Investigating a T shape which will be on a 9x9 grid and have an area of 5 squares.

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T-Total

Maths Coursework February 2004

Introduction

In this piece of coursework I will be investigating a T shape which will be on a 9x9 grid and have an area of 5 squares. The T-total is all the numbers in the T shape added up together and the T-number is the bottom number in the T highlighted in green below.

 

In this T there are five numbers 2, 3, 4, 12 and 21 if you add these numbers up it makes the T-total    

                           2+3+4+12+21=42

The highest number in this T is 21 so 21 would be the T-number.

Once I have investigated that I will investigate whether or not using grids of different sizes would make a difference to the formulae and any relationship found. I will try and find a relationship between the T-Total, the T-Number and the grid size.

In the third part of this coursework I will use different transformations and combinations of transformations. I will investigate the relationship between the T-Total, the T-Number, the grid size and the transformations.  

After that I drew a table of the first few T-Numbers and T-Totals for the first few T’s.

The first T is the T shown in the introduction, the second T is

And so on.

In the table there is a pattern, when the T-Number goes up one the T-Total goes up five, this pattern also works for T’s anywhere on the grid

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This pattern occurs because each number inside the T goes up one as you move it across the grid and there are five numbers in the T. This pattern also works for every T on the grid.

The next thing I did was name each of the squares in relation to the T-Number  

The N stands for the T-Number and the other numbers are in relation ...

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