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.
@article{7489,
title = {O Teorema de Banach- Tarski - doi: 10.5269/bspm.v22i2.7489},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v22i2.7489},
language = {EN},
url = {http://dml.mathdoc.fr/item/7489}
}
Panek, Luciano. O Teorema de Banach- Tarski - doi: 10.5269/bspm.v22i2.7489. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v22i2.7489. http://gdmltest.u-ga.fr/item/7489/