Maths Coursework on Diagonal Differences

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Naila Parveen         Maths Coursework

Maths Coursework on Diagonal Differences

Introduction:

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

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

Aim:

I am going to investigate the diagonal difference of a 2 by 2 box inside a 10 by 10 grid. I will then try to find a formula which should relate to the diagonal difference of each square, I will then further this investigation by trying to find the diagonal difference of a 5 by 5 grid and an 11 by 11 grid, and find the formula to see if they are the same for a 10 by 10 grid. I will also do an extension by doing a rectangle as well as 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 grid, and then try to find any pattern, which would help me in finding the formula by drawing a grid. This method would be useful because it will show me the diagonal difference of any square by any size, because I will just have to insert the value of ‘n’ in the formula to find out the diagonal difference of that square, therefore I should be able to predict the next diagonal differences of each square.

Results:

First I am trying 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 difference size boxes.

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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 2 by 2 box is 10, but I will try another 2 by 2 box just to check this

15 x 26 = 39

16 x 25 = 400

Diagonal difference: 400 – 390 = 10

The diagonal ...

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