# 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

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |

28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 |

37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 |

46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 |

55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 |

64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 |

73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 |

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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