T Totals Maths Coursework

Investigating the Relationship Between T-totals and T-numbers

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Investigating the Relationship Between T-totals and T-numbers

In my maths coursework I will be focusing on T-Numbers. I will be
investigating the relationship between T-totals and T-numbers.

In my investigation I will also try and find out the relationships
between the grid size and the transformations. The T-number is always
the number at the bottom of the T shape and the T-total is always all
the numbers inside the T shape added together.

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[IMAGE]


9 By 9 Grid:

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The total of the numbers inside the T-shape is 1+2+3+11+20=37 this is
called the T-total.

The number at the bottom of the T-shape is called the T-number.

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For
the t-shape in red the T-number for this T-shape is 20. When you take
the other numbers in the T-Shape away from the T-Number you get
something like this:

N-17

N-18

N-19

N-9

N

When you get the T-shape like this you can see that the centre numbers
always go up by 9's because of the table size, with the table set out
like this a formula can be worked out to find the formula to find any
T-Total on this size grid. This can be achieved by using this below:

T-Total =A

T-Number =N

T-total = N-19+N-18+N-17+N-9+N

So the formula for this grid is: 5N-63

The Testing Process for grid 9x9:

Testing the formula can be done using the variables A and N.

T-Total =A

T-Number =N

(I have used the number 5 in the formula to multiply N because there
are 5 grid boxes in one T shape on any grid)

(Example T-number = 20)

A = 5N-63

N = 20

A = 5x20

= 100-63 = 37

I will now test to see if this will work any were on the 9x9 grid.

N=43

A=5x43 24+25+26+34+43=152

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A=215-63


A=152
-----


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N=49
====

A=5x49 30+31+32+40+49=182

A=245-63

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49

A=182

I have fully tested the formula for three different T-numbers and the
formula works any were correctly on a 9 by 9 grid.

The full formula for this size grid is: A=5N-63

6 By 6 Grid:

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If you take the other numbers in the T-Shape away from the T-Number
you get a T-Shape like this.

T-Total =A

T-Number =N

N-13

N-12

N-11

N-6

N

When you get the T-shape like this you can see that the centre numbers
always go up by 6's because of the table size, with the table set out
like this a formula can be worked out to find the formula to find any
T-Total on this size grid. This can be achieved by using this below:

T-Total = N-13+N-12+N-11+N-6+N

= 5N-42

The Testing Process for grid 6x6:

Testing the formula can be done using the variables A and N.

T-Total =A

T-Number =N

(I have used the number 5 in the formula to multiply N because there
are 5 grid boxes in one T shape on any grid)

A = 5N-42

N = 14

A = 5x14

= 70-42 = 28

I will now test to see if this will work any were on the 6x6 grid.

N=22

A=5x22 9+10+11+16+22=68

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A=110-42


A=68
----


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N=35
====

A=5x35 22+23+24+29+35=133

A=175-42

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A=113


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N=32
====

A=5x32 19+20+21+26+32=118

A=160-42

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32

A=118

I have fully tested the formula for three different T-numbers and the
formula works any were correctly on a 6 by 6 grid.

The full formula for this size grid is: A=5N-42



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