实数的连分数展开及程序设计

摘要

运用数学软件实现了实数的连分数展开.首先介绍连分数的结构,并设计相应的程序,用以实现任一实数的连分数展开;然后分析连分数与渐进分数的关系,给出无理数e的渐进分数形式,并对渐进分数所蕴含的规律进行演示.%The continued fraction＇s expansion of real number was realized with mathematical soft.Firstly,based on the structure of continued fractions,the corresponding program was designed to realize the continued fraction＇s expansion of real number.Then the relation of continued fraction and progressive fraction was analyzed.Finally,the progressive fractions of irrational number of e were given,and some laws contained in the progressive fractions were demonstrated.