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T Total - Investigation into T-shapes

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Introduction

T Total - Investigation into T-shapes! Aim 1- the solution You need to draw your own grids T69= 50+51+52+60+69 =282 T22=3+4+5+13+22 =47 In the diagram below it shows the difference between the T-number and the other numbers. First is the T-shape in question: 1 2 3 11 20 This is the T-shape and here is the Difference T-shape: N-19 N-18 N-17 N-9 N This shows the difference N= T-number In the T on the previous page, I have noticed that the first difference from N is 9, which is also the Width of the square. I'll put that idea into another T. ...read more.

Middle

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. ...read more.

Conclusion

St64=26+27+28+29+30+40+52+64 =296 I think I can work out the formula using my previous method so: 12+24+36+(436)=216 216/12 =18 This means the formula is: 8N-18W=T-total 8N= number of integers in the T-shape 18W=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. ...read more.

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