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Maths Investigation- Grids

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Introduction

                                                                                                    Karen Ng

                                                                                             10H

Maths Investigation- Grids

The first part of my task was to investigate the number of squares, which can be drawn on grids made from 11 lines.

I used 11 lines to make different grids on paper, alternating the use of lines. Starting with 1 horizontal and 10 vertical lines I work up (or down) so my grid then is 2 horizontal and 9 vertical. I counted the number of squares by outlining the shape of the square; this is shown in diagram 3.  

Here is my table of results using 11 lines only.

Lines Down

Lines Across

1x1 square

2x2 Square

3x3 square

4x4 square

Total Squares

0

0

0

0

0

0

0

10

1

0

0

0

0

0

9

2

8

0

0

0

8

8

3

14

6

0

0

20

7

4

18

10

4

3

35

6

5

20

12

6

2

40

5

6

20

12

6

2

40

4

7

18

10

4

3

35

3

8

14

6

0

0

20

2

9

8

0

0

0

8

1

10

0

0

0

0

0

0

0

0

0

0

0

0

As you can see, after the 6x5 result comes up, the rest of the results are exactly the

...read more.

Middle

0

2

Total number of squares: 2

Best Combination: 3x2

This table of results is for 6 lines only

Lines Down

Lines across

1x1 squares

2x2 squares

3x3 squares

4x4 squares

Total Squares

0

0

0

0

0

0

0

5

1

0

0

0

0

0

4

2

3

0

0

0

3

3

3

4

1

0

0

5

Total number of squares: 8

Best Combination 3x3

This table of results is for 7 lines only

Lines Down

Lines across

1x1 squares

2x2 squares

3x3 squares

4x4 squares

Total Squares

0

0

0

0

0

0

0

6

1

0

0

0

0

0

5

2

4

0

0

0

4

4

3

6

2

0

0

8

Total number of squares: 12

Best Combination: 4x3

This table of results is for 8 lines only

Lines Down

Lines across

1x1 squares

2x2 squares

3x3 squares

4x4 squares

Total Squares

0

0

0

0

0

0

0

7

1

0

0

0

0

0

6

2

5

0

0

0

5

5

3

8

3

0

0

11

4

4

9

4

1

0

14

Total number of squares: 30

...read more.

Conclusion

Conclusion

The more lines you have, the more squares you will get. The rules I found out are; if you were trying to find out how many 1x1 squares were in a 6x5 grid, you would do 6-1=5 and 5-1=4, then, you times the answer ( 5 and 4 ) together, and that number will be the amount of 1x1 squares you will get in the grid. To find out how many 2x2 squares are in a grid, you do exactly the same thing, except you subtract 2 instead of 1 because now there are 2 boxes missing from each side.

...read more.

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