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tfg_berlinches_planas_oriol.pdf (1.93 MB)

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Bachelor thesis

Publication date

2023-06-13

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cc-by-nc-nd (c) Oriol Berlinches Planas, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/202745

Variants of the Square Peg Problem

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Abstract

[en] The Square Peg Problem, also known as Toeplitz’ Conjecture, is an unsolved problem in the mathematical areas of geometry and topology that states the following: Every simple closed curve in the plane inscribed a square. Even though it seems like an innocent statement, it requires a lot of technical knowledge to proof even when applying certain smoothness conditions to the curve. Over time, variants of this problem have emerged. Some of them offer very interesting results with beautiful proofs. We intend on giving a general historical overview about the Square Peg Problem and the most known variants. Then we will explore the variants related to the inscription of rectangles and triangles and show a few strong results.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Juan Carlos Naranjo del Val

Subject

Topologia, Treballs de fi de grau, Geometria diferencial, Politops, Corbes

Subject (English)

Topology, Bachelor's theses, Differential geometry, Polytopes, Curves

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

BERLINCHES PLANAS, Oriol. Variants of the Square Peg Problem. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/202745

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