# Maths Investigation : The relationship between the base number and the T-number

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Introduction

Introduction For my course-work investigation I will be working out the relationship between the base number and the T-number. I will also be including two variables into my investigation to see how it can change the relationship between base number and T-number. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 31 33 34 35 36 37 38 39 40 41 41 42 44 43 45 47 48 49 50 51 52 53 54 55 56 57 58 59 60 To find out the formula and relationship I must firstly see if there is a pattern between one T-shape and another and any other patterns that could help me find the formula. I will also be displaying my work in graphs and tables. Number 1: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 31 33 34 35 36 37 38 39 40 41 41 42 44 43 45 47 48 49 50 51 52 53 54 55 56 57 58 59 60 The first T-shape I have indicated in red. ...read more.

Middle

70 = 110 110 / 5 = 22 Base Number = 22 Page: 5 Graph: A graph to show the relationship between the Base-Number and the T-Number From this graph we can see that the line of best fit goes through the Y=axis at -70 and that the T-number increases by 5 and the base number by 1. This backs up that the ratio between the T-number and base-number is 5:1, and that -70 is an important part of the equation I found out earlier. Variable One For my first variable I will be changing the size of my table and putting more numbers on a row to see if this has any affect on my formula or if it requires a totally different formula. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Here we are doing what we did in the last section but finding out more about the grid size and what it is cable of doing. ...read more.

Conclusion

Now I am going to rotate the angle of the T-Shape another 90 degrees to see what difference it has on the formula or if we have to make a new formula for this T-shape. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 31 33 34 35 36 37 38 39 40 41 41 42 44 43 45 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Base Number = 13 T-Number = 58 Unfortunately the 2nd formula to multiply the number of columns by 7 doesn't work when the T-shape is at this angle. Difference: 13 - 1 = 12 13 - 11 = 2 13 - 12 = 1 13 - 21 = - 8 Total = 12+2+1 - 8 = 7 So now the formula looks like this: T= 5b - 7 This is how the new formula works: 5*13 - 7 = 58 So by rotating the T-Shape by 90 degrees we are unable to use our 2nd rule to work out the last number in our formula, but rotating the T-Shape doesn't only still change the last number in the formula. ...read more.

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