Open AccessREDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES
Author(s) -
Marco Ripà
Publication year - 2021
Publication title -
journal of fundamental mathematics and applications
Language(s) - English
Resource type - Journals
eISSN - 2621-6035
pISSN - 2621-6019
DOI - 10.14710/jfma.v4i1.10106
Subject(s) - cartesian product , clockwise , combinatorics , extension (predicate logic) , euclidean geometry , set (abstract data type) , mathematics , product (mathematics) , euclidean distance , grid , algorithm , constraint (computer aided design) , computer science , geometry , rotation (mathematics) , programming language
In the present paper, we consider an optimization problem related to the extension in k-dimensions of the well known 3x3 points problem by Sam Loyd. In particular, thanks to a variation of the so called “clockwise-algorithm”, we show how it is possible to visit all the 3^k points of the k-dimensional grid given by the Cartesian product of (0, 1, 2) using covering trails formed by h(k)=(3^k-1)/2 links who belong to k (Euclidean) length classes. We can do this under the additional constraint of allowing only turning points which belong to the set B(k):={(0, 3) x (0, 3) x ... x (0, 3)}.