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Waffle Theorem

Eating a waffle, I just developed a new theorem.  First assume the waffle is square and made up of little squares.  If, like me, you eat around two edges, one square deep, so that the waffle stays square, you ALWAYS eat an odd number of squares.  Eg. 6x6, you eat 6 mini squares, follwed by 5, making 11 (odd number), so that the waffle itself stays square, now only 5x5.  My theorem hypothesises that this is true for all waffle sizes.  In fact it's called the "Waffle Theorem", and here is the mathematical proof:

y = x^2 - (x-1)^2

-> y = x^2 - (x^2 - 2x + 1)
-> y = 2x-1.

QED, because 2 times anything ("2x") is always even, and subtracting one ("-1") always makes an even number odd.  Hence my hypothesis holds true, regardless of waffle size.

Not bad for a Sunday night, all I wanted to do was eat the damn waffle...  I have to say though, it's this kind of thing that I love about maths.
 

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(c) 2010 Ant Kutschera

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