Abstract
We introduce a definition of coloring by using joint probability distribution “JPD-coloring” for the plane which is equipped by tilingI. We investigate the JPD-coloring of ther-monohedral tiling for the plane by mutually congruent regular convex polygons which are equilateral triangles atr= 3 or squares atr= 4 or regular hexagons atr= 6. Moreover we present some computations for determining the corresponding probability values which are used to color in the three studied cases by MAPLE-Package.
Highlights
A tiling of the plane is a family of sets—called tiles—that cover the plane without gaps or overlaps
Let R2 be equipped by r-monohedral tiling I, and let
The authors declare that there is no conflict of interests regarding the publication of this paper
Summary
A tiling of the plane is a family of sets—called tiles—that cover the plane without gaps or overlaps. . .} of closed topological discs (tiles) which covers the Euclidean plane R2 and is such that the interiors of its tiles are disjoint. A point of the plane that is a vertex of one of the polygons in an edge-to-edge tiling is a vertex of every other polygon to which it belongs and it is called a vertex of the tiling. It should be noted that the only possible edge-to-edge tilings of the plane by mutually congruent regular convex polygons are the three regular. Some computations by MAPLE-Package to determine the probability values (vertices) for the three studied tilings are presented We introduce this alternative technique to expand and update the coloring technique to implement tiling according to a probabilistic approach. In this paper we consider pij having equal denominators (the large common multiplication of the denominators of the probabilities) “n”
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