plane curve oor Indonesies
plane curve
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(mathematics) the locus of points in the Euclidean plane that satisfies some geometric or algebraic definition
Vertalings in die woordeboek Engels - Indonesies
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curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane
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A smooth plane curve is a curve in a real Euclidean plane R2 and is a one-dimensional smooth manifold.
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In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane.
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In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
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An algebraic plane curve is a curve in an affine or projective plane given by one polynomial equation f(x, y) = 0 (or F(x, y, z) = 0, where F is a homogeneous polynomial, in the projective case.)
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For instance, the introduction of coordinates by René Descartes and the concurrent developments of algebra marked a new stage for geometry, since geometric figures such as plane curves could now be represented analytically in the form of functions and equations.
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Equivalently, a smooth plane curve can be given locally by an equation f(x, y) = 0, where f : R2 → R is a smooth function, and the partial derivatives ∂f/∂x and ∂f/∂y are never both 0 at a point of the curve.
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He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations.
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If the surface is a plane, then the shortest curve is a line.
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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.
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The idea of self-similar curves was taken further by Paul Lévy, who, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole described a new fractal curve, the Lévy C curve.
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Modernist architects were free to make use of curves as well as planes.
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Various concepts based on length, such as the arc length of curves, area of plane regions, and volume of solids all possess natural analogues in Riemannian geometry.
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In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve.
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As with the hyperbolic plane, anti-de Sitter space is curved in such a way that any point in the interior is actually infinitely far from this boundary surface.
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Lyapunov orbits around a Lagrangian point are curved paths that lie entirely in the plane of the two primary bodies.
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It employs an array of plane mirrors to gather sunlight, reflecting it onto a larger curved mirror.
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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, though its first proof is due to Bernhard Riemann and is the two-dimensional special case of the more general Kelvin–Stokes theorem.
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