Tarski's circle squaring problem
F.N.P. van Ruiten (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Klaas Pieter Hart – Mentor
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Abstract
In this thesis, we take a look Tarski's circle squaring problem: Are an open disk and an open square equidecomposable by using finitely many Borel pieces? The proof is a special case of the one given by Marks and Unger and as such will be based on their proof. We have distilled the original proof to make it understandable for a bachelor student without requiring extra knowledge. We give an example of another case that can be solved without using the method used in the proof. We also take a look at what Borel complexity is, calculate the complexity of the sets used in the example and go over the process of calculating the complexity of the pieces used by Marks and Unger in broad strokes.
Since the proofs of the used lemmas are very long and/or technical, they have not been included in this report, but can be found in their respective source material.