# Diagonal Difference.

Naila Parveen        Maths Coursework        year 11

Maths Coursework-Diagonal Difference

Introduction

I am given a 10 by 10 grid. I am going to find the diagonal difference of different size grids (For e.g. 3 by 3, 4 by 4) within the 10 by 10 grid, by multiplying the opposite corners which results in two answers, we then deduct these two to get a final answer for that size.

This is the grid that I will use to help me investigate.

Aim

I am going to investigate the diagonal difference of a 2 by 2 grid inside a 10 by 10 grid.  I will then try to find a formula which relates to the diagonal difference of each square, I will then further this investigation by trying to find the diagonal difference of an 11 by 11 grid and a 12 by 12 grid and find the formula and see if it is the same. I will also do an extension by doing a rectangle and a square and then find the diagonal difference and the formula for this.

I am going to find the formula by finding the diagonal difference of all the sizes within the 10 by 10 grids, and then try to find any patterns, which would help me in finding the formula by drawing a grid.  This method would be good because it will show me the diagonal difference of any square of any size, because I would just have to insert the value of n in the formula to find out the diagonal difference of that square, therefore I will not have to write out all the squares and work out the diagonal difference.

Results

First I am going to try out all the squares then I will start with the rectangular.

I will first find the sequence of the diagonal difference in all of the different size grids.

I am trying to calculate the differences between these products.

I am going to multiply the opposite corners and then find the difference.

11 x 22= 242

12 x 21= 252

The diagonal difference is 242– 252 = 10

I have found out that the diagonal difference for the two by two grids is 10, but I will try another two by two grid just to check this.

15 x 26 = 390

16 x 25 = 400

Diagonal difference: 400 – 390 = 10

The diagonal difference is 10 again.

I again found that the diagonal difference is 10 so I know that the diagonal difference of two by ...