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Mathematics Coursework 2003 T-Totals For my investigational piece of coursework I will be investigating the 'T-Totals' of number grids. 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 Look at the 'T-Shape' drawn on a 9 by 9 number grid: The total of the numbers inside of the T-Shape is 1+2+3+11+20 = 37 This is called the T-Total The number at the bottom of the T-Shape is called the T-Number The T-number for this T-Shape is 20. Part 1: Investigating the relationship between the T-Total and T-Number: To begin with I drew some more T-Shapes (positions chosen at random) onto the grid to allow me to find a formula for the T-Totals a lot quicker. The results are listed 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 Red shape: T-Number = 20 and T-Total = 37 Blue shape: T-Number = 23 and T-Total = 52 Dark blue shape: T-Number = 43 and T-Total = 152 Gold shape: T-Number = 66 and T-Total = 267 I noticed that every time you translate the T-Shape one place to the right the...

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