most recent 30 from http://mathoverflow.net 2013-05-22T07:06:53Z http://mathoverflow.net/feeds/user/9601 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40337/ingenuity-in-mathematics/40377#40377 Fubini 2010-09-28T19:51:02Z 2010-09-28T19:51:02Z

<p>Linear algebra proof of Binet's formula for Fibonacci numbers.</p> <p>Fibonacci numbers satisfy</p> <p>$\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}^{n} = \begin{pmatrix} F_{n+1} &amp; F_{n} \\ F_{n} &amp; F_{n-1} \end{pmatrix}$</p> <p>Diagonalize the matrix on left.</p>