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Mathematics Coursework - T Shapes

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Introduction

2. Translate the T-shape to different positions.

Using a grid of any size, I will investigate how the original T-number is related to the T-total of the translated T-shape. First, I will use

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image01.png

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Here is a table showing the results so far for the different grid sizes, t-numbers, t-totals and the vector.

Vector ((a,b))

(3,0)

(2,0)

(1,0)

Grid Size (g)

9x9

8x8

6x6

Original T-number (n)

20

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Original T-total

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Final T-number

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Final T-total (T)

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image03.png

From this table I can see a pattern. It shows that when you take an Original T-total (37) and add on 5 times the vector a (3) you get the final T-total. In equation form this is:
Final T-total = Original T-total + (5xMovement in Horizontal Direction)
However this equation requires us to know the T-total In advance when we only know the T-number. So I can substitute a previous equation for the Original T-total (5n-7g). This gives me the final equation of:
Final T-total = (5n-7g)+(5a)

Therefore, I have a final formula of:
(T=Final t-total) (n=original T-number) (a=the horizontal direction on the vector)

T = (5n-7g)+5a

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Conclusion

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Justification
To prove that this formula will always work with any grid size and any T-shape using a horizontal vector I can use this T-shape, Grid and vector:

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                   First T-shape                                           Final T-shape         

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This student written piece of work is one of many that can be found in our GCSE T-Total section.

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