1999/12/11 by Ashok Kumar Gupta, Gupta, Ashok Kumar, Ashok Mittal +2 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Numerical Methods and Algorithms #math.GM
paper · pdf · doi:10.48550/arxiv.math/9912090
arxiv created 1999/12/11 · openalex publication_date 1999/12/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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