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  • Level: GCSE
  • Subject: Maths
  • Word count: 2692

For my investigation, I will be investigating if there is a relationship between t-total and t-number. I will first try to find a relationship between T-number and T-Total on a 9x9 grid then change the variables such as grid size.

Extracts from this document...

Introduction

Maths Coursework

By James Lathey

For my investigation, I will be investigating if there is a relationship between t-total and t-number. I will first try to find a relationship between T-number and T-Total on a 9x9 grid then change the variables such as grid size. I will also be looking at what effect rotation has.

image00.pngimage09.pngimage10.pngimage08.pngimage00.pngimage00.pngimage01.png

N-7

N-9

N-8

image11.png

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1

image10.png

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image12.png

N-9

image03.pngimage02.png

11

N

20

T number is the number at the bottom of the T shape

T Number= blue number

To calculate T total add all the numbers inside the T together.

T Total = 1+2+3+11+20 = 37

I will represent T number as T and T total as N

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The numbers in red represent all the places were the T shape cant fit. I will ignore these and only use the squares were the t shape fully fits.

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First I put the T shape onto my 9x9 grid and translated it right by 1 space each time.  As shown above I started on 20 and finished on 25 I then constructed the tale below.

T-Number (T)

T-Total (N)

Difference

20

1+2+3+11+20=37

-

21

2+3+4+12+21=42

5

22

3+4+5+13+22=47

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23

4+5+6+14+23=52

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5+6+7+15+24=57

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6+7+8+16+25=62

5

The table above shows the difference between the consecutive T-Totals as the T-Number increases by one. On the above 9x9 grid, the T-Shapes can be seen being translated across the 9 x 9 grid by one square each time. There is a pattern between the T-Totals as the T-Shape is translated each time, as each time the T-Total increases by 5, as shown in the table above.

...read more.

Middle

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T-total = (N-21)+ (N-20) + (N-19) + (N-10)+( N)

I then can simplify this to:

T-total = 5N-70

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T-total = (N-23)+(N-22)+(N-21)+(N-11)+(N)

I then can simplify this to:

T-total = 5N-77

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T-total = (N-25)+(N-24)+(N-23)+(N-12)+(N)

...read more.

Conclusion

image05.png

I then used simple logic to work out  the formula for a 270˚rotation. If 90˚ was 5N + 7 and the angle is  90˚ in the other direction (270˚ of a complete 360˚ rotation) then the formula must be 5N-7. I tested and tried this formula again on a 6 by 6 grid:

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The T-Total for this shape is 42 when calculated. When put into the formula it becomes 5(7) + 7 which also equals 42. This proves my theory that:

image06.png

   As with the last formula, I used simple logic to solve the 180˚ rotation formula. If the formula for 0˚ is 5N -7G then the logical formula to solve the 180˚ rotation would be 5N + 7G. I tried and tested the theory below:

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The calculated T-Total for this T-Shape is 57 and the T-Total when put into the formula above also equals 57. This proves that

image07.png

Conclusion

In this investigation I have successfully established a relationship between T-Total and Grid size, and found a rule for grids ranging from 9-14. I have also found a general rule which will find the T-total for any grid size. I then move onto rotations I looked at 90˚, 180˚, 270˚ and 360˚, I worked out my formulas for rotating the T-shape on a 6x6 grid and successfully found and tested and proved my formula correct. Overall I think the investigation went well.

Evaluation

If I was to do the investigation again I would do grid rotations on larger grid sizes and make a general rule for rotating the T- shape.

...read more.

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