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. 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.
| Magic hexagram M = 26 |
Magic heptagram M = 30 |
Magic octagram M = 34 |
Famous quotes containing the words magic and/or star:
“Self-esteem is the real magic wand that can form a child’s future. A child’s self-esteem affects every area of her existence, from friends she chooses, to how well she does academically in school, to what kind of job she gets, to even the person she chooses to marry.”
—Stephanie Martson (20th century)
“Events, actions arise, that must be sung, that will sing themselves. Who can doubt, that poetry will revive and lead in a new age, as the star in the constellation Harp, which now flames in our zenith, astronomers announce, shall one day be the pole- star for a thousand years?”
—Ralph Waldo Emerson (1803–1882)