%0 Journal Article
%T A simple proof of AbelĄ¯s theorem on the lemniscate
%A Leonardo Solanilla
%A Uriel Hern¨ĸndez
%A ¨Žscar Palacio
%J -
%D 2010
%X Since AbelĄ¯s original paper of 1827, his remarkable theorem on the constructibilityof the lemniscate splitting has been proven with the aid of Elliptic Functions. Nowadays, RosenĄ¯s proof of 1981 is considered definitive. He also makesuse of (modern and more elaborate) Class Field Theory. Here we present anovel, short and simple proof of AbelĄ¯s Theorem on the lemniscate and itsconverse. Our only ingredients are the addition formulas of Gauss lemniscaticfunctions and some basic facts of Galois Theory
%K AbelĄ¯s theorem on the lemniscate
%K Gauss lemniscatic functions
%K geometric constructions.
%U http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/331