Magic star
Special arrangement of numbers on a star
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 integers from 1 to 2n with no numbers 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 hexagrams (n = 6), magic heptagrams (n = 7), etc.
| Magic hexagram M = 26 |
Magic heptagram M = 30 |
Magic octagram M = 34 |
The number of distinct normal magic stars of type {n/2} for n up to 15 is,
Sources and credits
This article is adapted from the Wikipedia article “Magic star”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Magic6star-sum26.svg by Fred the Oyster iThe source code of this SVG is valid. This vector image was created with Adobe Illustrator by v., CC BY-SA 4.0
Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.
