Abstract

SOLANILLA, Leonardo; PALACIO, Óscar  and  HERNANDEZ, Uriel. A simple proof of Abel's theorem on the lemniscate. ing.cienc. [online]. 2010, vol.6, n.12, pp.43-49. ISSN 1794-9165.

Since Abel's original paper of 1827, his remarkable theorem on the constructibility of the lemniscate splitting has been proven with the aid of Elliptic Functions. Nowadays, Rosen's proof of 1981 is considered definitive. He also makes use of (modern and more elaborate) Class Field Theory.Here we present a novel, short and simple proof of Abel's Theorem on the lemniscate and its converse. Our only ingredients are the addition formulas of Gauss lemniscatic functions and some basic facts of Galois Theory.

Keywords : Abel's theorem on the lemniscate; Gauss lemniscatic functions; geometric constructions.

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