=33
T-number – 16
T-total – 16+10+3+4+5
=38
Algebra
T-total = (Tn - 6) + (Tn - 11) + (Tn - 12) + (Tn -13) + Tn
5Tn - 42
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T15 5 × 15 = 75 - 42 = 33
Relationship between the grid size, T-number and T-total
T15 5 × 15 = 75 - 42 = 33
Grid Size (g) = 6
42/g = 7
5Tn-42
42 can also be written as G×7 because G=6, so 6×7 = 42
So the formula is 5Tn-(G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 17. If translated (-2,-2) co-ordinates then we can see in the grid on the next page that the TTn is 27.
So if I take away 17-27 then I get -10. I took 2 factors of -10 and put them in an equation.
17-(-2×5)
17--10
=27
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×5) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 27. If translated (2,2) co-ordinates then we can see in the grid on the next page that the TTn is 17.
So if I take away 27-17 then I get 10.
27-(22+6)
27-10
=17
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+6) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and positive
5×5 Grid size investigation
T-number – 12
T-total – 12+7+1+2+3
=25
T-number – 13
T-total – 13+8+2+3+4
=30
Algebra
T-total = (Tn - 5) + (Tn - 9) + (Tn - 10) + (Tn - 11) + Tn
5Tn - 35
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T12 5 × 12 = 60 - 35 = 25
Relationship between the grid size, T-number and T-total
T12 5 × 12 = 60 - 35 = 25
Grid Size (g) = 5
35/g = 7
5Tn-35
35 can also be written as G×7 because G=5, so 5×7 = 35
So the formula is 5Tn-(G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 14. If translated (-2,-2) co-ordinates then the TTn is 22.
So if I take away 14-22 then I get -8. I took 2 factors of -8 and put them in an equation.
14-(-2×4)
14--8
=22
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 22. If translated (2,2) co-ordinates then the TTn is 14.
So if I take away 22-14 then I get 8.
22-(22+4)
22-14
=8
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and positive.
Investigation Part 3
180º Rotated T-shape 9×9 Grid size Investigation
Tn – 56
T-total – 56+65+73+74+75
=343
Tn – 57
T-total – 57+66+74+75+76
=348
Algebra
T-total = (Tn + 9) + (Tn + 17) + (Tn + 18) + (Tn + 19) + Tn
5Tn + 63
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T21 5 × 56 = 280 + 63 = 343
Relationship between the grid size, T-number and T-total
T21 5 × 56 = 280 + 63 = 343
Grid Size (g) = 9
63/g = 7
5Tn + 63
63 can also be written as G×7 because G=9, so 9×7 = 63
So the formula is 5Tn + (G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 4. If translated (-2,-2) co-ordinates then the TTn is 20.
So if I take away 4-20 then I get -16. I took 2 factors of -16 and put them in an equation.
14-(-2×8)
4--16
=20
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×8) = TTn
This formula is going to work for all 9×9 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 20. If translated (2,2) co-ordinates then the TTn is 4.
So if I take away 20-4 then I get 16.
20-(22+12)
20-16
=4
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+12) = TTn
This formula is going to work for all 9×9 Grid T-shape translations when both vectors are same and positive.
180º Rotated T-shape 8×8 Grid size Investigation
Tn – 42
T-total – 42+50+57+58+59
=266
Tn – 43
T-total – 43+51+58+59+60
=271
Algebra
T-total = (Tn + 8) + (Tn + 15) + (Tn + 16) + (Tn +17) + Tn
5Tn + 56
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T42 5 × 42 = 210 + 56 = 266
Relationship between the grid size, T-number and T-total
T42 5 × 42 = 210 + 56 = 266
Grid Size (g) = 8
56/g = 7
5Tn + 56
56 can also be written as G×7 because G=8, so 8×7 = 56
So the formula is 5Tn + (G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 4. If translated (-2,-2) co-ordinates then the TTn is 18.
So if I take away 4-18 then I get -14. I took 2 factors of -14 and put them in an equation.
4-(-2×7)
4--14
=18
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×7) = TTn
This formula is going to work for all 8×8 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 18. If translated (2,2) co-ordinates then the TTn is 4.
So if I take away 18-4 then I get 14.
