curve

Once chloracne has been identified, the primary action is to remove the patient and all other individuals from the source of contamination. Further treatment is symptomatic. Severe or persistent lesions may be treated with oral antibiotics or isotretinoin. However, chloracne may be highly resistant to any treatment. The course of the disease is highly variable. In some cases the lesions may resolve within two years or so; however, in other cases the lesions may be effectively permanent (mean duration of lesions in one 1984 study was 26 years, with some workers remaining disfigured over three ...

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Chloracne, Chloracne - Etiology and progression, Chloracne - Treatment, Chloracne - Related conditions, Chloracne - Notable cases

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The modern format of angle used to indicate longitude or latitude is hemisphere degree minute.decimal, where there are 60 minutes in a degree, for instance N 51 23.438 or E 090 58.928. The obsolete (but still commonly used) format of angle used to indicate longitude or latitude is hemisphere degree minute' second", where there are 60 minutes in a degree and 60 seconds in a minute, for ins ...

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Angle, Angle - Units of measure for angles, Angle - Conventions on measurement, Angle - Types of angles, Angle - Some facts, Angle - A formal definition, Angle - Angles in different contexts, Angle - Angles in Riemannian geometry, Angle - Angles in astronomy, Angle - Angles in maritime navigation

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There are two types of integral in calculus, the indefinite and the definite. The indefinite integral is simply the antiderivative. That is, F is an antiderivative of f when f is a derivative of F. (This use of capital letters and lower case letters is common in calculus. The lower case letter represents the derivative of the capital letter.) The definite integral evaluates the cumulative effect of many small changes in a quantity. The simples ...

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Calculus, Calculus - Differential calculus, Calculus - Integral calculus, Calculus - Foundations, Calculus - Fundamental theorem of calculus, Calculus - Applications, Calculus - History, Calculus - Footnotes

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The fundamental theorem of calculus states that differentiation and integration are, in a certain sense, inverse operations. More precisely, if one defines one function as the integral of another function, then differentiating the newly defined function returns the function you started with. Furthermore, if you want to find the value of a definite integral, you usually do so by evaluating an antiderivative. Here is the mathematical formulation of the Fundamental Theorem of Calculus: If a function f is continuous on the interval ...

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Calculus, Calculus - Differential calculus, Calculus - Integral calculus, Calculus - Foundations, Calculus - Fundamental theorem of calculus, Calculus - Applications, Calculus - History, Calculus - Footnotes

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The origins of integral calculus are generally regarded as going back no farther than to the time of the ancient Greeks, circa 200 B.C., though there is some evidence that the ancient Egyptians may have had some hint of the idea at a much earlier date. (See Moscow Mathematical Papyrus.) The Hellenic mathematician Eudoxus is generally credited with the method of exhaustion, which made it possible to compute the areas of regions and the volumes of solids. Archimedes developed this method further, and invented heuristic methods which resemble m ...

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Calculus, Calculus - Differential calculus, Calculus - Integral calculus, Calculus - Foundations, Calculus - Fundamental theorem of calculus, Calculus - Applications, Calculus - History, Calculus - Footnotes

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The SI derived unit of work is the joule (J), which is defined as the work done by a force of one newton acting over a distance of one meter. The dimensionally equivalent newton-meter (N·m) is sometimes used instead; however, it is also sometimes reserved for torque to distinguish its units from work or energy. Non-SI units of work include the erg, the foot-pound, the foot-poundal, and the liter-atmosphere. ...

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Mechanical work, Mechanical work - Definition, Mechanical work - Units, Mechanical work - Simpler formulae, Mechanical work - Types of work, Mechanical work - PV work, Mechanical work - Mechanical energy, Mechanical work - Conservation of mechanical energy

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In the simplest case, that of a body moving in a steady direction, and acted on by a force parallel to that direction, the work is given by the formula where F is the force and s is the distance traveled by the object. The work is taken to be negative when the force opposes the motion. More generally, the force and distance are taken to be vector quantities, and combined using the dot product: where φ is the ...

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Mechanical work, Mechanical work - Definition, Mechanical work - Units, Mechanical work - Simpler formulae, Mechanical work - Types of work, Mechanical work - PV work, Mechanical work - Mechanical energy, Mechanical work - Conservation of mechanical energy

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Flux, or diffusion, for gaseous molecules can be related to the function: where N is the total number of gaseous particles, k is Boltzmann's constant, T is the relative temperature in kelvins, and σab is the mean free path between the molecules a and b. Chemical flux is also defined in ...

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Flux, Flux - Flux definition and theorems, Flux - Thermal systems, Flux - Chemical diffusion, Flux - Flux definition and theorems, Flux - Maxwell's equations, Flux - Poynting vector

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The flux of electric and magnetic field lines is frequently discussed in electrostatics. This is because in Maxwell's equations in integral form involve integrals like above for electric and magnetic fields. For instance, Gauss's law states that the flux of the electric field out of a closed surface is proportional to the electric charge enclosed in the surface (regardless of how that charge is distributed). The constant of proportionality is the reciprocal of the permittivity of free space. < ...

