Magic Polygon on:
[Wikipedia]
[Google]
[Amazon]
A magic polygon is a polygonal magic graph with
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
s on its vertices.Perimeter magic polygon
A magic polygon, also called a perimeter magic polygon, is apolygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...
with an integers on its sides that all add up to a magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
. It is where positive integers (from 1 to ''N'') on a ''k''-sided polygon add up to a constant. Magic polygons are a generalization
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common character ...
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 2''n''+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 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
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...
References
External links
* https://udayton.edu/artssciences/academics/mathematics/images_and_files/umd_proceedings_files/2018/Jakicic-journal.pdf Magic shapes {{math-stub