Definition:Semi-Magic Square
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Definition
A semi-magic square is an arrangement of $n^2$ numbers into an $n \times n$ square array such that:
are the same.
Hence a semi-magic square is like a magic square, but without the property that the sum of the elements along each diagonal are the same as those of the rows and columns.
Also known as
A semi-magic square is also seen unhyphenated: semimagic square.
Some sources refer to a semi-magic square as a magic square, and a true magic square as a diagonally magic square.
So let's be careful out there.
Also see
- Results about semi-magic squares can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): magic square
- Weisstein, Eric W. "Magic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MagicSquare.html
- Weisstein, Eric W. "Semimagic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemimagicSquare.html