Magic polygon explained

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. Magic polygons are a generalization of other magic shapes^[5] such as magic triangles.^[6]

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

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.^[8]

See also

• Magic square

External links

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

Notes and References

1. Web site: Perimeter Magic Polygons. www.trottermath.net. 2017-02-12. https://web.archive.org/web/20180112073607/http://www.trottermath.net/simpleops/pmp.html. 2018-01-12. dead.
2. Web site: Perimeter Magic Polygon >k=3. www.magic-squares.net. 2017-02-12.
3. Book: Staszkow, Ronald. Math Skills: Arithmetic with Introductory Algebra and Geometry. registration. 199. Magic polygon math.. 2003-05-01. Kendall Hunt. 9780787292966. en.
4. Book: Bolt, Brian. Even More Mathematical Activities. 1987-04-09. Cambridge University Press. 9780521339940. en.
5. Book: Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics. Croft. Hallard T.. Falconer. Kenneth. Guy. Richard K.. 2012-12-06. Springer Science & Business Media. 9781461209638. en.
6. Web site: Perimeter Magic Triangles. Heinz. Harvey D.. recmath.org. 2017-02-12.
7. 1801.02262. Jakicic. Victoria. Bouchat. Rachelle. Magic Polygons and Their Properties. 2018. math.CO.
8. 1906.11342. Danniel Dias Augusto. Josimar da Silva Rocha. Magic Polygons and Degenerated Magic Polygons: Characterization and Properties. 2019. math.CO.