Opposite Corners

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Opposite Corners

In this piece course work I am going to investigate opposite corners

in grids. I will start by investigating a 7x7 grid. Within this grid I

will use 2x2, 3x3, 4x4, 5x5, 6x6 and a 7x7 grid. I will do this to

find whether I can find a pattern. I will do this by multiplying the

two opposite corners together then subtracting them. I will try to

find the patterns and do a formula that will work for all grid sizes

and shapes. I will experiment shapes and sizes of all different grids.

Prediction

I predict that in a 7x7 grid all the opposite corners will be a

multiple of 7 and in an 8x8 grid they will be a multiple of 8 and so

on. They will only do this if I multiply the two opposite corners then

subtract the two from each other.

To check my hypothesis I will use 6x6, 7x7, 8x8 and maybe if I have

time I will do a 9x9 and 10x10 grid. Also I will be looking at all

different shapes and sizes. I hope to find a formula for all grids and

all shapes and sizes.

7x7 Grid

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Here is a grid of numbers in sevens. It is called a seven grid. In

this section I will multiply the opposite corners and then subtract

them.

2x2

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