The Orange T Shape is a 3 by 2 and the green is a 5 by 3, both of these are on a 9 by 9 grid.
T Shape T No Tt
Orange 3 by 2 20 37
Other 3 by 2 34 107
Other 3 by 2 56 217
At this point I thought if I put a T Shape into the Nth term:
For a 3 by 2
Goes to
n-19 n-18 n-17
n-9
n
= 5n-63
Therefore to make it a formula it becomes Tt=5n-63
Now I began to explore how to find certain numbers such as the 5 and the minus 63.
The only numbers I can work with are the 3 and the 2 from the t shape, the 9 from the grid.
So the obvious way to get the 5 is from the t shape.
So the 3 we call the T width or W.
And the 2 is the t height or H
Now we have Tt = (H+W)n-63
Next I tested this out with a 3 by 2 t shape, with a T No of 20
Tt = (3+2)20-63
Tt= 100-63
Tt = 37
We now from the table above that this does actually work. Although from testing I discovered that it only works for a 3 by 2 shape on a 9 by 9 grid.
Part 2
Now I’m going to use different grid sizes, like 10 by 10 and 11 by 11.
Expression Grid Shape Position
5n-63 9x9 3x2 T
The difference is 7 between expressions.
After discovering this and trying to link it in I realised that these numbers are all multiples of 7 and the other number is 9.
Tt = (H+W)n-7xS
S is one side of the grid e.g. on a 9x9 it would equal 9.
Now I tried to use this formula for a 5 by 3 but I had no luck, this formula only works for a 3 by 2 on any grid.
Expression Works for
5n-7S 3 by 2, Any Grid, No Rotation
From these results I can form this formula which works for any size T Shape, Any Grid but no rotation.
The formula is:
Tt = (W+H)n- 7xS
I put 7 because that’s the number you need to multiply the grid by.
So we know this works, after doing the investigation I had trouble linking it all together and in the end ran out of time, the key points in the formula were what you times the grid by. So my final formulae were.
For a 3 by 2 any grid Tt = (W+H)n- 7xS
For other sizes you must use the one up the page and substitute into it.
By Julie Smith 10CE
