Resumen

SOLANILLA CH., Leonardo; PALACIO M., Óscar Jhoan  y  HERNANDEZ R., Uriel. Abel's theorem on the lemniscate. Rev. ing. univ. Medellín [online]. 2010, vol.9, n.17, pp. 207-213. ISSN 1692-3324.

In this article, Abel's theorem for lemniscates has been demonstrated without the help of elliptical function theory and without any reference to the modern theory of fields. Essential ingredients of the demonstration are Gauss' lemniscates functions and some elementary on factorization in the ring of rational coefficients. The procedure is very powerful. It was proved that geometric construction is possible. Algebraic operations which indicated the construction were also indicated.

Palabras llave : Lemniscates division; elliptical functions; geometrical constructions; Abel's theorem; Galois' theorem.