Magic polygon

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

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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 sum. [3] [4] It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant, or magic sum. [1] Magic polygons are the generalization of other magic shapes [5] such as magic triangles. [6]

This displays order 3 magic triangles, a type of magic polygon. Order 3 Magic Triangles.gif
This displays order 3 magic triangles, a type of magic polygon.

Magic polygon with a center point

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

Magic polygons and degenerated magic polygons

Danielle Dias Augustoa 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

Related Research Articles

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Schröder–Hipparchus number

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References

  1. 1 2 "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. Staszkow, Ronald (2003-05-01). Math Skills: Arithmetic with Introductory Algebra and Geometry . Kendall Hunt. p.  199. ISBN   9780787292966. Magic polygon math.
  4. Bolt, Brian (1987-04-09). Even More Mathematical Activities. Cambridge University Press. ISBN   9780521339940.
  5. Croft, Hallard T.; Falconer, Kenneth; Guy, Richard K. (2012-12-06). Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics. Springer Science & Business Media. ISBN   9781461209638.
  6. Heinz, Harvey D. "Perimeter Magic Triagonals". recmath.org. Retrieved 2017-02-12.
  7. Jakicic, Victoria; Bouchat, Rachelle (2018). "Magic Polygons and Their Properties". arXiv: 1801.02262 [math.CO].
  8. Danniel Dias Augusto; Josimar da Silva Rocha (2019). "Magic Polygons and Degenerated Magic Polygons: Characterization and Properties". arXiv: 1906.11342 [math.CO].