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Maths Coursework T-Total

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Introduction

Matthew Russell Maths Coursework T-Total Using a 9 by 9 grid, a 'T' shape was made covering 5 numbers. The grid 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 All the numbers in this 'T' shape added together make a total of 37, (1+2+3+11+20=37). This total is known as the "T-total". The number at the bottom of this T-shape (20) is known as the T-number. To investigate if there was any relationship between the T-total and the T-number, the T-shape was translated onto different positions on the grid. ...read more.

Middle

Turquoise = 21 x 5 = 105, 105 - 63 = 42. Green = 25 x 5 = 125, 125 - 63 = 62. Pink = 32 x 5 = 160, 160 - 63 = 97. This proves that the nth term on this grid is definitely, 5n - 63. Would these rules follow through on a different grid, would the position of the T-shape make any difference? Here is a 7 by 7 grid to find out. 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 T-number 16 17 18 19 T-total 31 36 41 144 T-number 20 21 22 23 T-total 51 56 61 66 T-number 24 25 26 27 T-total 113 76 81 86 This shows that the rule of going up in 5's applies in all size grids but only in T-shapes that are made in the same manner. ...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 T-number 7 8 9 10 T-total 13 17 21 25 T-number 11 12 13 14 T-total 29 33 37 41 The nth term here is 4n - 15. Because; 7 x 4 = 28, 28 -15 = 13. 14 x 4 = 56, 56 - 15 = 41. Would a different shape make a difference? This time will use an L-shape. 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 L-number 6 7 8 9 L-total 9 12 15 18 The nth term here is 3n - 9, as shown below; 6 x 3 = 18, 18 - 9 = 9. 9 x 3 = 27, 27 - 9 = 18. In conclusion, you can see it is not the shape that affects the correlation or the nth term, but the number of numbers in the shape. ...read more.

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