Sputsoft » continued fraction http://sputsoft.com/blog Mathematics and Computer Programming Sun, 25 Jul 2010 10:20:33 +0000 en hourly 1 http://wordpress.org/?v=3.0 The Stern-Brocot Tree of Fractions http://sputsoft.com/blog/2009/12/the-stern-brocot-tree-of-fractions.html http://sputsoft.com/blog/2009/12/the-stern-brocot-tree-of-fractions.html#comments Fri, 04 Dec 2009 20:21:54 +0000 sput http://sputsoft.com/?p=998 \frac{m_1}{n_1} and \frac{m_2}{n_2} with positive numerators and denominators. The fraction \frac{m_1+m_2}{n_1+n_2} is called the mediant of \frac{m_1}{n_1} and \frac{m_2}{n_2}. It is straightforward to show that the mediant is placed numerically between the original fractions,
\frac{m_1}{n_1} < \frac{m_2}{n_2} \quad \Rightarrow \quad \frac{m_1}{n_1} < \frac{m_1+m_2}{n_1+n_2} < \frac{m_2}{n_2}.
Consider now the following simple procedure [...]]]> http://sputsoft.com/blog/2009/12/the-stern-brocot-tree-of-fractions.html/feed 1 Continued Fractions and Continuants http://sputsoft.com/blog/2009/11/continued-fractions-and-continuants.html http://sputsoft.com/blog/2009/11/continued-fractions-and-continuants.html#comments Tue, 10 Nov 2009 15:27:42 +0000 sput http://sputsoft.com/?p=904 a_0 + \displaystyle\frac{1}{a_1 + \displaystyle\frac{1}{\ddots + \displaystyle\frac{1}{a_{n-1} + \displaystyle\frac{1}{a_n}}}} where the a_k's are real numbers called the partial quotients [...]]]> http://sputsoft.com/blog/2009/11/continued-fractions-and-continuants.html/feed 4