Magic polygon

Source: Wikipedia, the free encyclopedia.
Not to be confused with Polygon Magic.

A magic polygon is a polygonal magic graph with integers on its vertices.

Perimeter magic polygon

A magic polygon, also called a perimeter magic polygon,[1][2] is a polygon with an integers on its sides that all add up to a magic constant.[3][4] It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant.[1] Magic polygons are a generalization of other magic shapes[5] such as magic triangles.[6]

This displays order 3 magic triangles, a type of magic polygon.

Magic polygon with a center point

Victoria Jakicic and Rachelle Bouchat defined magic polygons as n-sided regular polygons with 2n+1 nodes such that the sum of the three nodes are equal. In their definition, a 3 × 3 magic square can be viewed as a magic 4-gon. There are no magic odd-gons with this definition.[7]

Magic polygons and degenerated magic polygons

Danniel Dias Augusto and Josimar da Silva defined the magic polygon P(n,k) as a set of vertices of concentric n-gon and a center point. In this definition, magic polygons of Victoria Jakicic and Rachelle Bouchat can be viewed as P(n,2) magic polygons. They also defined degenerated magic polygons.[8]

See also

References

  1. ^ a b "Perimeter Maghic Polygons". www.trottermath.net. Archived from the original on 2018-01-12. Retrieved 2017-02-12.
  2. ^ "Perimeter Magic Polygon >k=3". www.magic-squares.net. Retrieved 2017-02-12.
  3. ISBN 9780787292966
    . Magic polygon math.
  4. ISBN 9780521339940
    .
  5. ISBN 9781461209638
    .
  6. ^ Heinz, Harvey D. "Perimeter Magic Triangles". recmath.org. Retrieved 2017-02-12.
  7. arXiv:1801.02262 [math.CO
    ].
  8. arXiv:1906.11342 [math.CO
    ].

External links


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