Crespo Vicente, TeresaSoler Terricabras, Toni2023-10-312023-10-312023-06-13https://hdl.handle.net/2445/203293Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Teresa Crespo Vicente[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.63 p.application/pdfcatcc-by-nc-nd (c) Toni Soler Terricabras, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Teoria de GaloisCossos algebraicsGeometria algebraica aritmèticaFuncions el·líptiquesTreballs de fi de grauGalois theoryAlgebraic fieldsArithmetical algebraic geometryElliptic functionsBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess