Borders Maths Coursework

                             

                         With this shape there are now 12 borders.

                             

                                                 

                                This shape has 16 borders 

I can now see a pattern in the number of square, which is that there are 4 more each time.

Here is a table to show what I have found.

Using this I can guess what the next number of white squares will be 20.

 

A you can see there are 20 white cubes.

                                                  This shape has 24 borders

Now I will try to find the nth term for the white cubes (Borders).

      1st   2nd      3rd      4th      5th        6th 

      4   8   12   16    20     24    

   

        4    4     4       4      4  

The nth term for this is 4n so I wanted to work out how many borders there are the 10th shape I will times 4 by 10 and the number of borders will be 40

Now I will work out the nth term for all the squares in the pictures.

1st      2nd        3rd        4th 

5    13     25    41

1st   8      12      16

       

2nd      4        4

             

The nth term for all the cubes is 22n-1.

The 10th number will be worked out by 4 times 10 minus 1 which is 39.