# Maths Coursework - T-Shape

Extracts from this document...

Introduction

## Maths Coursework

## T-Shape

There have been a number of ways in which I have looked at to tackle this task. One of which is trying to find a correlation between T numbers and T-Totals for a vertically standing T (e.g. T) on a 9x9 grid (randomly selected):

T Number | 29 | 57 | 41 | 79 |

T Total | 66 | 234 | 138 | 366 |

And I obtained this graph from the results:

I had found this quite surprising and so I did the same for a T shape rotated at 180°

T – Number | 2 | 22 | 24 | 53 |

T - Total | 120 | 240 | 252 | 426 |

These results were very interesting. I found that both of the gradients were 6. But the intercepts through the y axis were different yet they did correspond with each other because the

Middle

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*

*

*

T

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*

*

This correlation has helped me to find a suitable equation to find the T-Total (T-Total = T + T-9 + T-18 + T-26 + T-27 + T-28 = 6T – 108). I have tested this equation only on a 9x9 grid and it has worked fine, only as long as:

- The T is in a 9x9 grid
- The T remains facing vertically (e.g. like “T” is here T)
- The T remains the same size/shape

After discovering this, I decided to investigate how this equation is affected on a larger grid. I decided to investigate this on a larger grid because I found it quite ironic that the numbers involved in the equation on the 9x9 grid are quite closely related to 9. So therefore I would predict this to be the outcome:

T-31 |

Conclusion

11

12

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19

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22

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28

29

30

31

…

* | T | * | * | * |

* | T + (G) | * | * | * |

* | T + (2*G) | * | * | * |

T + (3*G) - 1 | T + (3*G) | T + (3*G) + 1 | * | * |

These results are somewhat exceedingly fascinating. They show that the equation to this:

#### T + (T+G) + (T+2G) + (T+3G) – 1 + (T+3G) + (T+3G) + 1 = T-Total

#### 6T + 12G = T-Total

(Where T = T number and G = grid length/width)

I’m now going to rotate the T by 90° and find what I get:

* | * | * | T - G + 3 | * |

T | T + 1 | T + 2 | T + 3 | * |

* | * | * | T + G + 3 | * |

Which is unsurprisingly:

T + T + 1 + T + 2 + T - G + 3 + T + 3 + T + G +3 = T-Total

#### 6T + 12 = T-Total

(Where T = T number and G = grid length/width)

And so:

T – G – 3 | * | * | * | * |

T - 3 | T - 2 | T - 1 | T | * |

T + G – 3 | * | * | * | * |

Is:

T + T – 1 + T – 2 + T – G – 3 + T – 3 + T + G – 3 = T-Total

#### 6T – 12 = T-Total

(Where T = T number and G = grid length/width)

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

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