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In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set.
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mathematics and hyperbola
In mathematics, a hyperbolic angle is a geometric figure that divides a hyperbola.
mathematics and is
This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.
Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.
But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.
Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.
In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.
So, too, is the mathematical competence of a college graduate who has majored in mathematics.
The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.
In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.
The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.
In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.
The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.
In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".
The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.
The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.
:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.
Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.
One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.
There is no prize awarded for mathematics, but see Abel Prize.
mathematics and curve
Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level when proving null and alternative hypotheses.
In mathematics, an ellipse ( from Greek ἔλλειψις elleipsis, a " falling short ") is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve.
Points through which curve is spline ( mathematics ) | splined are red ; the blue curve connecting them is interpolation.
* Integration, in mathematics, a fundamental concept of calculus — the operation of calculating the area between the curve of a function on the x-axis or y-axis
* Meander ( mathematics ), a self-avoiding closed curve which intersects a line a number of times
As a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point.
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.
In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point.
In mathematics, a curve ( also called a curved line in older texts ) is, generally speaking, an object similar to a line but which is not required to be straight.
In mathematics, a Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral.
In mathematics, a helix is a curve in 3-dimensional space.
* Area under the curve, in mathematics, including:
In mathematics, the Menger sponge is a fractal curve.
In mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. It is named after George Green, and is the two-dimensional special case of the more general Stokes ' theorem.
In the branch of mathematics known as topology, the topologist's sine curve is a topological space with several interesting properties that make it an important textbook example.
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.
In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line ( the axis ) that lies on the same plane.
In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold together with the structure of an intrinsic quasimetric space in which the length of any rectifiable curve is given by the length functional
* Cubic plane curve ( mathematics ), a plane algebraic curve C defined by a cubic equation
mathematics and specifically
In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.
In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of X ; this is known as the σ-algebra of Borel sets.
In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.
* Change of any variable quantity, in mathematics and the sciences ( More specifically, the difference operator.
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.
In mathematics, and more specifically set theory, the empty set is the unique set having no elements ; its size or cardinality ( count of elements in a set ) is zero.
In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.
In mathematics, more specifically algebraic topology, the fundamental group ( defined by Henri Poincaré in his article Analysis Situs, published in 1895 ) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
In mathematics, specifically group theory, a quotient group ( or factor group ) is a group obtained by identifying together elements of a larger group using an equivalence relation.
In pure mathematics, the magnitude of a googolplex could be related to other forms of large-number notation such as tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation, though neither googol nor googolplex are anywhere near the largest representable or even specifically named numbers.
In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
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.
In mathematics, more specifically in general topology and related branches, a net or Moore – Smith sequence is a generalization of the notion of a sequence.
) Later on this will be corrected to include specifically quantum mathematics, following Feynman.
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold.
In combinatorial mathematics, a Steiner system ( named after Jakob Steiner ) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2.
In mathematics, specifically in ring theory, the simple modules over a ring R are the ( left or right ) modules over R which have no non-zero proper submodules.
In mathematics, specifically in real analysis, the Bolzano – Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space R < sup > n </ sup >.
In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object.
In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects.
In mathematics, more specifically in ring theory, a maximal ideal is an ideal which is maximal ( with respect to set inclusion ) amongst all proper ideals.
In mathematics, specifically in group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup.
In the branch of mathematics known as abstract algebra, a ring is an algebraic concept abstracting and generalizing the algebraic structure of the integers, specifically the two operations of addition and multiplication.
In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path.
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