Visualizing paradoxical sets
type: Item
instance of: scholarly article
title: Visualizing paradoxical sets
zbMATH Open document ID: 1316.51011
author: Grzegorz Tomkowicz
author: Stan Wagon
published in: The Mathematical Intelligencer
publication date: 2014-12-17T00:00:00Z
review text: This paper shows how several counterintuitive ideas of set theory, such as the Banach-Tarski paradox and the existence of a certain type of Sierpiński set, can be given concrete interpretations in the hyperbolic plane. The authors use the upper-half plane model of hyperbolic geometry and the Poincaré disk model. The article ends with a conjecture which states that there is no discrete weak Sierpiński set in \(\mathbb R^3\).
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 6380988
zbMATH Keywords: Banach-Tarski paradox
zbMATH Keywords: Sierpiński set
zbMATH Keywords: Hausdorff paradox
zbMATH Keywords: paradoxical set
describes a project that uses: Wolfram Demonstrations
MaRDI profile type: Publication
full work available at URL: s00283-013-9433-1
OpenAlex ID: W2078796666
cites work: Q3657123
cites work: A paradoxical view of Escher's angels and devils.
cites work: Banach-Tarski Decompositions Using Sets with the Property of Baire
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cites work: On a problem of W. Sierpiński on the congruence of sets
cites work: Q3687182
DOI: 10.1007/S00283-013-9433-1
description: scientific article; zbMATH DE number 6380988