A counting method for finding rational approximates to arbitrary order roots of integers

Ashok Kumar Gupta; Ashok Kumar Mittal

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A counting method for finding rational approximates to arbitrary order roots of integers

Ashok Kumar Gupta·Ashok Kumar Mittal

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Abstract

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

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Ashok Kumar Gupta, Ashok Kumar Mittal. 1999-12-11. A counting method for finding rational approximates to arbitrary order roots of integers. https://arxiv.org/abs/math/9912090

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