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	Encyclopedia :: encyclopedia : Metric space (Site not responding. Last check: 2007-10-23)
		The Euclidean metric of this space defines the distance between two points as the length of the straight line connecting them.
		A metric space is a 2-tuple (X,d) where X is a set and d is a metric on X, that is, a function
		An important consequence is that every metric space admits partitions of unity and that every continuous real-valued function defined on a closed subset of a metric space can be extended to a continuous map on the whole space (Tietze extension theorem).
	www.hallencyclopedia.com /Metric_space (1591 words)

	Metric tensor - Wikipedia, the free encyclopedia
		In mathematics, the metric tensor is a symmetric tensor field of rank 2 that is used to measure distance in a space.
		is conventionally used for the components of the metric tensor (i.e., the elements of the matrix).
		In the later case, the geodesic equations are seen to arise from the principle of least action: they describe the motion of a "free particle" (a particle feeling no forces) that is confined to move on the manifold, but otherwise moves freely, with constant momentum, within the manifold.
	en.wikipedia.org /wiki/Metric_tensor (1164 words)

	Metric space - Wikipedia, the free encyclopedia
		In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.
		Similarly, in 3D, the metrics on the surface of a polyhedron include the ordinary metric, and the distance over the surface; a third metric on the edges of a polyhedron is one where the "paths" are the edges.
		Every metric space is automatically a topological space, the topology being the set of all open sets.
	en.wikipedia.org /wiki/Metric_space (1999 words)

	Euclidean space - ExampleProblems.com
		A Euclidean space is a particular metric space that enables the investigation of topological properties such as compactness.
		Euclidean space plays a part in the definition of a manifold which embraces the concepts of both Euclidean and non-Euclidean geometry.
		Since Euclidean space is a metric space it is also a topological space with the natural topology induced by the metric.
	exampleproblems.com /wiki/index.php?title=Euclidean_space&printable=yes (736 words)

	Ball (mathematics) - Wikipedia, the free encyclopedia
		A subset of a metric space is bounded if it is contained in a ball.
		This means, among other things, that all open sets in a metric space can be written as a union of open balls.
		In n-dimensional Euclidean space with the ordinary (Euclidean) metric, if the space is the line, the ball is an interval, and if the space is the plane, the ball is the disc inside a circle.
	en.wikipedia.org /wiki/Ball_(mathematics) (422 words)

	New Page 1
		And it was later found that both the Euclidean and the two non-Euclidean geometries were relative to a specialised treatment of certain aspects of the more general space of projective geometry.
		But, as we have seen in the previous section, this Euclidean matrix space is itself a limited and limiting 'perspective' of consciousness on a subtler, deeper and richer matrix space: the non-metric, mobile, metamorphic, projective space of ratios and relative proportions.
		Indeed, clairvoyant exploration of the Euclidean matrix of, say, a room already seems to be done from the projective matrix, with many viewpoints from the lines of interacting planes.
	www.human-inquiry.com /expsr10.htm (3538 words)

	[No title]
		The choices for the metric are currently restricted to `"euclidean"', `"maximum"', `"manhattan"', and `"binary"'.
		If the metric is `"euclidean"' and `ng' is the number of columns in which no missing values occur for the given rows, then the distance returned is `sqrt(ncol(x)/ng)' times the Euclidean distance between the two vectors of length `ng' shortened to exclude `NA's.
		The rule is similar for the `"manhattan"' metric, except that the coefficient is `ncol(x)/ng'.
	astro.u-strasbg.fr /~fmurtagh/mda-sw/splus/distance.d (425 words)

	8 Euclidean Four-Vectors
		as used in the previous Sections use the 4D velocity of the moving object and 4D Euclidean distances as invariants, which is in fact the essence of Eq.
		It provides a Euclidean basis for the definition of vectors in the direction of the time dimension.
		In general, the new Euclidean four-vectors can be derived from the Minkowski four-vectors by using the time component in the Minkowski four-vector as the invariant (the vector sum) for the new four-vector.
	www.euclideanrelativity.com /dimensionshtml/node8.html (193 words)

