Minimal Number of Steps in Euclidean Algorithm and its Application to Rational Tangles
Abstract
We define the regular Euclidean algorithm and the general form which leads to the method of least absolute remainders and also the method of negative remainders. We are going to show that if looked from the perspective of subtraction, the method of least absolute remainders and the regular method have the same number of steps which is in fact the minimal number of steps possible. This enables us to apply the theory in rational tangles to determine the most efficient way to untangle a rational tangle.
Keywords
Cite
@article{arxiv.1311.7171,
title = {Minimal Number of Steps in Euclidean Algorithm and its Application to Rational Tangles},
author = {M. Syafiq Johar},
journal= {arXiv preprint arXiv:1311.7171},
year = {2015}
}
Comments
15 Pages. This project was supervised by Professor David Gauld (University of Auckland). This is my first academic paper, written as an undergraduate. Therefore, I would appreciate pointers and tips. It is going to be published in Rose-Hulman Undergraduate Mathematics Journal