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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, is a polygon with an integers on its sides that all add up to a magic constant. It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant. Magic polygons are a generalization of other magic shapes such as magic triangles.

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.

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 ${\displaystyle k/2}$ 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.

See also

• Magic square

References

1. ^ "Perimeter Magic 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 Triangles". recmath.org. Retrieved 2017-02-12.
7. Jakicic, Victoria; Bouchat, Rachelle (2018). "Magic Polygons and Their Properties". arXiv:1801.02262 .
8. Danniel Dias Augusto; Josimar da Silva Rocha (2019). "Magic Polygons and Degenerated Magic Polygons: Characterization and Properties". arXiv:1906.11342 .

External links

• https://udayton.edu/artssciences/academics/mathematics/images_and_files/umd_proceedings_files/2018/Jakicic-journal.pdf

v t e Magic polygons
Types	Magic circle Magic hexagon Magic hexagram Magic square Magic star Magic triangle
Related shapes	Alphamagic square Antimagic square Geomagic square Heterosquare Pandiagonal magic square Prime reciprocal magic square Most-perfect magic square
Higher dimensional shapes	Magic cube classes Magic hypercube Magic hyperbeam
Classification	Associative magic square Pandiagonal magic square Multimagic square
Related concepts	Latin square Word square Number Scrabble Eight queens puzzle Magic constant Magic graph Magic series

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