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T-total.I have taken the T-shape template from the example and moved it along the row from the T-number 20 to 26. I will then work out the T-total of each T-number by adding all the numbers in the T-shape.

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Introduction

T-total Coursework

Part 1 – Investigate the relationship between the T-total and the             T-number

T-shapeimage00.png

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image01.png

T-number

I have taken the T-shape template from the example and moved it along the row from the T-number 20 to 26. I will then work out the T-total of each T-number by adding all the numbers in the T-shape. The results were as follows:

T-number

T-total

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42

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47

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57

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52

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67

I have found a pattern emerging, which is, as the T-number increases by 1 the T-total increases by 5. I will try and find out the relationship between the T-total and the other numbers in the T-shape.

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I have chosen a random T-number of 60 and will try and find a relationship between all of the other numbers in the T-shape.

First I will try and take away all the other numbers from the T-number:

60-41 = 19

60-42 = 18

60-43 = 17

60-51 = 9

I will now try the same thing again but using a different T-number to see if the same pattern occurs:

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I will use the T-number

of 31

...read more.

Middle

337

I have substituted the T-number into the equation

My formulae is correct as if I were to do the sum manually without using the formulae by adding 61+62+63+71+80 (all the numbers in the T-shape) it will equal 337 the same answer I got using my formulae. This proves that my formulae Is correct.

Part 2 – Use grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total, the T-numbers and the grid size.

To investigate the relationship between the T-total, T-number and the grid size I will need to put the template into algebraic form.

image10.png

image29.pngimage03.pngimage27.pngimage28.pngimage10.pngimage10.pngimage10.png

image02.pngimage03.pngimage02.pngimage04.png

image06.pngimage07.pngimage05.png

image05.png

I have changed the template into algebraic form. When I added the equations in the T-shape (Tn + Tn-g + Tn-2g-1 + Tn-2g + Tn-2g+1) and got the answer 5Tn – 7g, where Tn is the T-number and g is the grid size.

I will now try and see if the formulae are correct for different grid sizes.

...read more.

Conclusion

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In my grid I have chosen a random T-number of 40 and will find a formulae for rotation

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                                        Tn-19 + Tn-18 + Tn-17 + Tn-image11.pngimage09.pngimage08.png

=                                        9 + Tn image12.png

                                        = 5Tn-63

image13.png

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                                        Tn + Tn+1 + Tn+2 + Tn-7 +         

=                                        Tn+11                                                                         = 5Tn+7image17.pngimage16.pngimage15.pngimage13.png

image18.png

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                        Tn + Tn+9 + Tn+17 +         

=                         Tn+18 + Tn+19image19.png

                        = 5Tn+63

image22.pngimage21.pngimage20.png

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=                        Tn-11 + Tn-2 +Tn+7 + Tn-1 image13.pngimage23.pngimage25.pngimage24.png

                        + Tnimage26.png

                        = 5Tn-7

I can see from this that:

When the T is at 0° the formulae will be 5T-7g

When the T is at 90° the formulae will be 5Tn+7

When the T is at 180° the formulae will be 5Tn+7g

When the T is at 240° the formulae will be 5Tn-7

I will now test my formulae to see if they are correct by using the formulae I found and seeing if I get the same results as I would doing it manually.

0°90°

5Tn-7g                                5Tn+7

5x40 – 7x9 =137                                5x40+7 =207

180°240°

5Tn+7g                                5Tn-7

5x40 + 7x9 =263                                5x40-7 = 193

Now I will do the calculations manually:

0°90°

Tn=40                                                Tn=40

Tn+21+22+23+31 = 137                 Tn+41+42+33+51 =207

180°240°

Tn=40                                Tn=40

Tn+49+57+58+59 =263                Tn+39+38+47+29 =193

I got the same results as I did by using my formulae this proves that my formulae is correct for rotation.

...read more.

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