Magic squares

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A magic square is a square arrangement of numbers in which each row, column and diagonal adds up to the same value (called the magic constant). Usually, the magic square has the numbers

1

to

n 2

(such squares are called normal). One of the best known magic squares has

n = 3

and magic constant

15

:

9	1	5
3	4	8
6	7	2

Magic constant

The magic constant of an

n  ×  n

magic square with numbers

1

to

n 2

is

${\frac {T_{n^{2}}}{n}}={\frac {n^{2}(n^{2}+1)}{2n}}={\frac {n(n^{2}+1)}{2}},$ (A006003)

where

Tk

is the k-th triangular number.

External links

• Weisstein, Eric W., Franklin Magic Square, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/FranklinMagicSquare.html]