Investigating T-shapes.

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Sheena Robinson        Maths Coursework        30/04/2007

Investigative Maths Coursework

We looked at a T-shape drawn on a nine width grid like this:

The total of the numbers inside the T-shape is called the T-total.

        (1+2+3+11+20=37)

The number at the end of the stem of the T-shape is the T-number. This remains the same even if you rotate the T-shape.

        

Our first task was to translate the T-shape into different positions on the same sized grid and investigate the relationship between the T-total and T-number.

        n = T-number                                        t = T-total

(By ‘difference between’ I mean the amount added or subtracted to get to the next number in the second column)

So the equation for finding the T-total anywhere on a nine width grid if you only know the T-number is 5n – 63 = t.

You can prove his by using algebra:

n + (n - 9) + (n – 18) + (n – 17) + (n – 19)

=         5n – (9 + 18 +17 + 19)

=        5n – 63

This is so because each time you move up a row on a grid you take away one grid width and down you add it. A move right and you add one, left and you take away one.

You can now carry this formula on to task two. This was to investigate the relationship between the grid width and the T-total.

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To find the equations for different grid widths I used the algebra method shown above.

8 width:

n + (n – 8) + (n – 16) + (n – 15) + (n – 17)

=        5n – (8 + 16 + 15 + 17)

=        5n – 56

9 width:         5n – 63

10 width:        

 

n + (n – 10) + (n – 20) + (n – 19) + (n – 21)

=        5n – (10 + 20 + 19 + 21)

=        5n – 70

11 width:

 

n + (n – 11) + (n – ...

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