (chess), the standard system for recording movement of pieces in a chess game
In linguistics, recur... |
https://en.wikipedia.org/wiki/Euler%20line | In geometry, the Euler line, named after Leonhard Euler (), is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and t... |
https://en.wikipedia.org/wiki/Liouville%E2%80%93Neumann%20series | In mathematics, the Liouville–Neumann series is an infinite series that corresponds to the resolvent formalism technique of solving the Fredholm integral equations in Fredholm theory.
Definition
The Liouville–Neumann (iterative) series is defined as
which, provided that is small enough so that the series converges, ... |
https://en.wikipedia.org/wiki/It%C3%B4%27s%20lemma | In mathematics, Itô's lemma or Itô's formula (also called the Itô-Doeblin formula, especially in the French literature) is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heurist... |
https://en.wikipedia.org/wiki/Directed%20acyclic%20graph | In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed lo... |
https://en.wikipedia.org/wiki/The%20Nine%20Chapters%20on%20the%20Mathematical%20Art | 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. This book is one of the earliest surviving mathematical texts from China, the first being the Suan shu shu (202 BCE – 186 BC... |
https://en.wikipedia.org/wiki/Normal%20number | In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digit... |
https://en.wikipedia.org/wiki/Translation%20%28geometry%29 | In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean s... |
https://en.wikipedia.org/wiki/List%20of%20mathematical%20probabilists | See probabilism for the followers of such a theory in theology or philosophy.
This list contains only probabilists in the sense of mathematicians specializing in probability theory.
This list is incomplete; please add to it.
David Aldous (born 1952)
Siva Athreya
Thomas Bayes (1702–1761) - British mathematician and P... |
https://en.wikipedia.org/wiki/Jean-Pierre%20Serre | Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
Biography
Personal life
Born in Bages, Pyrénées... |
https://en.wikipedia.org/wiki/George%20Peacock | George Peacock FRS (9 April 1791 – 8 November 1858) was an English mathematician and Anglican cleric. He founded what has been called the British algebra of logic.
Early life
Peacock was born on 9 April 1791 at Thornton Hall, Denton, near Darlington, County Durham. His father, Thomas Peacock, was a priest of the Churc... |
https://en.wikipedia.org/wiki/Dyirbal%20language | Dyirbal (also Djirubal) is an Australian Aboriginal language spoken in northeast Queensland by the Dyirbal people. In 2016, the Australian Bureau of Statistics reported that there were 8 speakers of the language. It is a member of the small Dyirbalic branch of the Pama–Nyungan family. It possesses many outstanding fea... |
https://en.wikipedia.org/wiki/Spectrum%20of%20a%20matrix | In mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if is a linear operator on any finite-dimensional vector space, its spectrum is the set of scalars such that is not invertible. The determinant of the matrix equals the product of its eigenvalues. Similarly, the trace of the mat... |
https://en.wikipedia.org/wiki/Spectrum%20%28functional%20analysis%29 | In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number is said to be in the spectrum of a bounded linear operator if
either has no se... |
https://en.wikipedia.org/wiki/Analytical%20Society | The Analytical Society was a group of individuals in early-19th-century Britain whose aim was to promote the use of Leibnizian notation for differentiation in calculus as opposed to the Newton notation for differentiation. The latter system came into being in the 18th century as a convention of Sir Isaac Newton, and wa... |
https://en.wikipedia.org/wiki/Constraint | Constraint may refer to:
Constraint (computer-aided design), a demarcation of geometrical characteristics between two or more entities or solid modeling bodies
Constraint (mathematics), a condition of an optimization problem that the solution must satisfy
Constraint (classical mechanics), a relation between coordina... |
https://en.wikipedia.org/wiki/Isaac%20Todhunter | Isaac Todhunter FRS (23 November 1820 – 1 March 1884), was an English mathematician who is best known today for the books he wrote on mathematics and its history.
Life and work
The son of George Todhunter, a Nonconformist minister, and Mary née Hume, he was born at Rye, Sussex. He was educated at Hastings, where his ... |
https://en.wikipedia.org/wiki/William%20Feller | William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian–American mathematician specializing in probability theory.
Early life and education
Feller was born in Zagreb to Ida Oemichen-Perc, a Croatian–Austrian Catholic, and Eugen Viktor Feller, son of a Polish–Jewish father ... |
https://en.wikipedia.org/wiki/Weibull%20distribution | In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The distribution i... |
https://en.wikipedia.org/wiki/Beta%20distribution | In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the... |
https://en.wikipedia.org/wiki/Gamma%20distribution | In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use:
With a ... |
https://en.wikipedia.org/wiki/Triangulation | In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.
Applications
In surveying
Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point dire... |
https://en.wikipedia.org/wiki/Put%E2%80%93call%20parity | In financial mathematics, the put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to (and hence has the same value as) a single forw... |
https://en.wikipedia.org/wiki/Th%C4%81bit%20ibn%20Qurra | Thābit ibn Qurra (full name: , , ); 826 or 836 – February 19, 901, was a polymath known for his work in mathematics, medicine, astronomy, and translation. He lived in Baghdad in the second half of the ninth century during the time of the Abbasid Caliphate.
