T-Total Investigation

Maths Coursework – T-Total

I have looked at the T-Number and I called it N. Then I saw how much difference there was between the T-Number and the other numbers in the T. when I did this the numbers came out like this: 20, 20-9, 20-19, 20-18, 20-17. These sums when added together will come out with the T-Total. The T-Total is 37. I have tried out this method with other T-Numbers and the results ended up like this.

T-Number T-Total

This rule showed a pattern. The next T-Total has 5 added to it. This means that there has to be a 5 in the algebraic rule. Because there are 5 squares in a T the 5 in the rule will be 5N. 5N for the first T-Number is 100. To get to the proven T-Total for this T-Number I have to minus 63. So the rule for this T-Number is 5N – 63. I will now test whether this rule works for the other

T-Numbers. 5 times 25 is 125, then 125 minus 63 is 62, this is the correct T-Total. 5 times 28 is 140, then minus 63 is 77, again this is the correct T-Total.

The Nth Term for finding out the T-Total from the T-Number is 5N – 63.

Now I will try to find the rules for different size grids. First of all I will try a 10x10 grid. I have started of with a T-Number of 22. I will multiply that by 5, that equals 110. Then I will do the same as above to find ...

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T-Numbers. 5 times 25 is 125, then 125 minus 63 is 62, this is the correct T-Total. 5 times 28 is 140, then minus 63 is 77, again this is the correct T-Total.

The Nth Term for finding out the T-Total from the T-Number is 5N – 63.

22, 22-10, 22-20, 20-21, 20-19. This ends up minusing 70 from the 5N.The final T-Total now is 40. I will now try this for other T-Numbers. 5 times 25 is 125, then minus 70 is 55. I tested this and it is correct. 5 times 26 is 130 then minus 70 is 60. This is correct aswell.

The Nth Term for finding out the T-Total on a 10x10 grid is 5N – 70.

I will now try on an 8x8 grid. I will start off with the T-Number 30. 30 times 5 is 150. Now I will do the same as before to get the T-Total. 30, 30-8, 30-16, 30-17, 30-15. Now I have to minus 56. This comes out with 94. I added up the numbers and they do equal 94. I tried this for other T-Numbers and it worked.

The Nth Term for finding out the T-Total on an 8x8 grid is 5N – 56.

I have looked at all of the Nth Terms and I can see a pattern. The number needed to minus to get the T-Total is related to the grid size. The grid size times 7 equals the number. 7x8=56. 7x9=63. 7x10=70. This means that there is a better Nth Term that covers grid size, and the T-Number.

The overall Nth Term is 5N – (7G). This work on any T-Number on any grid.

Now that I have got all of the rules for the T, I have decided to turn the T upside down. I will start on a 9x9 grid. I will start with the T-Number 2. I have to add this time to get the T-Total. 2, 2+9, 2+18, 2+17, 2+19. This comes out with 5N + 63. This is the opposite to the right way up T. This works with other T-Numbers. I have also tried this for the different grid sizes. For 10x10 the rule also is the opposite. I have used the T-Number 2 again. 2, 2+10, 2+20, 2+21, 2+19. This is 5N +70. I have done the same on an 8x8 grid and it is also opposite. This means that the overall rule must be opposite too.

The overall Nth Term for upside down T is 5N + (7G).

Now that I have done the upside down rule, I will do it with the T on its side. I will do it on a 9x9 grid first. I have got the T-Number as12 and it is facing right. I will do the same as before to find out what I need to minus to get the T-Total. 12, 12-1, 12-2, 12-11, 12+7. It all adds up to 5N – 7. After adding the numbers up, this rule is correct. I have done it using a different T-Number. 5 times 40 is 200 then minus seven is 193. 40 + 39 + 38 + 47 + 29 = 193. The rule works.

The Nth Term for the T on its side facing right on a 9x9 grid is 5N – 7.

I will guess that for the T facing left it will be the opposite of facing right. I will now test my theory with the T-Number 10. 10, 10+1, 10+2, 10-7, 10+11. It does come out with 5N +7. This works for other T-Numbers aswell.

The Nth Term for the T on its side facing left on a 9x9 grid is 5N + 7.

I will now try it on a 10x10 grid facing right with the T-Number 13. 13, 13-1, 13-2, 13-12, 13+8. It is again 5N – 7. So I predict that it will be the opposite for the facing left. I will test it with the T-Number 15. 15, 15+1, 15+2, 15+12, 15-8. It does come out as 5N + 7. Because the rule is the same for the grid sizes 9x9 and 10x10 grid that it will be the same again for the grid size 8x8. I will now test it with the T facing left with the T-Number 9. 9, 9+1, 9+2, 9-6, 9+10. This adds up to 5N + 7. Now I will try it facing right with the T-Number 11. 11, 11-1, 11-2, 11+6, 11-10. I adds up to 5N – 7 again.

The overall Nth Term for the T on its side facing left on is 5N + 7.

The overall Nth Term for the T on its side facing right on is 5N - 7.