	Why commodity space is non-Euclidean
		Spatial metrics are so much part of our mode of thought that to imagine a different metric is conceptually difficult.
		Within the context of the Euclidean metric the second step is illegal, since it involves operating upon one of the coordinates independently.
		In a hypothetical society in which commodity bundles could not be separated into distinct components, and exchange obeyed a Euclidean metric, the labour theory of value could not hold.
	reality.gn.apc.org /econ/METRIC/node9.html (457 words)

	Tools of Tensor Calculus - Riemann manifolds
		The essential elements in a riemannian manifold are the metric and the connection and we will consider only riemannian connections.
		Besides this, given a coordinate system or, better, a natural basis, several metrics can be defined, so, in order to specify a metric, two arguments are needed: the name of the metric and the basis in which it is expanded.
		In physics, the result of applying the Hodge star operator to a tensor is known as the dual of a tensor and their components are given by the above expression.
	baldufa.upc.es /xjaen/ttc/tutorial/metr.htm (985 words)

	[No title]
		Instead one used the Riemannian geometry which is a more complicated generalization of the Euclidean geometry, because it is based on a use of two structures (topological structure and metric one).
		The T-geometry uses only metric structure, and it is more general than the Riemannian geometry, including it as a special case.
		T-geometry is as rich and pithy as the Riemannian geometry, because the pithiness of geometry depends mainly on the number sorts of geometrical objects described by the geometry and, hence, on the mathematical technique used.
	rsfq1.physics.sunysb.edu /~rylov/tgastm.htm (1481 words)

	Relativistic proof of God
		metrical law we would not be able to rotate or translate a
		"metric" of E,N,P,g in Thurstone's equation and in Einstein's equation
		metric, what we see is that God is identified with the entire Spacetime Metric.
	proof-of-god.freewebsitehosting.com /mathweb.html (955 words)

	Math Forum Discussions
		Does there exist a metric m on P(R^n) such that for every x,y in R^n we have m({x},{y})=d(x,y), where d is the usual euclidean metric of R^n?
		Re: Extension of the Euclidean Metric to Subsets
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/thread.jspa?threadID=1227150&messageID=3949257 (178 words)

	Home
		metric (with exponents of 1 and 2 respectively).
		Many datamining applications rely upon some form of distance metric to compute how similiar one vector of numbers is to another.
		There are a large number of distance metrics and I will add more to the class as I have the time.
	www.phpmath.com (2828 words)

	The Foundations of Relativity
		The metric you cite is actually that of "flat" Minkowski space of special relativity, not the more general metric of Einstein's pseudo-Riemannian manifold.
		From the Minkowski metric you can define the causal structure ("light cones") of his spacetime and then define the Lorentz transformations as the set of linear transformations the leave that metric invariant.
		is the metric of flat Minkowsky space, it's diagonal and all 1's in the diagonal slots, except for the -1 in the time position (either the upper left or bottom right, depening on which book you're looking at).
	www.physicsforums.com /showthread.php?t=104683 (3935 words)

	On Series with Alternating Signs in Euclidean Metric - Dindos (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Namely, given a sequence of elements of a Hilbert space we consider all different ways the signs plus or minus could be put in front of each of these elements.
		Choosing convenient metric we ask what is the 'size' of the set of those choices of + or \Gamma for which the resulting series with alternating signs converges.
		On One Interesting New Metric And Its Application On Sign..
	citeseer.ist.psu.edu /17758.html (468 words)

	On the locally branched Euclidean metric gauge, Juha Heinonen, Dennis Sullivan
		On the locally branched Euclidean metric gauge, Juha Heinonen, Dennis Sullivan
		A metric gauge on a set is a maximal collection of metrics on the set such that the identity map between any two metrics from the collection is locally bi-Lipschitz.
		We characterize metric gauges that are locally branched Euclidean and discuss an obstruction to removing the branching.
	projecteuclid.org /getRecord?id=euclid.dmj/1087575355 (680 words)

	Ars Mathematica » Blog Archive » US law uses a euclidean metric
		Ars Mathematica » Blog Archive » US law uses a euclidean metric
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		2 Responses to “US law uses a euclidean metric”
	arsmathematica.net /archives/2006/01/19/us-law-uses-a-euclidean-metric (109 words)

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