Full Euclidean Algorithm by Means of a Steady Walk

Autor:	Claudia Falcon, Carlos Manuel Falcón Rodríguez, María Antonia García Cruz
Rok vydání:	2021
Předmět:	Discrete mathematics Rational number Euclidean algorithm Diophantine equation Greatest common divisor Order (group theory) General Medicine Interval (mathematics) Extended Euclidean algorithm Positive real numbers Mathematics
Zdroj:	Applied Mathematics. 12:269-279
ISSN:	2152-7393 2152-7385
DOI:	10.4236/am.2021.124018
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::bb51ba6c16617bcc500c76f47fad3a60 https://doi.org/10.4236/am.2021.124018 Zobrazit plný text záznamu