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 November 10th, 2011, 09:03 PM #1 Newbie   Joined: Nov 2011 Posts: 1 Thanks: 0 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
 November 11th, 2011, 06:08 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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 $(x+1)^2-x^2=2x+1$ where $^2$ 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: $1+3=2\times2$ $1+3+5=3\times3$ $1+3+5+7=4\times4$ and so forth. That's because to get from, say, $3\times3$ to $4\times4$ you need to add $4\times4-3\times3$ 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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