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Menger sponge

In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpiński cube, or Sierpiński sponge) is a fractal curve. It is a three-dimensional generalization of the two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.

Properties, MegaMenger & Similar fractals

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Overview

Construction

Properties

Formal definition

MegaMenger

Similar fractals

Advanced semantic analysis

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Map overview Semantic statistics

Menger sponge

Nodes53
Edges52
Triples80
Avg. degree1.96
Density0.037736
Components1

How this topic connects Entity context

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Menger sponge

Top relations

related to External links · 21
Menger sponge → Business Card Menger Sponge, Dickau, Discussion, Dr, Further, Hunt, Institute For FiguringAn, Java, Jeannine Mosely, Jerusalem Cube, Mathekniticians, Menger, Number, Post-itsThe Mystery, Sierpinski, Sliced, SunFlowPost-It Menger Sponge, Video, Wolfram MathWorldThe, Woolly Thoughts Level
related to MegaMenger · 18
Menger sponge → BathA, Cambridge Level-3 MegaMenger, Cambridge Science Festival, Each, In, James Madison University, Laura Taalman, London, Matt Parker, MegaMenger, MegaMengers, Menger, One, Queen Mary University, Sierpinski, Tetrix, The, University
related to Further reading · 17
Menger sponge → American Mathematical Monthly, Chromatic, Gaven, Geometric, ISBN, Iwaniec, JSTOR, Li, Martin, Menger, MR, Oxford Mathematical Monographs, Problem, Tadeusz, The Clarendon Press Oxford, University Press, Zhou
related to Construction · 8
Menger sponge → Begin, Divide, Menger, Remove, Repeat, Rubik's Cube, The, This
related to Properties · 7
Menger sponge → Cantor, Each, Menger, Sierpinski, The, Therefore, Yet
related to Jerusalem cube · 6
Menger sponge → Eric Baird, Greek, It, Jerusalem, Menger, The
related to Formal definition · 2
Menger sponge → Formally, Menger
is a · 1
Menger sponge → closed set

Important terminology Word statistics

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Important terminology

cube menger sponge fractal cubes dimension construction jerusalem displaystyle curve sierpinski also smaller number carpet set similar 20 hausdorff described

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Menger spongeis aclosed set0.90text
Menger spongerelated to ConstructionThe0.60section
Menger spongerelated to ConstructionMenger0.60section
Menger spongerelated to ConstructionBegin0.60section
Menger spongerelated to ConstructionDivide0.60section
Menger spongerelated to ConstructionRubik's Cube0.60section
Menger spongerelated to ConstructionThis0.60section
Menger spongerelated to ConstructionRemove0.60section
Menger spongerelated to ConstructionRepeat0.60section
Menger spongerelated to External linksMenger0.60section
Menger spongerelated to External linksWolfram MathWorldThe0.60section
Menger spongerelated to External linksBusiness Card Menger Sponge0.60section

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    Min side: 3
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