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  • Level: GCSE
  • Subject: Maths
  • Word count: 4152

T-Total and T-Number

Extracts from this document...

Introduction

T-Total and T-Number We have a grid nine by nine with the numbers starting from 1 to 81. There is a shape in the grid called the t-shape. This is highlighted in the colour red. This is shown below: - 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 number 20 at the bottom of the t-shape will be called the t-number. All the numbers highlighted will be called the t-total. In this section there is an investigation between the t-total and the t-number. 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 For this t-shape the T-number is 20 And the T-total is 37 For this t-shape the T-number is 21 and the T-total is 42 We can see from this information is that every time the t-number goes up one the t-total goes up five. Therefore the ratio between the t-number and the t-total is 1:5 This helps us because when we want to translate a t-shape to another position. Say we move it to here 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...read more.

Middle

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 5tn + 7 = t-total 5* 70 + 7 = 357 Check T-number = 70 T-total = 70+71+72+63+81 = 357 If we were to put the t-shape diagonally on the grid we find that the same rule applies again apart from you can not use the 2nd rule were you times the grid size by seven. 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 red t-shape has t-number of 33 and the t-total = 7+17+27+25+33 = 109 The difference between the t-number and the rest of the numbers in the t-shape. 33-25= 8 33-7= 26 33-17= 16 33- 27 = 6 TOTAL= 56 5tn+56= t-total 5 * 33 - 56 =109 The reverse triangle the sign should be reversed to a plus. The t-shape used here is the one in blue. T-number is 13 T-total = 19+29+39+21+13 = 121 5tn+56= t-total 5*13+ 56= 121 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 ...read more.

Conclusion

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 5tn-7= t-total R 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 5tn+7= t-total L 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 5tn-70= t-total DR 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 5tn+70 = t-total UL 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 5tn-56= t-total DL 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 5tn+56 = t-total UR The different size of grid changes means the formula has to change slightly. This is what happened. T-shapes number to x by 7 D & U Grid size L & R nothing DL & UR Grid size -1 DR & UL Grid size +1 We also have formula for rotation, which are angle formula 45 degrees 5tn-(7xG)+7= t-total 90 degrees 5tn-(7xG)+70= t-total 135 degrees 5tn-(7xG)+133= t-total 180 degrees 5tn-(7xG)+126 = t-total 225 degrees 5tn-(7xG)+119= t-total 270 degrees 5tn-(7xG)+56 = t-total 315 degrees 5tn-(7xG)-7= t-total We have a formula for reflection which is 5tn+(12*gridsize)= t-total. ?? ?? ?? ?? ...read more.

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