T-Total and T-Number - page 4
Keywords: T-Total and T-Number
By Grant867 on 07/12/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 4 of 6 pages: 1 2 3 4 5 6
is the opposite of the red t-shape so therefore the formula for the blue t-shape is 5tn – 70 = t-total. The sign has become the opposite of what it use to be. This has happened in many cases before.
Now that we have worked out all the formulas for the position in the normal sized t-shape. We can try enlarging the t-shape. If we double the t-shape (volume is four times bigger). The grid below shows the new shape. I have added all the numbers together in the squares of the t-shape. This leaves us with our original t-shape but with larger numbers in the grid.
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54
55 56 57 58 59 60 61 62 63
64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81
The t-number turns out to be 176. This is the bottom four numbers added together. The t-total is 356. I have worked out the differences between the t-number and the rest of the t-shape.
Difference
176-24 = 153
176-32 = 144
176-40 = 136
176-84 = 92
TOTAL= 524
Now we have the rest of the formula. The formula is very much the same apart from the number we minus or plus by is vaster.
Formula
5tn – 524 = t-total
5*176-524 = 356
Formula has proven to work.
We have seen that there is a relationship with all the transformations made to the t-shape. Everything that we have done the t-shape has seemed to link to the part that was discovered before. These still stays the same apart from we add an extra part on to the end of the formula. This is because we are not looking for a link between all the positions of the t-shape when it is a certain way up. Here we want to find out whether there is a link between only two t-shapes. Here first of all we are looking for a link when we rotate this t-shape 90 degrees.
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27
28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45
46 47 48 49 50 51 52 53 54
55 56 57 58 59 60 61 62 63
64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81
Here we have t-shapes with the same t-number. Now we want a formula for rotating a t-shape 90 degrees. We already have two separate formulas. The red t-shapes formula is 5tn- 63= t-total. The blue t-shapes formula is 5tn + 7= t-total. If we add the 63 and the 7 together from the two formulas we get 70. This is the difference in the t-total between the two t-shapes. The t-number for both t-shapes is 41. The red t-shape t-total is 142. The blue t-shape t-total is 212.
If we keep our original formula which is 5tn - (7 * grid size)
Then we add the difference in the t-shapes
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