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Flux, Flux - Flux definition and theorems, Flux - Thermal systems, Flux - Chemical diffusion, Flux - Flux definition and theorems, Flux - Maxwell's equations, Flux - Poynting vector

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Drawing an ellipse is a common graphics primitive in standard display libraries, such as the QuickDraw and GDI interfaces on the Macintosh and Windows systems. Often such libraries are limited and can only draw an ellipse with either the major axis or the minor axis horizontal. Jack Bresenham at IBM is most famous for the invention of 2D drawing primitives, including line and circle drawing, using only fast integer operations such as addition and branch on carry bit. An efficient generalization to draw ellipses was invented in 1984 by ...

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Ellipse, Ellipse - Parametrisation, Ellipse - Eccentricity, Ellipse - Semi-latus rectum and polar coordinates, Ellipse - Area, Ellipse - Circumference, Ellipse - Stretching and Projection, Ellipse - Reflection property, Ellipse - Ellipses in physics, Ellipse - Ellipses in computer graphics

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Indian astronomer Aryabhata discovered that the orbits of the planets around the sun are ellipses in 499, which he described in his book, the Aryabhatiya [1]. In the 17th century, Johannes Kepler explained that the orbits along which the planets travel around the Sun are ellipses, which is Kepler's first law. Later, Isaac Newton explained this as a corollary of his law of universal gravitation. More generally, in the gravitational two-body problem, if the two bodies are bound to each other (i.e., the total energy is nega ...

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Ellipse, Ellipse - Parametrisation, Ellipse - Eccentricity, Ellipse - Semi-latus rectum and polar coordinates, Ellipse - Area, Ellipse - Circumference, Ellipse - Stretching and Projection, Ellipse - Reflection property, Ellipse - Ellipses in physics, Ellipse - Ellipses in computer graphics

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Now consider a function f from one metric space (X, dX) to another metric space (Y, dY). Then f is continuous at the point c in X if for any positive real number ε, there exists a positive real number δ such that all x in X satisfying dX(x, c) < δ will also satisfy dY(f(x), f(c)) < ε. This can also be formulated in terms of sequences and limits: the function ...

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Continuous function, Continuous function - Real-valued continuous functions, Continuous function - Epsilon-delta definition, Continuous function - Heine definition of continuity, Continuous function - Examples, Continuous function - Facts about continuous functions, Continuous function - Continuous functions between metric spaces, Continuous function - Continuous functions between topological spaces, Continuous function - Continuous functions between partially ordered sets

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The shape of an ellipse is usually expressed by a number called the eccentricity of the ellipse, conventionally denoted e (not to be confused with the mathematical constant e). The eccentricity is related to a and b by the statement or where c (the linear eccentricity of the ellipse) equals the distance from the cen ...

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Ellipse, Ellipse - Parametrisation, Ellipse - Eccentricity, Ellipse - Semi-latus rectum and polar coordinates, Ellipse - Area, Ellipse - Circumference, Ellipse - Stretching and Projection, Ellipse - Reflection property, Ellipse - Ellipses in physics, Ellipse - Ellipses in computer graphics

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The semi-latus rectum of an ellipse, usually denoted (lowercase L), is the distance from a focus of the ellipse to the ellipse itself, measured along a line perpendicular to the major axis. It is related to and (the ellipse's semi-axes) by the formula or, if using the eccentricity, . In polar coordinates, an ellipse with one focus at the origin and the other on the negative x-axis is given by the equation An ellipse can also be thought of as a projection of a circle: a circle on a plane at angle φ to the horizontal projected vertically onto a horizontal plane giv ...

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Ellipse, Ellipse - Parametrisation, Ellipse - Eccentricity, Ellipse - Semi-latus rectum and polar coordinates, Ellipse - Area, Ellipse - Circumference, Ellipse - Stretching and Projection, Ellipse - Reflection property, Ellipse - Ellipses in physics, Ellipse - Ellipses in computer graphics

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The circumference of an ellipse is 4aE(e), where the function E is the complete elliptic integral of the second kind. The exact infinite series is: A good approximation is Ramanujan's: which can also be written as: More generally, the arc length of a portion of the circumference, as a function of the angle subtended, is given by an incomplete elliptic integral. The inverse function, the angle subtended as a function of the arc le ...

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Ellipse, Ellipse - Parametrisation, Ellipse - Eccentricity, Ellipse - Semi-latus rectum and polar coordinates, Ellipse - Area, Ellipse - Circumference, Ellipse - Stretching and Projection, Ellipse - Reflection property, Ellipse - Ellipses in physics, Ellipse - Ellipses in computer graphics

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Newton's law of universal gravitation states the following: Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them: where: F is the magnitude of the (repulsive) gravitational force between the two point masses G is the gravitational constant m1 is the mass of t ...

