T Total - Investigation into T-shapes

N-W

N

This is the same thing as before but shown algerbrecly.

The formula for the Value of the T-total now is shown as:

5N-7W=T-total

Aim 2- different sizes and relationship

I know this works for the grid 9 by 9 but I'm not sure if it'll work for any other grids.

You need to draw your own grids

T22=1+2+3+12+22

=42 I notice this is five more than 9 by 9

T69=48+49+50+59+69

=275 Obviously no pattern there.

Method test.

(695)-70=275 it worked

My method seems to have worked out.

You need to draw your own grids

As there are 10 in each row it's obvious that the row above will be 10 less than the row below. So 68 is 10 less than the T-number 78. If you calculate the whole T you realise that row 2 is 10 less than row 1 and row 3 is 20 less than row 1,but there are three relevant numbers in row 3 which are 19 less and 21 less than the T-number. These cancel out to form 20 each, so finally we get (110)+(610)=(710)

=70

Or =7W

You need to draw your own grids

T62=37+38+39+50+62 also =(625)-(712)

= 226 =226

T141=116+117+118+129+141 also =(1415)-(712)

=621 =621

Aim3- Transformations stretches and there effects on the formula

I will do this with a 12 by 12 first, as this will give me enough accuracy to start with.

2 3 4 5 6 7 8 9 10 11 12

3 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 82 83 84

85 86 87 88 89 90 91 92 93 94 95 96

97 98 99 100 101 102 103 104 105 106 107 108

09 110 111 112 113 114 115 116 117 118 119 120

21 122 123 124 125 126 127 128 129 130 131 132

33 134 135 136 137 138 139 140 141 142 143 144

Stretch A will be called ST64 as it starts at 64; it is a stretch of 2 in both directions.

St64=26+27+28+29+30+40+52+64

=296

I think I can work out the formula using my previous method so:

2+24+36+(436)=216

216/12 =18

This means the formula is:

8N-18W=T-total

8N= number of integers in the T-shape

8W=difference number calculated

Conclusion:

The size of the T-shape calculates the number before N in the formula and the grid size calculates the value of W. the number before W is calculated by looking at the rows and finding how many rows away from the T-number they are. If the T is regular then the W number is negative but if the T is flipped upside down, the W number is positive.

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