18-(22+10)
18-14
=4
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+10) = TTn
This formula is going to work for all 8×8 Grid T-shape translations when both vectors are same and positive.
180º Rotated T-shape 7×7 Grid size Investigation
Tn – 30
T-total – 30+37+43+44+45
=199
Tn – 31
T-total – 31+38+44+45+46
=204
Algebra
T-total = (Tn + 7) + (Tn + 13) + (Tn + 14) + (Tn + 15) + Tn
5Tn + 49
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T30 5 × 30 = 150 + 49 = 199
Relationship between the grid size, T-number and T-total
T21 5 × 30 = 150 + 49 = 199
Grid Size (g) = 7
49/g = 7
5Tn + 49
49 can also be written as G×7 because G=7, so 7×7 = 49
So the formula is 5Tn + (G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 4. If translated (-2,-2) co-ordinates then the TTn is 16.
So if I take away 4-16 then I get -12. I took 2 factors of -12 and put them in an equation.
4-(-2×6)
4--12
=16
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×6) = TTn
This formula is going to work for all 7×7 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 16. If translated (2,2) co-ordinates then the TTn is 4.
So if I take away 16-4 then I get 12.
16-(22+8)
16-4
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+8) = TTn
This formula is going to work for all 7×7 Grid T-shape translations when both vectors are same and positive.
180º Rotated T-shape 6×6 Grid size Investigation
Tn – 20
T-total – 20+26+31+32+33
=142
Tn – 21
T-total – 21+27+32+33+34
=147
Algebra
T-total = (Tn + 6) + (Tn + 11) + (Tn +12) + (Tn + 13) + Tn
5Tn + 42
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T20 5 × 20 = 100 + 42 = 142
Relationship between the grid size, T-number and T-total
T20 5 × 20 = 100 + 42 = 142
Grid Size (g) = 6
42/g = 7
5Tn + 42
42 can also be written as G×7 because G=6, so 6×7 = 42
So the formula is 5Tn + (G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 4. If translated (-2,-2) co-ordinates then we can see in the grid on the next page that the TTn is 14.
So if I take away 4-14 then I get -10. I took 2 factors of -10 and put them in an equation.
4-(-2×5)
4--10
=14
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×5) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 14. If translated (2,2) co-ordinates then we can see in the grid on the next page that the TTn is 4.
So if I take away 14-4 then I get 10.
14-(22+6)
14-10
=4
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+6) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and positive.
180º Rotated T-shape 5×5 Grid size Investigation
Tn – 12
T-total – 12+17+21+22+23
=95
Tn – 13
T-total – 13+18+22+23+24
=100
Algebra
T-total = (Tn + 5) + (Tn + 9) + (Tn + 10) + (Tn + 11) + Tn
5Tn + 35
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T12 5 × 12 = 60 + 35 = 95
Relationship between the grid size, T-number and T-total
T21 5 × 12 = 60 + 35 = 95
Grid Size (g) = 5
35/g = 7
5Tn + 35
35 can also be written as G×7 because G=5, so 5×7 = 35
So the formula is 5Tn + (G×7)
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 4. If translated (-2,-2) co-ordinates then the TTn is 12.
So if I take away 4-12 then I get -8. I took 2 factors of -8 and put them in an equation.
4-(-2×4)
4--8
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 12. If translated (2,2) co-ordinates then the TTn is 4.
So if I take away 12-4 then I get 8.
12-(22+4)
12-4
=8
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and positive.
90º Clockwise Rotated T-shape 9×9 Grid size Investigation
Tn – 64
T-total – 64+65+66+57+75
=327
Tn – 65
T-total – 65+66+67+58+76
=332
Algebra
T-total = (Tn + 1) + (Tn + 2) + (Tn + 11) + Tn – 7 + Tn
5Tn + 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T64 5 × 64 = 320 + 7 = 327
Relationship between the grid size, T-number and T-total
T64 5 × 64 = 320 + 7 = 327
Grid Size (g) = 9
So the formula is 5Tn + 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 12. If translated (-2,-2) co-ordinates then the TTn is 28.
So if I take away 12-28 then I get -16. I took 2 factors of -16 and put them in an equation.
