Sikora, Julia (2025) Exploration of the Banach-Tarski paradox. Bachelor's Thesis, Mathematics.
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Abstract
This thesis covers the proof of the Banach-Tarski paradox for the unit ball in $\R^3$, as well as extensions of this result to various objects and spaces. The Banach-Tarski paradox is generalized to the rational unit sphere in $\R^3$, the unit sphere in $\R^n$ for $n\geq3$, and the unit square in $\R^2$. Notions such as free group, equidecomposability, and paradoxical decomposition are defined and applied to prove various results leading to the proof of the Banach-Tarski paradox. Based on the paradoxical decompositions that originate from the proofs of the Banach-Tarski paradox, Mathematica code that creates a visualisation of sets that are used in the construction of the Banach-Tarski is developed. This code is applied to create figures for the unit sphere and the unit square.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Veen, R.I. van der and Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 21 Jul 2025 14:12 |
| Last Modified: | 21 Jul 2025 14:12 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36399 |
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