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Gravity, Gravity - Overview of the history of gravitational theory, Gravity - Newton's law of universal gravitation, Gravity - Acceleration due to gravity, Gravity - Bodies with spatial extent, Gravity - Vector form, Gravity - Gravitational field, Gravity - The Earth's gravity, Gravity - Comparative gravities of the Earth Sun Moon and planets, Gravity - Mathematical equations for a falling body, Gravity - Gravitational potential, Gravity - Acceleration relative to the rotating Earth, Gravity - Gravity and astronomy, Gravity - Self-gravitating system, Gravity - Practical uses of gravity, Gravity - Problems with Newton's theory, Gravity - Theoretical concerns, Gravity - Disagreement with observation, Gravity - Newton's reservations, Gravity - Einstein's theory of gravitation, Gravity - Experimental tests, Gravity - Comparison with electromagnetic force, Gravity - Gravity and quantum mechanics, Gravity - Alternative theories, Gravity - Recent alternative theories, Gravity - Historical alternative theories, Gravity - Notes

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Given a subset S in Rn a vector field is represented by a vector-valued function in standard Euclidean coordinates (x1, ..., xn). If there is another coordinate system y, then is the expression for the same vector field in the new coordinates. In particular a vector field is not a bunch of scalar fields. We say V is a Ck vector field if V is k times continuously differentiable. A point p in S is called stationary if the vector at that point is zero (See also:

Vector field, Vector field - Definition, Vector field - Notes, Vector field - Examples, Vector field - Gradient field, Vector field - Central field, Vector field - Curve integral, Vector field - Flow curves, Vector field - Difference between scalar and vector field, Vector field - Example 3

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Vector fields should be compared to scalar fields, which associate a number or scalar to every point in space (or every point of some manifold). The divergence and curl are two operations on a vector field which result in a scalar field and another vector field respectively. The first of these operations is defined in any number of dimensions (that is, for any value of n). The curl however, is defined only for n=3, but it can be generalized to an arbitrary dimension using the ext ...

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Vector field, Vector field - Definition, Vector field - Notes, Vector field - Examples, Vector field - Gradient field, Vector field - Central field, Vector field - Curve integral, Vector field - Flow curves, Vector field - Difference between scalar and vector field, Vector field - Example 3

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A common technique in physics is to integrate a vector field along a curve: a path integral. Given a particle in a gravitational vector field, where each vector represents the force acting on the particle at this point in space, the curve integral is the work done on the particle when it travels along a certain path. The curve integral is constructed analogously to the Riemann integral and it exists if the curve is rectifiable (has finite length) and the vector field is continuous. Given a vector field V and a curve γ parametrized by [0, 1] the curve integral i ...

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Vector field, Vector field - Definition, Vector field - Notes, Vector field - Examples, Vector field - Gradient field, Vector field - Central field, Vector field - Curve integral, Vector field - Flow curves, Vector field - Difference between scalar and vector field, Vector field - Example 3

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Vector fields have a nice interpretation in terms of autonomous, first order ordinary differential equations. Given a vector field V defined on S, we can try to define curves γ on S such that for each t in an interval I γ'(t) = V(γ(t)) If V is Lipschitz continuous we can find a unique C1-curve γx for each point x in X so that γx ...

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Vector field, Vector field - Definition, Vector field - Notes, Vector field - Examples, Vector field - Gradient field, Vector field - Central field, Vector field - Curve integral, Vector field - Flow curves, Vector field - Difference between scalar and vector field, Vector field - Example 3

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Let y represent an unknown function of x, and let denote the derivatives An ordinary differential equation (ODE) is an equation involving The order of a differential equation is the order n of the highest derivative that appears. If the highest derivative appears only in integer powers, then the degree of ...

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Ordinary differential equation, Ordinary differential equation - Definition, Ordinary differential equation - General application, Ordinary differential equation - Existence and nature of solutions, Ordinary differential equation - Types of differential equations with some history, Ordinary differential equation - Homogeneous linear ODEs with constant coefficients, Ordinary differential equation - Linear ODEs with constant coefficients, Ordinary differential equation - Linear ODEs with variable coefficient, Ordinary differential equation - General solution method for first-order linear ODEs, Ordinary differential equation - Linear PDEs, Ordinary differential equation - First-order PDEs, Ordinary differential equation - Singular solutions, Ordinary differential equation - Reduction to quadratures, Ordinary differential equation - The Fuchsian theory, Ordinary differential equation - Lie's theory, Ordinary differential equation - Bibliography

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In Euclidean geometry, the inner angles of a triangle add up to π radians or 180°; the inner angles of a quadrilateral add up to 2π radians or 360°. In general, the inner angles of a simple polygon with n sides add up to (n − 2) ×   π radians or (n − 2)  ×  180°. If two straight lines intersect, four angles are formed. Each one has an equal measure to the angle across from it; these congruen ...

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Angle, Angle - Units of measure for angles, Angle - Conventions on measurement, Angle - Types of angles, Angle - Some facts, Angle - A formal definition, Angle - Angles in different contexts, Angle - Angles in Riemannian geometry, Angle - Angles in astronomy, Angle - Angles in maritime navigation

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