Maths T-Shapes Investigation

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Anand Patel                    Mathematics Coursework                                   Page  of

QUESTION 1

A T-shape is drawn onto grid like the one below (fig.1.1). The grid can be of any size, e.g. 9x9, 4x4, 100x100 etc. In question 1 the only grid size that will be used will be the 9x9 size.

        

(fig.1.1)

The T-shape has a T-number, this the number that is at the bottom of the T-shape. The T-number of the T-shape in fig.1 is 18.

The T-total of the T-shape is all of the numbers the total of all of the numbers in the T-shape. The T-total of T-shape in fig.1.1 is:

        7+8+9+13+18= 55

I will now investigate the relationship between the T-total and the T-number.

The coloured section in Fig.1.2 shows all of the possible positions that the T-number could be located in.

 

(Fig.1.2)

I noticed that if the number at the bottom of the T-shape is T, the   number above it is T-9. This is because if you start at the T and move backwards across the grid 9 squares, you will finish at the   number which is directly above the T. This can be seen in Fig.1.3, it shows the general structure of the grid.

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N.B- The section of grid 9 below does not show the general formulae for the grid, it shows the formulae if the T- number was placed in the position that it is in now. Therefore if the T-number was placed in a different position than the formulae in the grid will change accordinglly.

               

(Fig.1.3)                                                      Section from 9x9 grid

Therefore the general ...

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