Sputsoft » Stern-Brocot tree 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 Fractions and Circles http://sputsoft.com/blog/2010/02/fractions-and-circles.html http://sputsoft.com/blog/2010/02/fractions-and-circles.html#comments Sat, 06 Feb 2010 10:45:35 +0000 sput http://sputsoft.com/?p=1147 http://sputsoft.com/blog/2010/02/fractions-and-circles.html/feed 3 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