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# Mathematics Coursework - T Shapes

Extracts from this document...

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

Middle

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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 18 14 Original T-total 37 34 28 Final T-number 23 20 15 Final T-total (T) 52 44 43

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:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 25

First T-shape                                           Final T-shape

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

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