REDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES | Zendy

Marco Ripà | Zendy

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REDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES

Author(s) -

Marco Ripà

Publication year - 2021

Publication title -

journal of fundamental mathematics and applications (jfma)

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)}.

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