Maths Grid Coursework

T=63

Check

T=8+9+10+15+21

T=63

So the formula is correct.

I will now compare the formulas for the different grid sizes.

11 x 11= 5n - 77= 11x7= 77

9 x 9= 5n - 63 = 9x7= 63

6 x 6= 5n - 42 = 6 x 7= 42

5n is consistent because the T shape is always the same size. (With the same amount of numbers in side the T shape)

The numbers which are underlined are all divisible by 7.

This means that if you know the grid size you can multiply it by 7 and it would give you the number that you would subtract from the Tnumber. From this we can make a general formula for any size grid and any Tnumber.

g=grid size

The General Formula is:

T=5n-7g

N.B

This formula only applies to a T this way up:

Formulae

Formula

Shape of 'T'

)T=5n-3

T(in 9 by 9 grid)

2)T=5n-7g`

T(in any size grid)

From these formulae I will investigate whether you could find the Tnumber from them instead of the Ttotal.

Formula

Shape Of T

)n=(T+63)÷n

T(in 9 by 9 grid

2)n=(T+7g)÷5

T(any grid size)

I will now investigate turning the T, 90º, 180º and 270º to see if there are any formulae for them for them. First I will investigate an upside down Tshape. As this shape is the opposite of a normal T, I expect that the formula will be the same apart from the subtraction sign becoming an addition sign, it will change because the addition sign is the opposite of the subtraction sign.

Therefore I think that the formula is:

T=5n+7g on any grid size.

Test on 9 By 9

2 3 T= (5x2) + (7x9)

0 11 12 T= 10+63

9 20 21 T= 73

Check

2+11+20+19+21=73

This means that this formula is correct; I will do 1 more test just to make sure.

Test on 5 by 5

7 8 9 T= (5x8) + (7x5)

2 13 14 T= 40+35

7 18 19 T=75

Check

8+13+17+18+19=75

I now believe that the formula is: T=5n+7g works for an upside down T anywhere on a grid of any size.

I will now investigate a T like this: