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Curl Operator
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve. The notation is more common in North America. In the rest of the world, particularly in 20th century scientific literature, the alternative notation is traditionally used, which comes from the "rate of rotation" that it represents. To avoid conf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Curl
A uniform is a variety of costume worn by members of an organization while usually participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools, and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Public Health Service Commissioned Corps, Commissioned Corps of the United States Public Health Service or the France, French préfet, prefects. For some organizations, such as police, it may be illegal for non-members to wear the uniform. Etymology From the Latin ''unus'' (meaning one), and ''forma'' (meaning form). Variants Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers dress code, required to wear a uniform may include retail workers, bank and post-office workers, public security, pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO/IEC 80000
ISO/IEC 80000, ''Quantities and units'', is an international standard describing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC). It serves as a style guide for using physical quantities and units of measurement, formulas involving them, and their corresponding units, in scientific and educational documents for worldwide use. The ISO/IEC 80000 family of standards was completed with the publication of the first edition of Part 1 in November 2009. Overview By 2021, ISO/IEC 80000 comprised 13 parts, two of which (parts 6 and 13) were developed by IEC and the remaining 11 were developed by ISO, with a further three parts (15, 16 and, 17) under development. Part 14 was withdrawn. Subject areas By 2021 the 80000 standard had 13 published parts. A description of each part is available online, with the complete parts for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a Convention (norm), convention and a mnemonic, utilized to define the orientation (vector space), orientation of Cartesian coordinate system, axes in three-dimensional space and to determine the direction of the cross product of two Euclidean vector, vectors, as well as to establish the direction of the force on a Electric current, current-carrying conductor in a magnetic field. The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either right thumb or left thumb. History The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Vector
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular to a given object at a particular point. A normal vector of length one is called a unit normal vector or normal direction. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point is a vector perpendicular to the tangent plane of the surface at . The vector field of normal directions to a surface is known as '' Gauss map''. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of a for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Two different regions may have the same area (as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary (topology)
In topology and mathematics in general, the boundary of a subset of a topological space is the set of points in the Closure (topology), closure of not belonging to the Interior (topology), interior of . An element of the boundary of is called a boundary point of . The term boundary operation refers to finding or taking the boundary of a set. Notations used for boundary of a set include \operatorname(S), \operatorname(S), and \partial S. Some authors (for example Willard, in ''General Topology'') use the term frontier instead of boundary in an attempt to avoid confusion with a Manifold#Manifold with boundary, different definition used in algebraic topology and the theory of manifolds. Despite widespread acceptance of the meaning of the terms boundary and frontier, they have sometimes been used to refer to other sets. For example, ''Metric Spaces'' by E. T. Copson uses the term boundary to refer to Felix Hausdorff, Hausdorff's border, which is defined as the intersection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Function
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; that is, a function of class C^k is a function that has a th derivative that is continuous in its domain. A function of class C^\infty or C^\infty-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a C^-function. However, it may also mean "sufficiently differentiable" for the problem under consideration. Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Area
In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions. Every bounded surface in three dimensions can be associated with a unique area vector called its vector area. It is equal to the surface integral of the surface normal, and distinct from the usual ( scalar) surface area. Vector area can be seen as the three dimensional generalization of signed area in two dimensions. Definition For a finite planar surface of scalar area and unit normal , the vector area is defined as the unit normal scaled by the area: \mathbf = \hat \mathbfS For an orientable surface composed of a set of flat facet areas, the vector area of the surface is given by \mathbf = \sum_i \hat \mathbf_i S_i where is the unit normal vector to the area . For bounded, oriented curved surfaces that are sufficiently well-behaved, we can still define vector area. First, we split the su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tripod
A tripod is a portable three-legged frame or stand, used as a platform for supporting the weight and maintaining the stability of some other object. The three-legged (triangular stance) design provides good stability against gravitational loads as well as horizontal shear forces, and better leverage for resisting tipping over due to lateral forces can be achieved by spreading the legs away from the vertical centre. Variations with one, two, and four legs are termed '' monopod'', '' bipod'', and ''quadripod'' (similar to a table). Etymology First attested in English in the early 17th century, the word ''tripod'' comes via Latin ''tripodis'' ( GEN of ''tripus''), which is the romanization of Greek (''tripous''), "three-footed" (GEN , ''tripodos''), ultimately from (''tri-''), "three times" (from , ''tria'', "three") + (''pous''), "foot". The earliest attested form of the word is the Mycenaean Greek , ''ti-ri-po'', written in Linear B syllabic script. Cultural use Many c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James MacCullagh
James MacCullagh (1809 – 24 October 1847) was an Irish mathematician and scientist. He served as the Erasmus Smith's Professor of Mathematics at Trinity College Dublin beginning in 1835, and in 1843, he was appointed as the Erasmus Smith's Professor of Natural and Experimental Philosophy. MacCullagh received the Cunningham Medal of the Royal Irish Academy in 1838 for his work on the laws of crystalline reflexion and light refraction, and the Copley Medal in 1842 for his efforts on the nature of light. Early life MacCullagh was born in Landahaussy, near Plumbridge, County Tyrone, Ireland, but the family moved to Curly Hill, Strabane when James was about 10. He was the eldest of twelve children and demonstrated mathematical talent at an early age. He entered Trinity College Dublin as a student in 1824, winning a scholarship in 1827 and graduating in 1829. Career He became a fellow of Trinity College Dublin in 1832 and was a contemporary there of William Rowan Hamilton. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism achieved the Unification (physics)#Unification of magnetism, electricity, light and related radiation, second great unification in physics, where Unification (physics)#Unification of gravity and astronomy, the first one had been realised by Isaac Newton. Maxwell was also key in the creation of statistical mechanics. With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric force, electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. (Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Calculus
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to reproduce other mathematical theories including vector calculus, differential geometry, and differential forms. Differentiation With a geometric algebra given, let a and b be vectors and let F be a multivector-valued function of a vector. The directional derivative of F along b at a is defined as :(\nabla_b F)(a) = \lim_, provided that the limit exists for all b, where the limit is taken for scalar \epsilon. This is similar to the usual definition of a directional derivative but extends it to functions that are not necessarily scalar-valued. Next, choose a set of basis vector In mathematics, a set of elements of a vector space is called a basis (: bases) if every element of can be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
