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Maths Coursework - T-Shape

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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:

image00.png

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

image01.png

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

...read more.

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

...read more.

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:

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)

...read more.

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