Squares in a SquareDate: 01/23/2003 at 20:51:22 From: Curtis Subject: Squares in a box If you have a square that is 50x50 with small squares inside it, how many squares will there be altogether? I took a 4x4 box and tried to find how may squares were in it, and I found 30 different squares. Then my teacher told me to find all the squares in a 50x50 square box. Date: 01/26/2003 at 02:56:44 From: Doctor Ian Subject: Re: Squares in a box Hi Curtis, That was a good way to start! In fact, try it with a few different sizes, and see if you can spot a pattern. But don't just focus on the total number you get for each size. Look at the number you get for each size: +---+ | | 1 x 1: 1 +---+ +---+---+ | | | 1 x 1: 4 +---+---+ 2 x 2: 1 | | | +---+---+ +---+---+---+ | | | | 1 x 1: 9 +---+---+---+ 2 x 2: 4 | | | | 3 x 3: 1 +---+---+---+ | | | | +---+---+---+ +---+---+---+---+ | | | | | 1 x 1: 16 +---+---+---+---+ 2 x 2: 9 | | | | | 3 x 3: 4 +---+---+---+---+ 4 x 4: 1 | | | | | +---+---+---+---+ | | | | | +---+---+---+---+ Once you spot the pattern, you can compute the total number of squares for _any_ size, without having to count them. Is this enough to get started? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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