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Curl (mathematics)
In vector calculus, the curl 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. is a notation common today to the United States and Americas. In many European countries, particularly in classic scientific literature, the alternative notation is traditionally used, which is spelled as "rotor", and comes from the "rate of rotation", which it rep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Curl
A uniform is a variety of clothing worn by members of an organization while 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'', one, and ''forma'', form. 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, public-security and health-care workers, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO/IEC 80000
ISO 80000 or IEC 80000 is an international standard introducing 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 the use of 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 Part 1 in November 2009. Overview , ISO/IEC 80000 comprises 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 The 80000 standard currently has 13 parts. Part 1: General ISO 80000-1:2009 replaces ISO 31-0:1992 and ISO 1000:1992. It gives general information and definitions concer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors. Most of the various left-hand and right-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. One can see this by holding one's hands outward and together, palms up, with the thumbs out-stretched to the right and left, and the fingers making a curling motion from straight outward to pointing upward. (Note the picture to right is not an illustration of this.) The curling motion of the fingers represents a movement from the first (''x'' axis) to the second (''y'' axis); the third (''z'' axis) can point along either thumb. Left-hand and right-hand rules arise when dealing with coordinate axes. The rule can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Vector
In geometry, a normal is an object such as 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) line perpendicular to the tangent line to the curve at the point. A normal vector may have length one (a unit vector) or its length may represent the curvature of the object (a ''curvature vector''); its algebraic sign may indicate sides (interior or exterior). In three dimensions, a surface normal, or simply normal, to a surface at point P is a vector perpendicular to the tangent plane of the surface at P. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality (right angles). The concept has been generalized to differentiable manifolds of arbitrary dimension embedded in a Euclidean space. The normal vector space or normal space of a manifold at point P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A pl ... or planar lamina, while ''surface area'' refers to the area of an open surface or the boundary (mathematics), boundary of a solid geometry, 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 plane curve, curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by com ... [...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 of not belonging to the 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 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 Hausdorff's border, which is defined as the intersection of a set with its boundary. Hausdorff also introduced the term residue, which is defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Function
In mathematical analysis, the smoothness of a function (mathematics), function is a property measured by the number of Continuous function, continuous Derivative (mathematics), derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all Order of derivation, orders in its Domain of a function, domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). 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 open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of ... [...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 = \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 \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 surface into in ... [...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 cultur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James MacCullagh
James MacCullagh (1809 – 24 October 1847) was an Irish mathematician. 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. He became a member of the Royal Irish Academy in 1833. In 1835 he was appointed Erasmus Smith's Professor of Mathematics at Trinity College Dublin and in 1843 became Erasmus Smith's Professor of Natural and Experimental Philosophy. He was an inspiring teacher and taught notable scholars, including Samuel Haughton, Andrew Searle Hart, John Kells Ingram and George Salmon. Although he worked mostly on optics, he is also remembered for his work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist 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 have been called the " second great unification in physics" where the first one had been realised by Isaac Newton. With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that 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. (This article accompanied an 8 December 1864 presentation by Maxwell to the Royal Society. His statement that "light and magnetism are affections of the same substance" is at page 499.) The unification of light and electrical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Calculus
In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories including 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 vectors \ and consider the operators, denoted \partial_i, that perform directional derivatives in the directions of e_i: :\partial_i : F \mapsto (x\mapsto (\nabla_ F)(x)). Then, using the Einstein summation notation, consider the operator: :e^i\partial_i, which means :F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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