Hausdorff dimension
In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that part
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1918 in science2.5D (disambiguation)Abram BesicovitchAlexandrov spaceAnalytic capacityApollonian gasketArc lengthArtificial latticeAssouad dimensionBenoit MandelbrotBesicovitch - Hausdorff dimensionBorel measureBrownian motorCantor functionCantor setCapacity dimensionCircles of ApolloniusCoastCoastline of the United KingdomConformal dimensionConformal loop ensembleConvex hullCorrelation dimensionCurveDetrended fluctuation analysisDimensionDimension (disambiguation)Diophantine approximationDistance setEdward MarczewskiEffective dimensionEngel expansionExponential growthExterior dimensionFalconer's conjectureFelix HausdorffFibonacci word fractalFractalFractal curveFractal dimension
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Hausdorff dimension
In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that part
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Die Hausdorff-Dimension wurde ...... endung als fraktale Dimension.
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En mathématiques, et plus préc ...... ne pas être un entier naturel.
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Existem muitas abordagens sobr ...... to, é a Dimensão de Hausdorff.
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Hausdorffdimension är en matem ...... n på dimensionen hos en mängd.
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Hausdorffova míra (dále ) je „ ...... rů dobrého spočetného pokrytí.
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In de wiskunde is de hausdorff ...... ikkeld door Abram Besikovitsj.
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In matematica, la dimensione d ...... di esse è fortemente tecnica.
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In mathematics, Hausdorff dime ...... Minkowski–Bouligand dimension.
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La dimensió de Hausdorff o dim ...... era) per a un objecte fractal.
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La dimensión de Hausdorff o di ...... f como a la dimensión fractal.
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Die Hausdorff-Dimension wurde ...... endung als fraktale Dimension.
@de
En mathématiques, et plus préc ...... sion de Hausdorff-Besicovitch.
@fr
Existem muitas abordagens sobr ...... to, é a Dimensão de Hausdorff.
@pt
Hausdorffdimension är en matem ...... n på dimensionen hos en mängd.
@sv
Hausdorffova míra (dále ) je „ ...... rů dobrého spočetného pokrytí.
@cs
In de wiskunde is de hausdorff ...... zij het niet een geheel getal.
@nl
In matematica, la dimensione d ...... ione di Hausdorff-Besicovitch.
@it
In mathematics, Hausdorff dime ...... ed to the conclusion that part
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La dimensió de Hausdorff o dim ...... era) per a un objecte fractal.
@ca
La dimensión de Hausdorff o di ...... f como a la dimensión fractal.
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label
Dimension de Hausdorff
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Dimensione di Hausdorff
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Dimensió de Hausdorff-Bezikóvitx
@ca
Dimensión de Hausdorff-Besicovitch
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Dimensão de Hausdorff
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Hausdorff dimension
@en
Hausdorff-Dimension
@de
Hausdorff-dimensie
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Hausdorffdimension
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Hausdorffova míra
@cs