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  • Level: GCSE
  • Subject: Maths
  • Word count: 4225

T totals - translations and rotations

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Introduction

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T-totals coursework

By Michael Ogolo

My T number is 20 as you can see on my 9by9 grid and I will be representing this as N in my equation. My T total is 1+2+3+11+20= 37. The number in my T shape directly above the T number is 9 places back in the grid so it is N-9. The number directly above this number is also 9 places back in the grid so it is N-9-9= N-18. The two remaining numbers in the T shape are N-18+1 and N-18-1. Thus the T total is:

N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = 5N-63

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Rotated translation 90 degrees anti-clockwise

My T number is 21 as you can see on my 9by9 grid and I will be representing this as N in my equation. My T total is 28+19+10+20+21=98. The number in my T shape directly above the T number is 1 place back in the grid so it is N-1. The number directly above this is 1 place back in the grid so it is N-1-1= N-2. The two remaining numbers in the T shape are N-2+9 and N-2-9. Thus the T total is:

N+ (N-1) + (N-2) + (N-2+9) + (N-2-9) = 5N-63

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Vertical translation, rotated 180 degrees clockwise

My T number is 11 as you can see on my 9by9 grid and I will also be representing this as N in my equation. My T total is 11+12+13+4+22=62. The number in my T shape directly above the T number is 1 place ahead on my grid so it is N+1.

...read more.

Middle

N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = 5N-63

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Horizontal translation

My T number is 25 as you can see on my 9by9 grid and I will also be representing this as N in my equation. My T total is 25+16+7+6+8= 62. The number in my T shape directly above my T number is 9 places back on my grid so it is N-9.The number in my T shape directly above this is also 9 places back on the grid so it is N-9-9= N-18. The two remaining numbers in the T shape are N-18+1 and N-18-1. Thus the T total is:

N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = 5N-63

T-Number                                                                  T-Totalimage00.png

image01.png

20                                                                                37

21                                                                                42

22                                                                                47

23                                                                                52

24                                                                                57

25                                                                                62

Looking at my results above I have spotted a relationship between the T-Totals as I transform the T-shape horizontally. I have noticed that as I transform the T-shape horizontally my T-Total is increased by 5 I will test my theory by making a prediction on my T-Number 26. My prediction is that when my T-Number is 26 my T-Total will be 67.

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Horizontal translation

My T number is 26 as you can see on my 9by9 grid and I will also be representing this as N in my equation. My T total is 26+17+8+7+9= 67. The number in my T shape directly above my T number is 9 places back on the grid so it is N-9. The number directly above this is also 9 places back on my grid so it is N-9-9= N-18. The remaining two numbers are N-18+1 and N-18-1.

...read more.

Conclusion

N+ (N-6) + (N-12) + (N-12-1) + (N-12+1) = 5N-42

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My T-number is 16 as you can see above on my 6by6 grid I will be representing this as N in my equation. My T-total is 16+10+4+3+5= 38. The number in my T-shape directly above my T-number is 6 places back on my grid so therefore it is represented as N-6. The number directly above this is also 6 places back on my grid so it is represented as N-6-6= N-12. The two remaining numbers are N-12-1 and N-12+1. Thus my T-total is:

N+ (N-6) + (N-12) + (N-12-1) + (N-12+1) = 5N-42

T-number                                                                T-total

14                                                                             28

15                                                                             33

16                                                                             38

Using this data in my table I will try and predict my 17th T-number in my 6by6 grid. Analyzing the data in my table I have picked up on a sequence which is when my T-number increases by 1 my T-total increases by 5.

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My T-number is 17 as you can see above on my 6by6 grid I will be representing this as N in my equation. My T-total is 17+11+5+4+6= 43. The number in my T-shape directly above my T-number is 6 places back on my grid so therefore it is represented as N-6. The number directly above this is also 6 places back on my grid so it is represented as N-6-6= N-12. The two remaining numbers in the T-shape are N-12-1 and N-12+1. Thus my T-total is:

N+ (N-6) + (N-12) + (N-12-1) + (N-12+1) = 5N-42

I have proven my prediction correct because my T-total is 43 which is an increase from the 16th T-number which was 38.

...read more.

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