基于稳定行走的全欧几里德算法

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2021-04-14 DOI:10.4236/AM.2021.124018

Carlos Rodriguez, M. A. Cruz, C. Falcon

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引用次数: 0

摘要

设x和y为两个正实数，且x < y。考虑一个旅行者，在区间[0,y/2]上，从0出发，步数为x。每当一个步数到达区间的一个端点时，旅行者就会从端点反弹，以完成步数。我们证明，当y/x是有理数时，旅行者的足迹是x和y的完整欧几里得算法的输出。在y/x是无理数的情况下，算法在理论上不是有限的;然而，它是研究其不合理性的新工具。

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Full Euclidean Algorithm by Means of a Steady Walk

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.

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来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.