Square Numbers

Date: 07/27/99 at 04:10:20
From: Lisa-Jayne Smith
Subject: Square Numbers

We have been doing square numbers for a while in my class and I just 
do not understand the concept. At home no one is very good at maths, 
so I thought I would ask you.

Thank you.

Date: 07/27/99 at 12:31:47
From: Doctor Rob
Subject: Re: Square Numbers

Thanks for writing to Ask Dr. Math.

Square numbers are the number of objects in a square arrangement:

1-by-1 square:     O      - 1 object,

2-by-2 square:    O O
                  O O     - 4 objects,

3-by-3 square:   O O O
                 O O O
                 O O O    - 9 objects,

4-by-4 square:  O O O O
                O O O O
                O O O O
                O O O O   - 16 objects.

These numbers are found on the diagonal of the multiplication table:

        | 1  2  3  4  5 ...
      ----------------------
      1 | 1  .  .  .  .  .
      2 | .  4  .  .  .  .
      3 | .  .  9  .  .  .
      4 | .  .  . 16  .  .
      5 | .  .  .  . 25  .
     ...| .  .  .  .  . ...

You can compute them by multiplying a number by itself:

   1*1 = 1,  2*2 = 4,  3*3 = 9,  4*4 = 16,  5*5 = 25, ...

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/