Grids Investigation.

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INTRODUCTION

I was recently given an investigation for my maths coursework; it was an investigation on grids. Grids are a series of lines that cross each other vertically and horizontally to produce interior squares. In this specific investigation my task was to find the number of squares in a grid containing eleven lines in any order vertically and horizontally, we were able to overlap the squares within the grid, I then had to discover a formula which could tell me the number of one by one, two by two squares contained within the grid and so on.

Once this has been achieved I would have to use my formula to find the number of squares within a grid that has a different amount of lines, to see if it works correctly.

METHOD

To begin with in this investigation I drew out the various grid combinations using eleven lines changing the vertical and horizontal each time, there were five combinations. I then tried to find out the number of squares that fitted into that particular grid combination e.g. one by ones, two by twos and so forth. Once I had obtained all the possible results I laid them out in a table, which made it easier to view the results and see any connection that may lead me to a formula.
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I then followed the same procedure for part two of the project, which involved using different amounts of lines and testing the formula I had found to see if it worked.

Total

RESULTS

Here is my first set of results for eleven lines:

I have noticed that after a certain point the results are the same this is because the vertical and horizontal have just been flipped.

Table for grids made with 11 lines.

10 0 0 0 0

2 9 8 8

3 8 14 20

4 ...

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