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# Maths Coursework - T-Shape

Extracts from this document...

Introduction

## 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

*

*

*

*

T

*

*

*

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

">10

11

12

13

19

20

21

22

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:

#### 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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