|November 10th, 2011, 10:03 PM||#1|
Joined: Nov 2011
Young Math Student
So my 9 yr old tonight pointed out the following.
If X is any whole number
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.
|November 11th, 2011, 07:08 AM||#2|
Joined: Nov 2006
From: UTC -5
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
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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