most recent 30 from http://mathoverflow.net 2013-05-19T09:18:57Z http://mathoverflow.net/feeds/user/22915 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/10535/ways-to-prove-the-fundamental-theorem-of-algebra/94070#94070 J. M. Almira 2012-04-14T22:18:03Z 2012-04-14T22:18:03Z

<p>Perhaps it could be of interest for you to know that there exists purely geometric proofs of this result. Concretely, it can be shown that, if the FTA fails then there exists a plane Riemannian metric over the Sphere S^2. Of course, this produces a contradiction since the sphere is not flat. This proof can be located at the very recent paper by J M Almira and A Romero: "Some Riemannian Geometric proofs of the fundamental theorem of algebra", which is available at: <a href="http://www.mathem.pub.ro/dgds/v14/D14-al.pdf" rel="nofollow">http://www.mathem.pub.ro/dgds/v14/D14-al.pdf</a></p> <p>J. M. Almira</p>