Full Euclidean Algorithm by Means of a Steady Walk

作     者：Carlos M. Falcon Rodriguez Maria A. Garcia Cruz Claudia Falcon Carlos M. Falcon Rodriguez;Maria A. Garcia Cruz;Claudia Falcon

作者机构：Grupo de Investigación de Análisis Matemático Instituto de Formación docente Salomé Ureñ a Santo Domingo D.N. República Dominicana Wake Forest University Winstom-Salem NC USA 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2021年第12卷第4期

页      面：269-279页

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Extended Euclidean Algorithm Greatest Common Divisor Incommensurable Numbers Steady Walk Diophantine Equation 

摘      要：Let x and y be two positive real numbers with x y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case that y/x is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.