A counting method for finding rational approximates to arbitrary order roots of integers
综合数学
2007-05-23 v1
摘要
It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a 'replacement rule' that generates a word W* from another word W consisting of symbols belonging to a finite 'alphabet' of size m. This rule applied iteratively on almost any initial word W0, yields a sequence of words {Wi} such that the relative frequency of different symbols in the word Wi approaches powers of the m'th root of N as i tends to infinity
引用
@article{arxiv.math/9912090,
title = {A counting method for finding rational approximates to arbitrary order roots of integers},
author = {Ashok Kumar Gupta and Ashok Kumar Mittal},
journal= {arXiv preprint arXiv:math/9912090},
year = {2007}
}