Magic polygon
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]
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
Danielle Dias Augustoa and Josimar da Silva defined the magic polygon P(n,k) as a set of vertices of [math]\displaystyle{ k/2 }[/math] 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
- ↑ 1.0 1.1 "Perimeter Maghic Polygons". http://www.trottermath.net/simpleops/pmp.html.
- ↑ "Perimeter Magic Polygon >k=3". http://www.magic-squares.net/perimeter-2.htm.
- ↑ Staszkow, Ronald (2003-05-01) (in en). Math Skills: Arithmetic with Introductory Algebra and Geometry. Kendall Hunt. p. 199. ISBN 9780787292966. https://archive.org/details/mathskills00rona. "Magic polygon math."
- ↑ Bolt, Brian (1987-04-09) (in en). Even More Mathematical Activities. Cambridge University Press. ISBN 9780521339940. https://books.google.com/books?id=KPIPwdIrSE0C&q=%22Magic+polygon%22+math&pg=PA192.
- ↑ Croft, Hallard T.; Falconer, Kenneth; Guy, Richard K. (2012-12-06) (in en). Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics. Springer Science & Business Media. ISBN 9781461209638. https://books.google.com/books?id=rdDTBwAAQBAJ&q=perimeter+Magic+polygon&pg=PA168.
- ↑ Heinz, Harvey D.. "Perimeter Magic Triagonals". http://recmath.org/Magic%20Squares/perimeter.htm.
- ↑ Jakicic, Victoria; Bouchat, Rachelle (2018). "Magic Polygons and Their Properties". arXiv:1801.02262 [math.CO].
- ↑ Danniel Dias Augusto; Josimar da Silva Rocha (2019). "Magic Polygons and Degenerated Magic Polygons: Characterization and Properties". arXiv:1906.11342 [math.CO].
External links
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