12-(-2×8)
12--16
=28
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×8) = TTn
This formula is going to work for all 9×9 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 28. If translated (2,2) co-ordinates then the TTn is 12.
So if I take away 28-12 then I get 16.
28-(22+12)
28-16
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+12) = TTn
This formula is going to work for all 9×9 Grid T-shape translations when both vectors are same and positive.
90º Clockwise Rotated T-shape 8×8 Grid size Investigation
Tn – 49
T-total – 49+50+51+43+58
=252
Tn – 50
T-total – 50+51+52+44+60
=257
Algebra
T-total = (Tn + 1) + (Tn + 2) + (Tn + 10) + Tn – 6 + Tn
5Tn + 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T49 5 × 49 = 245 + 7 = 252
Relationship between the grid size, T-number and T-total
T49 5 × 49 = 245 + 7 = 252
Grid Size (g) = 8
So the formula is 5Tn + 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 12. If translated (-2,-2) co-ordinates then the TTn is 26.
So if I take away 12-26 then I get -14. I took 2 factors of -14 and put them in an equation.
12-(-2×7)
12--14
=26
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×7) = TTn
This formula is going to work for all 8×8 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 26. If translated (2,2) co-ordinates then the TTn is 12.
So if I take away 26-12 then I get 14.
26-(22+10)
26-14
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+10) = TTn
This formula is going to work for all 8×8 Grid T-shape translations when both vectors are same and positive.
90º Clockwise Rotated T-shape 7×7 Grid size Investigation
Tn – 36
T-total – 36+37+38+31+45
=187
Tn – 37
T-total – 37+38+39+32+46
=192
Algebra
T-total = (Tn + 1) + (Tn + 2) + (Tn + 9) + Tn – 5 + Tn
5Tn + 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T36 5 × 36 = 180 + 7 = 187
Relationship between the grid size, T-number and T-total
T49 5 × 36 = 180 + 7 = 187
Grid Size (g) = 7
So the formula is 5Tn + 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 12. If translated (-2,-2) co-ordinates then the TTn is 24.
So if I take away 12-24 then I get -12. I took 2 factors of -12 and put them in an equation.
12-(-2×6)
12--12
=24
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×6) = TTn
This formula is going to work for all 7×7 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 24. If translated (2,2) co-ordinates then the TTn is 12.
So if I take away 24-12 then I get 12.
24-(22+8)
24-12
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+8) = TTn
This formula is going to work for all 7×7 Grid T-shape translations when both vectors are same and positive
90º Clockwise Rotated T-shape 6×6 Grid size Investigation
Tn – 25
T-total – 25+26+27+21+33
=132
Tn – 26
T-total – 26+27+28+22+34
=137
Algebra
T-total = (Tn + 1) + (Tn + 2) + (Tn + 8) + Tn – 4 + Tn
5Tn + 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T25 5 × 25 = 125 + 7 = 132
Relationship between the grid size, T-number and T-total
T25 5 × 25 = 125 + 7 = 132
Grid Size (g) = 6
So the formula is 5Tn + 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 10. If translated (-2,-2) co-ordinates then we can see in the grid on the next page that the TTn is 20.
So if I take away 10-20 then I get -10. I took 2 factors of -10 and put them in an equation.
10-(-2×5)
10--10
=20
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×5) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 20. If translated (2,2) co-ordinates then we can see in the grid on the next page that the TTn is 10.
So if I take away 20-10 then I get 10.
20-(22+6)
20-10
=10
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+6) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and positive.
90º Clockwise Rotated T-shape 5×5 Grid size Investigation
Tn – 16
T-total – 16+17+18+13+23
=87
Tn – 17
T-total – 17+18+19+14+24
=92
Algebra
T-total = (Tn + 1) + (Tn + 2) + (Tn + 7) + Tn – 3 + Tn
5Tn + 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T16 5 × 16 = 80 + 7 = 87
Relationship between the grid size, T-number and T-total
T16 5 × 16 = 80 + 7 = 87
Grid Size (g) = 5
So the formula is 5Tn + 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 8. If translated (-2,-2) co-ordinates then the TTn is 16.
So if I take away 8-16 then I get -8. I took 2 factors of -8 and put them in an equation.
