Editing Magic star (section)

{{Short description|Special arrangement of numbers on a star}}
{{Distinguish|Star Magic}}

An ''n''-pointed '''magic star''' is a [[star polygon]] with [[Schläfli symbol]] {''n''/2}<ref>{{MathWorld |urlname=StarPolygon |title=Star Polygon}}</ref> in which numbers are placed at each of the ''n'' [[vertex (geometry)|vertices]] and ''n'' intersections, such that the four numbers on each line sum to the same [[magic constant]].<ref>{{Cite book|url=https://archive.org/details/mathskills00rona|url-access=registration|page=[https://archive.org/details/mathskills00rona/page/374 374]|quote=magic star math.|title=Math Skills: Arithmetic with Introductory Algebra and Geometry|last=Staszkow|first=Ronald|date=2003-05-01|publisher=Kendall Hunt|isbn=9780787292966|language=en}}</ref> A '''normal''' magic star contains the [[integer]]s from 1 to 2''n'' with no numbers repeated.<ref>{{Cite web|url=http://www.magic-squares.net/magic_stars_index.htm#Introduction|title=Magic Stars Index Page|website=www.magic-squares.net|access-date=2017-01-14}}</ref> The magic constant of an ''n''-pointed normal magic star is ''M''&nbsp;=&nbsp;4''n''&nbsp;+&nbsp;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|magic hexagrams]]'' (n&nbsp;=&nbsp;6), ''magic heptagrams'' (n&nbsp;=&nbsp;7), etc.

{| style="margin:auto"
|- valign="bottom"
| style="padding: 0 1em" | [[file:Magic6star-sum26.svg]]
| style="padding: 0 1em" | [[file:magic7star-sum30.svg]]
| style="padding: 0 1em" | [[file:magic8star-sum34.svg]]
|-
| align="center" | Magic hexagram<br>''M'' = 26
| align="center" | Magic heptagram<br>''M'' = 30
| align="center" | Magic octagram<br>''M'' = 34
|}

The number of distinct normal magic stars of type {''n''/2} for ''n'' up to 15 is, 
: 0, 80, 72, 112, 3014, 10882, 53528, 396930, 2434692, 15278390, 120425006, ... {{OEIS|A200720}}.