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tfg_soler_terricabras_toni.pdf (815.37 KB)

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Bachelor thesis

Publication date

2023-06-13

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cc-by-nc-nd (c) Toni Soler Terricabras, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/203293

Construcció de polı́gons regulars sobre la lemniscata

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Abstract

[en] The main goal of this study is to set a theoretical framework that allows us to determine in general sense which regular polygons can be constructed with ruler and compass on the lemniscate. To accomplish this, we compute the Galois groups arising from the division points of the curve. It is through the construction of lemnatomic extensions, analogous to cyclotomic extensions associated with the circle, that the constructibility of the desired polygons is determined. The present study puts forth two complementary formulations to address this problem: the first one, based on a purely geometric foundation, and the second one, with a broader approach incorporating the use of elliptic functions and elliptic curves.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Teresa Crespo Vicente

Subject

Teoria de Galois, Cossos algebraics, Geometria algebraica aritmètica, Funcions el·líptiques, Treballs de fi de grau

Subject (English)

Galois theory, Algebraic fields, Arithmetical algebraic geometry, Elliptic functions, Bachelor's theses

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

SOLER TERRICABRAS, Toni. Construcció de polı́gons regulars sobre la lemniscata. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/203293

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