Maths Opposite corners

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Maths Coursework

Opposite Corners

        My task is to investigate a number grid. If you take a 2x3 rectangle and place it on a 10x10 number grid the diagonal difference of the numbers inside is 20. I want to first investigate whether the diagonal difference is always 20, no matter where the rectangle is, and prove this. I will then investigate further by changing the size of the number grid and of the rectangle.

 First I investigated two rectangles to see if the diagonal difference of both was 20.

 Both of these diagonal differences were 20.

        I decided to make the rectangle larger by one square wider and one deeper to see what happens.

Again I investigated two rectangles to see if the diagonal difference is the same for both.

Both came out as 60 so the formula is:

x²+23x-(x²+60+23x)=60

So far the diagonal differences are both factors of twenty, meaning the first digit is an even number (When there are two digits) and the number ends in zero.To see if this changes I changed the first rectangle into a square by making it one square deeper.

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 Both of the diagonal differences were 40.

In a rectangle of 3 X 2 the diagonal difference was 20. This went up by 20 when I deepened the rectangle by one square. I then investigated whether the diagonal difference will go up by another 20 if I deepened the rectangle by another square.

 Both these were 60. So the diagonal difference has risen by 20 again. The diagonal differences are obviously going up in a sequence.

        I decided to make a formula for the diagonal difference of my first box by calling the number ...

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