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November 10th, 2011, 10:03 PM   #1
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Young Math Student

So my 9 yr old tonight pointed out the following.

If X is any whole number
and Y=X+1
Then
(Y*Y)-(X*X)=X+Y

I have written out this equation for him but he came upon and expressed the pattern himself.
Does anyone know anything about this equation. I would love to feed him some history.
Thanks.
Pround PAPA
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November 11th, 2011, 07:08 AM   #2
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Re: Young Math Student

It's correct, and it even holds if X is a rational or real number instead of just a whole number. It would usually be expressed

where is mathematical shorthand for "this thing times itself".

It can be used to show a remarkable property: the sum of consecutive odd numbers (starting from 1) yields a square:



and so forth. That's because to get from, say, to you need to add which is, as your 9-year-old pointed out, the same as 3+4 = 7, expanding 1 + 3 + 5 to 1 + 3 + 5 + 7. Neat, huh?
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