Thābit ibn Qurra made important discoveries in algebra, geomet... |
https://en.wikipedia.org/wiki/6 | 6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.
In mathematics
Six is the smallest positive integer which is neither a square number nor a prime number. It is the second smallest composite number after four, equal to the sum and the product of its th... |
https://en.wikipedia.org/wiki/Lucky%20number | In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural n... |
https://en.wikipedia.org/wiki/15%20%28number%29 | 15 (fifteen) is the natural number following 14 and preceding 16.
Mathematics
15 is:
The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime; its proper divisors are , , and , so the first of the form (3.q), where q is a higher prime.
a deficient number, a lucky number, a... |
https://en.wikipedia.org/wiki/20%20%28number%29 | 20 (twenty; Roman numeral XX) is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.
In mathematics
Twenty is a pronic number, as it is the product of consecutive integers, namely 4 and 5. It is the third composite number to be the product of a squared prime ... |
https://en.wikipedia.org/wiki/17%20%28number%29 | 17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.
Seventeen is the sum of the first four prime numbers.
In mathematics
Seventeen is the seventh prime number, which makes it the fourth super-prime, as seven is itself prime. It forms a twin prime with 19, a cousin prime with 13, ... |
https://en.wikipedia.org/wiki/19%20%28number%29 | 19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
Mathematics
is the eighth prime number, and forms a sexy prime with 13, a twin prime with 17, and a cousin prime with 23. It is the third full reptend prime in decimal, the fifth central trinomial coefficient, and the seventh M... |
https://en.wikipedia.org/wiki/18%20%28number%29 | 18 (eighteen) is the natural number following 17 and preceding 19.
In mathematics
Eighteen is the tenth composite number, its divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semiperfect number. Eighteen is the first inverted square-prime of the form p·q2.
In base ten... |
https://en.wikipedia.org/wiki/Menger%20sponge | In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his stu... |
https://en.wikipedia.org/wiki/Quotient%20of%20a%20formal%20language | In mathematics and computer science, the right quotient (or simply quotient) of a language with respect to language is the language consisting of strings w such that wx is in for some string x in Formally:
In other words, we take all the strings in that have a suffix in , and remove this suffix.
Similarly, the l... |
https://en.wikipedia.org/wiki/Quotient%20rule | In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let , where both and are differentiable and The quotient rule states that the derivative of is
It is provable in many ways by using other derivative rules.
Examples
Example 1: Bas... |
https://en.wikipedia.org/wiki/21%20%28number%29 | 21 (twenty-one) is the natural number following 20 and preceding 22.
The current century is the 21st century AD, under the Gregorian calendar.
In mathematics
Twenty-one is the fifth distinct semiprime, and the second of the form where is a higher prime.
As a biprime with proper divisors 1, 3 and 7, twenty-one has ... |
https://en.wikipedia.org/wiki/Su%20Buqing | Su Buqing, also spelled Su Buchin (; September 23, 1902 – March 17, 2003), was a Chinese mathematician, educator and poet. He was the founder of differential geometry in China, and served as president of Fudan University and honorary chairman of the Chinese Mathematical Society.
Early Life
Su was born in Pingyang Coun... |
https://en.wikipedia.org/wiki/Empty%20sum | In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero.
The natural way to extend non-empty sums is to let the empty sum be the additive identity.
Let , , , ... be a sequence of numbers, and let
be the sum of the first m terms of the sequence. This satisfies the recurrence
pr... |
https://en.wikipedia.org/wiki/Reflexive%20space | In the area of mathematics known as functional analysis, a reflexive space is a locally convex topological vector space (TVS) for which the canonical evaluation map from into its bidual (which is the strong dual of the strong dual of ) is an isomorphism of TVSs.
Since a normable TVS is reflexive if and only if it is ... |
https://en.wikipedia.org/wiki/Invariance%20of%20domain | Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space .
It states:
If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and .
The theorem and its proof are due to L. E. J. Brouwer, published in 1912.
The proof uses to... |
https://en.wikipedia.org/wiki/Direct%20limit | In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any category. The way they are put together is specified by a system of homomorphis... |
https://en.wikipedia.org/wiki/Tangent%20bundle | In differential geometry, the tangent bundle of a differentiable manifold is a manifold which assembles all the tangent vectors in . As a set, it is given by the disjoint union of the tangent spaces of . That is,
where denotes the tangent space to at the point . So, an element of can be thought of as a pair , w... |
https://en.wikipedia.org/wiki/Enumeration | An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to... |
https://en.wikipedia.org/wiki/Algebraic%20enumeration | Algebraic enumeration is a subfield of enumeration that deals with finding exact formulas for the number of combinatorial objects of a given type, rather than estimating this number asymptotically. Methods of finding these formulas include generating functions and the solution of recurrence relations.
References
Enum... |
https://en.wikipedia.org/wiki/Homotopy | In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from "same, similar" and "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy (, ; , ) between the two functions. A notable use of homotopy ... |
https://en.wikipedia.org/wiki/Whitehead%20problem | In group theory, a branch of abstract algebra, the Whitehead problem is the following question:
Saharon Shelah proved that Whitehead's problem is independent of ZFC, the standard axioms of set theory.
Refinement
Assume that A is an abelian group such that every short exact sequence
must split if B is also abelian. T... |
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