O Teorema de Banach- Tarski

O Teorema de Banach- Tarski

We will present in this work the curious and provocative Banach-Tarski Theorem: subsets of the three-dimensional Euclidean space with non-empty interior is part congruent, that is, one subset can be rearranged by isometries of a finite number of parts of the other. The proof, here (a free translation...

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Bibliographic Details
Main Author: Luciano Panek
Format: Article
Language:English
Published: Sociedade Brasileira de Matemática 2004-11-01
Series:Boletim da Sociedade Paranaense de Matemática
Subjects:
Banach- Tarski theorem.
Online Access:http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7489/4308
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spelling doaj-f3423b59953e47abacb0dffeccb0a0ce2020-11-24T20:58:03ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882004-11-01222127144O Teorema de Banach- TarskiLuciano PanekWe will present in this work the curious and provocative Banach-Tarski Theorem: subsets of the three-dimensional Euclidean space with non-empty interior is part congruent, that is, one subset can be rearranged by isometries of a finite number of parts of the other. The proof, here (a free translation from Karl Stromberg’s text, American Mathematical Monthly, 1979), is elegant and of elementary level, therefore accessible to the undergraduate student in Mathematics.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7489/4308Banach- Tarski theorem.
collection DOAJ
language English
format Article
sources DOAJ
author Luciano Panek
spellingShingle Luciano Panek
O Teorema de Banach- Tarski
Boletim da Sociedade Paranaense de Matemática
Banach- Tarski theorem.
author_facet Luciano Panek
author_sort Luciano Panek
title O Teorema de Banach- Tarski
title_short O Teorema de Banach- Tarski
title_full O Teorema de Banach- Tarski
title_fullStr O Teorema de Banach- Tarski
title_full_unstemmed O Teorema de Banach- Tarski
title_sort o teorema de banach- tarski
publisher Sociedade Brasileira de Matemática
series Boletim da Sociedade Paranaense de Matemática
issn 0037-8712
2175-1188
publishDate 2004-11-01
description We will present in this work the curious and provocative Banach-Tarski Theorem: subsets of the three-dimensional Euclidean space with non-empty interior is part congruent, that is, one subset can be rearranged by isometries of a finite number of parts of the other. The proof, here (a free translation from Karl Stromberg’s text, American Mathematical Monthly, 1979), is elegant and of elementary level, therefore accessible to the undergraduate student in Mathematics.
topic Banach- Tarski theorem.
url http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/7489/4308
work_keys_str_mv AT lucianopanek oteoremadebanachtarski
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