Subject: squaring numbers
Who are you: Parent (All)
did anyone ever try to teach that the easiest way to find the next square in a group of numbers is to add the next odd number in the sequence. for example: 1 squared is 1, 2 squared is 4,difference of 3.the next odd number is 5 so the next square would be 4 +5 or 9,3 squared.add 7 you get 4 squared 16,add 9 you get 5 squared 25 and so on.i think this would be an easier way to learn.if this is something no one else in the world knows i would like the rights to it, lol just kidding.but i would like to be noticed.
This is a well known property of square numbers, which can be proved as
Consider the formula (n+1)2 = (n2) + (2n+1)
Meaning of the formula:
Given the square of the nth whole number [n2], we can find the next square number in the sequence [(n+1)2] by adding the next odd number in the sequence [(2n+1)].
Proof that it works:
(n+1)2 = (n+1)(n+1) = n n + n 1 + n 1 + 1 = n2 + 2n + 1
It's good that you notice such properties of the numbers. It shows that you are thinking about arithmetic and not just treating it as routine operations.
Paul and Penny