# Grids Investigation.

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Introduction

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. ...read more.

Middle

PART TWO RESULTS. Part two of the investigation shows the number of squares that can be drawn from my chosen number of lines which is 12. Table for grids made with 12 lines. RESULTS FOR GRIDS WITH 10 LINES ON THE NEXT PAGE. RESULTS FOR 10 LINES. I will now be looking at the number of squares I can make from 10 lines. Table for grids made up of 10 lines. RESULTS FOR GRIDS WITH 9 LINES ON THE NEXT PAGE. RESULTS FOR 9 LINES Finally now I will in investigate the number of squares that go into grids made up of 9 lines. Each time a horizontal goes up two comes off the difference. DISCUSSION This is my discussion I will now take you through all of my findings. When investigating the grids I found that at a certain point you are unable to make any more grids, On an even numbered amount of lines this happens when the vertical and horizontal are the same, as you were able to see in my results. ...read more.

Conclusion

2. the next rule I will show you also works in the same way but takes slightly longer its [(V-1) + (H-1)] + [(V-2) + (H-2)] this will find out the amount of 3 x 3s in what ever length vertical & horizontal you want. 3. Another formula not as good is. 1 x 1 = (V x H) - 10 2 x 2 = (V x H) - 18 3 x 3 = (V x H) -24 4x 4 = (V x H) - 28 CONCLUSION In conclusion to this project about finding the different amounts of squares, which fit in to different size grids, there was no possible formula that I could find for the total amount. But I found the formulae shown in the discussion that help find how many squares in a grid. As for my prediction it worked as shown in the discussion. Q. Find how many 2 x 2s in a grid H = 3 V= 7 1 ...read more.

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