Definition:Magic Hexagon
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Definition
A magic hexagon is a centered hexagonal pattern of cells containing the natural numbers from $1$ to the number of cells such that the numbers in all the cells in a given straight line all add up to the same number.
Line
A line of a magic hexagon is a set of consecutively adjacent cells, in any of the three directions parallel to the sides of the underlying hexagon.
Order of Magic Hexagon
Let $H$ be an magic hexagon created on the $n$th centered hexagonal number.
That is, let $H$ have $n$ cells along each side.
Then $H$ is an order $n$ magic hexagon.
Magic Constant
The magic constant of a magic hexagon is the number that each of the lines adds up to.
Examples
Order $1$
Order $3$
Also see
- Results about magic hexagons can be found here.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $19$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $19$
- Weisstein, Eric W. "Magic Hexagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MagicHexagon.html