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	Curve - Wikipedia, the free encyclopedia
		A space curve is a curve for which X is of three dimensions, usually Euclidean space; a skew curve is a space curve which lies in no plane.
		A rectifiable curve is a curve with finite length.
		From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective geometry, and differential geometry; and later topology, when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis.
	en.wikipedia.org /wiki/Curve (1204 words)

	Curve
		In mathematics, a curve is a geometric object that is one-dimensional and continuous.
		In Euclidean space, every piecewise continuously differentiable curve is rectifiable and its length is given as the integral of its speed.
		Algebraic curves are also defined, in the setting of algebraic geometry, including the theory of elliptic curves that is now widely applied.
	www.guajara.com /wiki/en/wikipedia/c/cu/curve.html (704 words)

	Curve (Site not responding. Last check: 2007-09-10)
		This definition of curve captures our intuitive notion of a curve as a connected, continuous geometric figure that is "like" a line, although it also includes figures that are not called curves in common usage.
		Every piecewise continuously differentiable curve is rectifiable and its length is given as the integral of its speed.
		Curves are also defined in the setting of algebraic geometry and the theory of elliptic curves.
	www.enlightenweb.net /c/cu/curve.html (671 words)

	Encyclopedia: Curve
		A Brachistochrone curve, or curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and passes down along the curve to the second point, under the action of constant gravity and...
		A tautochrone curve is the curve for which the time taken by a particle sliding down it under uniform gravity to its lowest point is independent of its starting point.
		In mathematics, a cubic curve is a plane curve C defined by a cubic equation F(X,Y,Z) = 0 applied to homogeneous coordinates [X:Y:Z] for the projective plane; or the inhomogeneous version for the affine space determined by setting Z = 1 in such an equation.
	www.nationmaster.com /encyclopedia/Curve (3519 words)

	Curve -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-10)
		Simple examples are the (Ellipse in which the two axes are of equal length; a plane curve generated by one point moving at a constant distance from a fixed point) circle or the (A line traced by a point traveling in a constant direction; a line of zero curvature) straight line.
		A plane curve is a curve for which X is the (Click link for more info and facts about mathematical plane) mathematical plane — these are the examples first encountered — or in some cases the (Click link for more info and facts about projective plane) projective plane.
		A space curve is a curve for which X is of three dimensions, usually (A space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional) Euclidean space; a skew curve is a space curve which lies in no plane.
	www.absoluteastronomy.com /encyclopedia/c/cu/curve.htm (1980 words)

	CURVE FACTS AND INFORMATION (Site not responding. Last check: 2007-09-10)
		A plane curve is a curve for which ''X'' is the mathematical_plane — these are the examples first encountered — or in some cases the projective_plane.
		A space curve is a curve for which ''X'' is of three dimensions, usually Euclidean_space; a skew curve is a space curve which lies in no plane.
		From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective_geometry, and differential_geometry; and later topology, when for example the Jordan_curve_theorem was understood to lie quite deep, as well as being required in complex_analysis.
	www.dontpayyourtaxes.com /curve (1054 words)

	Curve article - Curve magazine called Curve mathematics circle straight line curves - What-Means.com (Site not responding. Last check: 2007-09-10)
		Then a curve $\!\,\gamma is a continuous mapping \,\!\gamma : I \rightarrow X, where X is a topological space .$
		A closed curve is thus a continuous mapping of the circle $S^1; a simple closed$ curve is also called a Jordan curve.
		A $C^k arc is an equivalence class of C^k$ curves under the relation of reparametrisation.
	www.what-means.com /encyclopedia/Curve (1377 words)

	Fractal dimension
		See this figure for an example of a curve approximated by a sequence of line segments, which is usually called a polygonal curve.
		Then the approximate length of the curve is the sum of the lengths of the line segments.
		This constant is the fractal dimension of the Koch curve.
	www.math.okstate.edu /mathdept/dynamics/lecnotes/node37.html (767 words)

	Rectifiable curve: Definition and Links by Encyclopedian.com - All about Rectifiable curve
		A rectifiable curve is a curve which has a well-defined finite length.
		Rectifiable curves are mainly important in complex analysis because they are needed to define the path integral.
		Every continuous and piecewise continuously differentiable[?] curve γ is rectifiable, and its length can be computed as the ordinary Riemann integral
	www.encyclopedian.com /re/Rectifiable-curve.html (151 words)

	Curve
		Then a curve γ is a continuous mapping γ : I → X, where X is a topological space.
		The curve γ is said to be simple if it is injective, i.e.
		The statement of Bézout's theorem showed a number of aspects which were not directly accessibel to the geometry of the time, to do with singular points and complex solutions.
	www.brainyencyclopedia.com /encyclopedia/c/cu/curve.html (1266 words)

	Mesothelioma - Curve (Site not responding. Last check: 2007-09-10)
		The property possessed by the curving of a line or surface.
		Curved segment (of a road or river or railroad track etc.).
		A curved line representing graphically a variable element as affected by one or more conditions.
	www.mesothelioma.me.uk /Curve+asbestos.html (897 words)

	Curve (Site not responding. Last check: 2007-09-10)
		A closed curve is thus a continuous mapping of the circle
		A plane curve is a curve for which X is the mathematical plane - these are the examples first encountered - or in some cases the projective plane.
		If X is a differentiable manifold, then we can define the notion of differentiable curve in X. This general idea is enough to cover many of the applications of curves in mathematics.
	www.yotor.com /wiki/en/cu/Curve.htm (1178 words)

	Calculus Animations with Mathcad
		The first example illustrates a sequence of polygonal approximations of a rectifiable curve, i.e., a curve with a finite arc length.
		A spoke of length R is connected to the center of the circle, and a pencil attached to the end of the spoke traces a resulting curve.
		A physical interpretation of the resulting curve could be based on considering the 2-D picture to be a projection of a "thin" 3-D picture.
	www.math.odu.edu /cbii/calcanim (666 words)

	Curve bei eLexi - das Onlinelexikon (Site not responding. Last check: 2007-09-10)
		Then a curve c is a continuous mapping c : I → X, where X is a topological space.
		See main article differential geometry of curves While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines in two-dimensional space), there are obvious examples such as the helix which exist naturally in three dimensions.
		k = ω, charts are expressible as power series), and c is an analytic map, then c is called an analytic curve.
	www.elexi.de /en/c/cu/curve.html (1512 words)

	Fractal Dimension
		See this illustration for an example of a curve approximated by a fixed line segment.
		The approximate length of the curve is the sum of the lengths of the line segments.
		So, we see that the fractal dimension of a rectifiable curve is 1.
	homepages.cwi.nl /~bens/6dim.htm (358 words)

	Hausdorff Dimension (Site not responding. Last check: 2007-09-10)
		Suppose we want to consider the Hausdorff 1-measure of a nice, smooth, rectifiable (i.e., non-fractal) curve
		So Hausdorff 1-measure for a smooth, rectifiable curve is just the length of the curve.
		So indeed, as we would hope, measuring the curve in a dimension that is too large gives an answer of zero.
	www.math.vt.edu /people/hoggard/FracGeomReport/node3.html (508 words)

Rectifiable curve (Site not responding. Last check: 2007-09-10)

Rectifiable curve

Rectifiable curve
article at Free Euro Online Encyclopedia

It uses material from the wikipedia article Rectifiable curve.

www.eurofreehost.com /re/Rectifiable_curve.html (194 words)

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Topic: Rectifiable curve

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