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Area 51 (other)
Area
Area
is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane
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Area (other)
Area
Area
is a quantity of a two-dimensional surface. Area
Area
or Areas may also refer to:Contents1 Art, entertainment, and media 2 Fauna 3 Organisations 4 Other uses 5 See alsoArt, entertainment, and media[edit]
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Analysis
Analysis
Analysis
is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle
Aristotle
(384–322 B.C.), though analysis as a formal concept is a relatively recent development.[1] The word comes from the Ancient Greek
Ancient Greek
ἀνάλυσις (analysis, "a breaking up", from ana- "up, throughout" and lysis "a loosening").[2] As a formal concept, the method has variously been ascribed to Alhazen,[3] René Descartes
René Descartes
(Discourse on the Method), and Galileo Galilei
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Polygon Triangulation
In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles,[1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs
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Calculus
Calculus
Calculus
(from Latin
Latin
calculus, literally 'small pebble', used for counting and calculations, as on an abacus)[1] is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus (concerning rates of change and slopes of curves),[2] and integral calculus (concerning accumulation of quantities and the areas under and between curves).[3] These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz
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History Of Calculus
Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Isaac Newton
Isaac Newton
and Gottfried Leibniz independently discovered calculus in the mid-17th century
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball"[1]) is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to a circular object in two dimensions). Like a circle, which geometrically is an object in two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space.[2] This distance r is the radius of the ball, and the given point is the center of the mathematical ball
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Greek Mathematics
Greek mathematics
Greek mathematics
refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture and language. Greek mathematics of the period following Alexander the Great
Alexander the Great
is sometimes called Hellenistic mathematics
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Multivariable Calculus
Multivariable calculus
Multivariable calculus
(also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one.[1]Contents1 Typical operations1.1 Limits and continuity 1.2 Partial differentiation 1.3 Multiple integration 1.4
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Geometry
Geometry
Geometry
(from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry
Geometry
arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or A
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Linear Algebra
Linear
Linear
algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , displaystyle a_ 1 x_ 1 +cdots +a_ n x_ n =b, linear functions such as ( x 1 , … , x n ) ↦ a 1 x 1 + … + a n x n , displaystyle (x_ 1 ,ldots ,x_ n )mapsto a_ 1 x_ 1 +ldots +a_ n x_ n , and their representations through matrices and vector spaces.[1][2][3] Linear
Linear
algebra is central to almost all areas of mathematics
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Differential Geometry
Differential geometry
Differential geometry
is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. Differential geometry
Differential geometry
is closely related to differential topology and the geometric aspects of the theory of differential equations
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Lebesgue Measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space. For n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called n-dimensional volume, n-volume, or simply volume.[1] It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called Lebesgue measurable; the measure of the Lebesgue measurable set A is here denoted by λ(A). Henri Lebesgue
Henri Lebesgue
described this measure in the year 1901, followed the next year by his description of the Lebesgue integral
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Circle
A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior
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Jordan Measure
In mathematics, the Peano– Jordan measure
Jordan measure
(also known as the Jordan content) is an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped. It turns out that for a set to have Jordan measure
Jordan measure
it should be well-behaved in a certain restrictive sense. For this reason, it is now more common to work with the Lebesgue measure, which is an extension of the Jordan measure
Jordan measure
to a larger class of sets. Historically speaking, the Jordan measure
Jordan measure
came first, towards the end of the nineteenth century. For historical reasons, the term Jordan measure is now well-established, despite the fact that it is not a true measure in its modern definition, since Jordan-measurable sets do not form a σ-algebra
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