Magic star
An n-pointed magic star is a star polygon with Schläfli symbol {n/2}[1] 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.[2] A normal magic star contains the integers from 1 to 2n with no numbers repeated.[3] 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.
| file:Magic6star-sum26.svg | file:magic7star-sum30.svg | file:magic8star-sum34.svg |
| Magic hexagram M = 26 |
Magic heptagram M = 30 |
Magic octagram M = 34 |
See also
| Types |  | |
|---|---|---|
| Related shapes | ||
| Higher dimensional shapes | ||
| Related concepts | ||
References
- ↑ Weisstein, Eric W.. "Star Polygon". http://mathworld.wolfram.com/StarPolygon.html.
- ↑ Staszkow, Ronald (2003-05-01) (in en). Math Skills: Arithmetic with Introductory Algebra and Geometry. Kendall Hunt. p. 374. ISBN 9780787292966. https://archive.org/details/mathskills00rona. "magic star math."
- ↑ "Magic Stars Index Page". http://www.magic-squares.net/magic_stars_index.htm#Introduction.
External links
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