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Topic: Differentiable curve

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	Curve
		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.
	www.brainyencyclopedia.com /encyclopedia/c/cu/curve.html (1350 words)

	VARIATIONS, CALCULUS OF - Online Information article about VARIATIONS, CALCULUS OF
		The Station- curves that are determined by it are called the stationary a curves, or the extremals, of the integral.
		According to this method the curve is defined by specifying x and y as one-valued functions of a parameter O. The integral is then of the form f fof(x, y, x, y)do, where the dots denote differentiation with respect to 0, and f is a homogeneous function of x, y of the first degree.
		curve is a stationary curve for this integral.
	encyclopedia.jrank.org /VAN_VIR/VARIATIONS_CALCULUS_OF.html (4356 words)

	Curve Article, Curve Information (Site not responding. Last check: 2007-09-19)
		A space curve is a curve forwhich X is of three dimensions, usually Euclidean space ; askew curve is a space curve which lies in no plane.
		While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines intwo-dimensional space), there are obvious examples such as the helix which existnaturally in three dimensions.
		From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensionalaspect of projective geometry, and differential geometry ; and later topology, when for example the Jordan curvetheorem was understood to lie quite deep, as well as being required in complex analysis.
	www.anoca.org /curves/example/curve.html (1168 words)

	Encyclopedia :: encyclopedia : Tangent space (Site not responding. Last check: 2007-09-19)
		The tangent space of a manifold is a concept which needs to be introduced when generalizing vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from one to the other.
		Such a vector field serves to define a generalized ordinary differential equation on a manifold: a solution to such a differential equation is a differentiable curve on the manifold whose derivative at any point is equal to the tangent vector attached to that point by the vector field.
		This is an equivalence relation, and the equivalence classes are known as the tangent vectors of M at p.
	www.hallencyclopedia.com /Tangent_space (1209 words)

	Time Supplement [Internet Encyclopedia of Philosophy]
		This requires it to be a differentiable space in which physical objects obey the equations of motion of the theory.
		Einstein's principal equation in his general theory of relativity implies that the curvature of spacetime is directly proportional to the density of mass in the spacetime.
		For 4-d spacetime obeying special relativity, a coordinate system is a grid of smooth timelike and spacelike curves on the spacetime that assigns to each point three space coordinate numbers and one time coordinate number.
	www.iep.utm.edu /ancillaries/time-sup.htm (12863 words)

	Fractal - Wikipedia, the free encyclopedia
		In 1872, Karl Weierstrass found an example of a function with the nonintuitive property that it is everywhere continuous but nowhere differentiable — the graph of this function would now be called a fractal.
		Actually, these fractals were described as curves, which is hard to realize with the well known modern constructions.
		The idea of self-similar curves was taken further by Paul Pierre 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.
	en.wikipedia.org /wiki/Fractal (1878 words)

	math lessons - Curve (Site not responding. Last check: 2007-09-19)
		Moreover, in this case, one can define speed of
		infinitely differentiable and charts are expressible as power series), and
		algebra arithmetic calculus equations geometry differential equations trigonometry number theory probability theory applied mathematics mathematical games mathematicians
	www.mathdaily.com /lessons/Curve (1186 words)

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