Construcció de polı́gons regulars sobre la lemniscata

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.