Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff....
24 KB (3,147 words) - 22:17, 26 April 2024
the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here is a list of fractals, ordered by increasing Hausdorff dimension...
52 KB (1,139 words) - 21:11, 7 August 2024
one-dimensional Hausdorff measure of a simple curve in R n {\displaystyle \mathbb {R} ^{n}} is equal to the length of the curve, and the two-dimensional Hausdorff measure...
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of the concept of a fractal dimension through the work of Hausdorff in the early 1900s who defined a "fractional" dimension that has come to be named after...
44 KB (4,750 words) - 05:42, 4 June 2024
leads to the definition of the Minkowski dimension and its more sophisticated variant, the Hausdorff dimension, but there are also other answers to that...
34 KB (3,895 words) - 05:43, 12 September 2024
Point (geometry) (section Hausdorff dimension)
r i d < δ . {\displaystyle \sum _{i\in I}r_{i}^{d}<\delta .} The Hausdorff dimension of X is defined by dim H ( X ) := inf { d ≥ 0 : C H d ( X ) = 0...
14 KB (1,582 words) - 16:37, 16 May 2024
named after him: Hausdorff completion Hausdorff convergence Hausdorff density Hausdorff dimension Hausdorff distance Hausdorff gap Hausdorff maximal principle...
55 KB (7,450 words) - 11:19, 18 July 2024
Hausdorff (1868–1942), the German mathematician after whom Hausdorff spaces are named Hausdorff dimension, a measure theoretic concept of dimension Hausdorff...
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and lower box dimensions are strongly related to the more popular Hausdorff dimension. Only in very special applications is it important to distinguish...
10 KB (1,593 words) - 22:31, 31 August 2024
should concern the Hausdorff dimension of the set of badly approximable numbers. And indeed, V. Jarník proved that the Hausdorff dimension of this set is...
30 KB (4,055 words) - 20:53, 8 September 2024