REAL Magic Squares, indeed!!!!!

Perhaps you've seen the magic square 8 1 6 3 5 7 4 9 2 which has the property that all rows, columns and diagonals sum to 15. Well, it has another "magic" and "square" property! If you read the rows as NUMBERS, forwards and backwards, and square them, then

816^{2} + 357^{2} + 492^{2} = 618^{2} + 753^{2} + 294^{2}.

Magic?

The Math Behind the Fact: This holds for ANY 3x3 magic square (though if the entries contain more than one digit, you will have to carry the extra places) using techniques of linear algebra.

#NumberTheory #TorqueGroup #LinearAlgebra #MagicSquares #FUNTHEOREMS

Easy Math Editor

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Comments

Curious, is this something you discovered, or was this already known?

Drex Beckman - 5 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$