Magic star
Encyclopedia
An n-pointed magic star is a star polygon with Schläfli symbol {n/2} in which numbers are placed at each of the n vertices
and n intersections, such that the four numbers on each line sum to the same magic constant
. A normal magic star contains the consecutive integer
s 1 to 2n. The magic constant of an n-pointed normal magic star is M = 4n + 2.
No star polygons with fewer than 5 points exist, and the construction of a normal 5-pointed magic star turns out to be impossible. The smallest examples of normal magic stars are therefore 6-pointed. Some examples are given below. Notice that for specific values of n, the n-pointed magic stars are also known as magic hexagram etc.
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
and n intersections, such that the four numbers on each line sum to the same magic constant
Magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....
. A normal magic star contains the consecutive integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s 1 to 2n. The magic constant of an n-pointed normal magic star is M = 4n + 2.
No star polygons with fewer than 5 points exist, and the construction of a normal 5-pointed magic star turns out to be impossible. The smallest examples of normal magic stars are therefore 6-pointed. Some examples are given below. Notice that for specific values of n, the n-pointed magic stars are also known as magic hexagram etc.
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| Magic hexagram M = 26 | Magic heptagram M = 30 | Magic octagram M = 34 |