Magic star

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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 integers 1 to 2n. No numbers are ever repeated. 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. It can be proven that there exists no 4-pointed star that will satisfy the conditions here. 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.

Magic6star-sum26.png Magic7star-sum30.png Magic8star-sum34.png
Magic hexagram
M = 26
Magic heptagram
M = 30
Magic octagram
M = 34

See also[edit]

External links[edit]