Paradoks Banach–Tarski

Paradoks Banach–Tarski adalah sebuah teorema geometri teori himpunan, yang dinyatakan sebagai berikut: Sebuah bola padat ditempatkan di ruang 3 dimensi, bola tersebut kemudian dipecah berkeping-keping dan disatukan kembali menjadi dua bola dengan ukuran yang sama dengan bola yang asli. Rekonstruksi dapat dilakukan dengan setidaknya lima kepingan.

Referensi

Banach, Stefan; Tarski, Alfred (1924). Review at JFM. "Sur la décomposition des ensembles de points en parties respectivement congruentes" (PDF). Fundamenta Mathematicae. 6: 244–277.
Churkin, V. A. (2010). "A continuous version of the Hausdorff–Banach–Tarski paradox". Algebra and Logic. 49 (1): 91–98. doi:10.1007/s10469-010-9080-y.
Edward Kasner & James Newman (1940) Mathematics and the Imagination, pp 205–7, Simon & Schuster.
Stromberg, Karl (March 1979). "The Banach–Tarski paradox". The American Mathematical Monthly. Mathematical Association of America. 86 (3): 151–161. doi:10.2307/2321514. JSTOR 2321514.
Su, Francis E. "The Banach–Tarski Paradox" (PDF).
von Neumann, John (1929). "Zur allgemeinen Theorie des Masses" (PDF). Fundamenta Mathematicae. 13: 73–116.
Wagon, Stan (1994). The Banach–Tarski Paradox. Cambridge: Cambridge University Press. ISBN 0-521-45704-1.
Wapner, Leonard M. (2005). The Pea and the Sun: A Mathematical Paradox. Wellesley, Massachusetts: A.K. Peters. ISBN 1-56881-213-2.
Tomkowicz, Grzegorz; Wagon, Stan (2016). The Banach–Tarski Paradox 2nd Edition. Cambridge: Cambridge University Press. ISBN 9781107042599.

Pranala luar

Paradoks Banach–Tarski di ProofWiki

The Banach-Tarski Paradox by Stan Wagon (Macalester College), the Wolfram Demonstrations Project.
Irregular Webcomic! #2339 by David Morgan-Mar provides a non-technical explanation of the paradox. It includes a step-by-step demonstration of how to create two spheres from one.
Vsauce. "The Banach–Tarski Paradox" – via YouTube gives an overview on the fundamental basics of the paradox.