Investigation – T-Shapes

Authors Avatar

                        Kyla Middleditch

Investigation – T-Shapes

The task set is to investigate the way the totals within a 2D ‘T-shape’ can be calculated on a grid of various sizes in various positions.

1 . Investigate the relationship between the T-Total and the T-Number.

Diagram 1.

 The area defined by cyan shading on Diagram 1 is the “T-Shape”.

I will call the total of the numbers inside the T-Shape the T-Total.

I will also consistently use one number square of the T-Shape through out my investigation to relate my formulas to. I will call this number in the shape the T-Number, this number is indicated by the bold blue font on the T-Shape in Diagram 1.

For the purpose of consistency and methodical working all diagrams in Part 1 will be displayed on

    9x9 grids.

For the T-Shape shown in Diagram 1 the total is: 1 + 2 + 3 + 11 + 20 = 37

I continued to investigate the totals of the following T-Shapes, I created each new T-Shape by moving the shape one square to the right each time across the top row of the grid.

Join now!

        

Diagram 7 – Table of Results For Diagrams 1-6

        From this table I have discovered two consistent number patterns, I can see that for every square I move the T-shape to the right, the T-total increases by five from its previous T-total on its previous position on the grid. I can also see from Diagram 8 that the difference between ((T-total and the T-Shape) N) and ((T-total and the T-Shape) N +1) is 4 each time. N = position ...

This is a preview of the whole essay