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In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side ( and, if the setting is a Euclidean space, then the inequality is strict if the triangle is non-degenerate ).< ref name = Khamsi >
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mathematics and triangle
In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT ( P ) such that no point in P is inside the circumcircle of any triangle in DT ( P ).
Although Escher did not have mathematical training — his understanding of mathematics was largely visual and intuitive — Escher's work had a strong mathematical component, and more than a few of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle.
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
For example, a typical mathematics question will not ask what the second leg of a right-angled triangle is when the lengths of the first leg and the hypotenuse are given.
In mathematics, an ultrametric space is a special kind of metric space in which the triangle inequality is replaced with.
* Golden triangle ( mathematics ), in reference to the golden ratio
Apian's work included in mathematics — in 1527 he published a variation of Pascal's triangle, and in 1534 a table of sines — as well as astronomy.
This treatise later had a " strong influence on European mathematics ", and his " definition of ratios as numbers " and " method of solving a spherical triangle when all sides are unknown " are likely to have influenced Regiomontanus.
In recreational mathematics, a polydrafter is a polyform with a triangle as the base form.
In recreational mathematics, a polyabolo ( also known as a polytan ) is a polyform with an isosceles right triangle as the base form.
In mathematics, the Kantorovich inequality is a particular case of the Cauchy-Schwarz inequality, which is itself a generalization of the triangle inequality.
In mathematics, the Heilbronn triangle problem is a typical question in the area of irregularities of distribution, within elementary geometry.
In mathematics, the term hyperbolic triangle has more than one meaning.
In mathematics, a δ-hyperbolic space is a geodesic metric space in which every geodesic triangle is δ-thin.
Becker, as did several others, emphasized the " crisis " in Greek mathematics occasioned by the discovery of incommensurability of the side of the pentagon ( or in the later, simpler proofs, the triangle ) by Hippasus of Metapontum, and the threat of ( literally ) " irrational " numbers.
In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.
In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
In mathematics, a congruent number is a positive integer that is the area of a right triangle with three rational number sides.
Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, it is named after the ancient Greek mathematician Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem.
Another approach to find a point within the triangle, from where sum of the distances to the vertices of triangle is minimum, is to use one of the optimization ( mathematics ) methods.
mathematics and inequality
In mathematics, the Cauchy – Schwarz inequality ( also known as the Bunyakovsky inequality, the Schwarz inequality, or the Cauchy – Bunyakovsky – Schwarz inequality, or Cauchy – Bunyakovsky inequality ), is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, and other areas.
In mathematics, an inequation is a statement that an inequality holds between two values.
In mathematics, an inequality is a relation that holds between two values when they are different ( see also: equality ).
# REDIRECT inequality ( mathematics )
In mathematics, Fatou's lemma establishes an inequality relating the integral ( in the sense of Lebesgue ) of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions.
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
In mathematics, Yamamoto may refer to the Lubell – Yamamoto – Meshalkin inequality, named for Koichi Yamamoto et al.
In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations.
* Cauchy – Schwarz inequality, a concept in inner product space mathematics
* Hardy's inequality in mathematics
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.
In mathematics, Hadamard's inequality, first published by Jacques Hadamard in 1893, is a bound on the determinant of a matrix whose entries are complex numbers in terms of the lengths of its column vectors.
In combinatorial mathematics, the Lubell – Yamamoto – Meshalkin inequality, more commonly known as the LYM inequality, is an inequality on the sizes of sets in a Sperner family, proved by,,, and.
mathematics and states
His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.
In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.
In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.
In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
In mathematics, specifically commutative algebra, Hilbert's basis theorem states that every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated.
Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle which states that for any proposition, either that proposition is true, or its negation is.
The thought experiment illustrates quantum mechanics and the mathematics necessary to describe quantum states.
The thesis states that Turing machines indeed capture the informal notion of effective method in logic and mathematics, and provide a precise definition of an algorithm or ' mechanical procedure '.
The Church – Turing thesis states that this is a law of mathematics — that a universal Turing machine can, in principle, perform any calculation that any other programmable computer can.
Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order ( number of elements ) of every subgroup H of G divides the order of G. The theorem is named after Joseph Lagrange.
In mathematics, the well-ordering theorem states that every set can be well-ordered.
Hilbert's goals of creating a system of mathematics that is both complete and consistent were dealt a fatal blow by the second of Gödel's incompleteness theorems, which states that sufficiently expressive consistent axiom systems can never prove their own consistency.
During the 290s BC, Hellenistic civilization begins its emergence throughout the successor states of the former Argead Macedonian Empire of Alexander the Great resulting in the diffusion of Greek culture throughout the Ancient world and advances in Science, mathematics, philosophy and etc.
In mathematics, Tait's conjecture states that " Every 3-connected planar cubic graph has a Hamiltonian cycle ( along the edges ) through all its vertices ".
In mathematics, the convolution theorem states that under suitable
In mathematics, de Moivre's formula ( a. k. a. 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 ) x and integer n it holds that
The Sumerians were incredibly advanced: as well as inventing writing, they also invented early forms of mathematics, early wheeled vehicles, astronomy, astrology and the calendar and they created the first city states / nations such as Uruk, Ur, Lagash, Isin, Umma, Eridu, Nippur and Larsa.
In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact.
In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements for short exact sequence are equivalent.
In mathematics, the parity of an object states whether it is even or odd.
In mathematics, the well-ordering principle states that every non-empty set of positive integers contains a smallest element.
In mathematics the modularity theorem ( formerly called the Taniyama – Shimura – Weil conjecture and several related names ) states that elliptic curves over the field of rational numbers are related to modular forms.
In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space.
In engineering, mathematics and the physical and biological sciences, common terms for the points around which the system gravitates include: attractors, stable states, eigenstates / eigenfunctions, equilibrium points, and setpoints.
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