In this unit, we analyze the Magic Polygons of order 3 (P(n, 2)) and present sure properties that were constructive in the implementation of an treasure to determine the number of magic polygons for formal polygons up to 24 hands. First, is made an sameness between Magic Polygons and aspects of the Symmetric Group, such sameness is clear once the Magic Polygons is a fixed arrangement of numbers. Made aforementioned equivalence, it's incidental that in order to find all Magic Polygons for a regular shape of n sides, it's enough to produce all permutations of the set {1,2. . . 2n+1} and verify that ones answer the definition. But this is not highest in rank way, cause the same change would be restored many times, due the action of the Dihedral Group in the consistent polygon. Therefore, a analytical approach is needed so that simplify the computational process. This habit, we reach the concept of Equivalents Magic Polygons, and located in some features here began, we avoid few of them. Yet, is introduced the idea of Derivatives Magic Polygons because a Magic Polygon maybe built from some Arithmetic Progression, and is not restricted to the everyday sequence.
Author(s) Details:
Danniel Dias Augusto,
Departamento
de Matematica - Universidade de Brasilia (UnB), Distrito Federal- 70297-400,
Brasil.
Please see the link here: https://stm.bookpi.org/RHMCS-V4/article/view/9159
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