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I am investigating the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Dan Bloom        

Introduction

I am investigating the relationship between the T-total and the T-number.

I am going to move the T until I find a pattern.

Collect the results

I started with 22.

The T-Number is 22.

The T-Total is 47 (3 + 4 + 5 + 13 + 22).

I then moved the T-Number along 1.

The T-Number is 23.

The T-Total is 52 (4 + 5 + 6 + 14 + 23).

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I then moved the T-Number along to 24.

The T-Number is 24.

The T-Total is 57 (5 + 6 + 7 + 15 + 24).

I then moved the T-Number along to 25.

The T-Number is 25.

The T-Total is 62 (6 + 7 + 8 + 16 + 25).

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This is my table of my results:

T- Number

T-Total

22

47

23

52

24

57

25

62

Patterns

I have noticed that the T- Number’s and the T-Total’s are linked. To get from 47 to 52 to 57 to 62 in the T-Total column, I have to plus 5.

...read more.

Middle

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If we add up the numbers in the T, it should add up to 67.

7 + 8 + 9 + 17 +26 = 67

This shows that the equation works.

Also there is another way of finding out if the equation works.

If you call the T-Total ‘N’ then the number above that, would be N – 9 and so on. I will show this on a diagram:

image00.png

                N – 19        N – 18        N – 17

                        N – 9

                        N

If you then put the numbers from the T, (N-19) + (N-18) + (N-17) + (N-9) + (N) = 5N – 63.

This is another way of showing that the equation works.

I will now do the same only this time I will change my grid size from 9 to 10 across. This is to see if there is a pattern.

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...read more.

Conclusion

I will now change the grid from 10 to 11. Everything else will stay the same.

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T-Number = 24

T-Total = 43

T-Number = 25

T-Total = 48

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T- Number = 26

T- Total = 53

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T- Number = 27

 T- Total = 58

This is my table of results:        

T- Number

T-Total

Because the T-Total is going up in fives I know that it is T = 5N.

5 x 24 = 120

This does not fit so if you take 72 away from 120. That fits.

Therefore the equation must be: T= 5N -72

To prove this equation works, I will use another way to show it.

image02.png

        N -         21    N - 22        N -23

             N - 11

             N

If you then put the numbers from the T, (N-11) + (N-22) + (N-23) + (N-21) + (N) = 5N – 72.

This is another way of showing that the equation works.

I will now do the same, expect the grid size will be 12 instead of 11.

...read more.

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