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Douglas Carter Mathematics Coursework Problem: You are given a 9x9 number grid with a 2x2 square on it. Investigate when pairs of diagonal corners are multiplied and subtracted from each other. Come up with an algebraic formula that gives the difference for any size square/rectangle on any size grid. Method: Starting with the problem given, a 9x9 number grid with a 2x2 square on it, I gave each number in the square its equivalent in algebra. If the first number is a the number grid would be as follows... This can be used to make a formula that gives the difference (Dif) when diagonals are multiplied and subtracted from each other, for a 2x2 square on a 9x9 grid, where 9 represents the width of the grid and a is the top left number in the square. This is: By changing the size of the grid I found that the width of the grid is equal to the difference...

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