8-(-2×4)
8--8
=16
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 16. If translated (2,2) co-ordinates then the TTn is 8.
So if I take away 16-8 then I get 8.
16-(22+4)
16-4
=8
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and positive.
90º Anti-Clockwise Rotated T-shape 9×9 Grid size Investigation
Tn – 66
T-total – 66+65+64+55+73
=323
Tn – 67
T-total – 67+66+65+56+74
=328
Algebra
T-total = (Tn - 1) + (Tn - 2) + (Tn - 11) + (Tn + 7) + Tn
5Tn - 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T66 5 × 66 = 330 – 7 = 323
Relationship between the grid size, T-number and T-total
T66 5 × 66 = 330 - 7 = 323
Grid Size (g) = 9
So the formula is 5Tn - 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 14. If translated (-2,-2) co-ordinates then the TTn is 30.
So if I take away 14-30 then I get -16. I took 2 factors of -16 and put them in an equation.
14-(-2×8)
14--16
=30
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×8) = TTn
This formula is going to work for all 9×9 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 30. If translated (2,2) co-ordinates then the TTn is 14.
So if I take away 30-14 then I get 16.
30-(22+12)
30-16
=14
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+12) = TTn
This formula is going to work for all 9×9 Grid T-shape translations when both vectors are same and positive.
90º Anti-Clockwise Rotated T-shape 8×8 Grid size Investigation
Tn – 51
T-total – 51+50+49+41+57
=248
Tn – 52
T-total – 52+51+50+42+58
=253
Algebra
T-total = (Tn - 1) + (Tn - 2) + (Tn - 10) + (Tn + 6) + Tn
5Tn - 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T51 5 × 51 = 255 – 7 = 248
Relationship between the grid size, T-number and T-total
T51 5 × 51 = 255 - 7 = 248
Grid Size (g) = 8
So the formula is 5Tn - 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 13. If translated (-2,-2) co-ordinates then the TTn is 27.
So if I take away 13-27 then I get -14. I took 2 factors of -14 and put them in an equation.
13-(-2×7)
13--14
=27
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×7) = TTn
This formula is going to work for all 8×8 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 27. If translated (2,2) co-ordinates then the TTn is 13.
So if I take away 27-13 then I get 14.
27-(22+10)
27-14
=13
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+10) = TTn
This formula is going to work for all 8×8 Grid T-shape translations when both vectors are same and positive.
90º Anti-Clockwise Rotated T-shape 7×7 Grid size Investigation
Tn – 38
T-total – 38+37+36+29+43
=183
Tn – 39
T-total – 39+38+37+30+44
=188
Algebra
T-total = (Tn - 1) + (Tn - 2) + (Tn - 9) + (Tn + 5) + Tn
5Tn - 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T38 5 × 38 = 190 – 7 = 183
Relationship between the grid size, T-number and T-total
T38 5 × 38 = 190 - 7 = 183
Grid Size (g) = 7
So the formula is 5Tn - 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 12. If translated (-2,-2) co-ordinates then the TTn is 24.
So if I take away 12-24 then I get -12. I took 2 factors of -12 and put them in an equation.
12-(-2×6)
12--12
=24
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×6) = TTn
This formula is going to work for all 7×7 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 24. If translated (2,2) co-ordinates then the TTn is 12.
So if I take away 24-12 then I get 12.
24-(22+8)
24-12
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+8) = TTn
This formula is going to work for all 7×7 Grid T-shape translations when both vectors are same and positive
90º Anti-Clockwise Rotated T-shape 6×6 Grid size Investigation
Tn – 27
T-total – 27+26+25+19+31
=128
Tn – 28
T-total – 28+27+26+20+32
=133
Algebra
T-total = (Tn - 1) + (Tn - 2) + (Tn - 8) + (Tn + 4) + Tn
5Tn - 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T27 5 × 27 = 135 – 7 = 128
Relationship between the grid size, T-number and T-total
T27 5 × 27 = 135 - 7 = 128
Grid Size (g) = 6
So the formula is 5Tn - 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 12. If translated (-2,-2) co-ordinates then we can see in the grid on the next page that the TTn is 22.
So if I take away 12-22 then I get -10. I took 2 factors of -10 and put them in an equation.
12-(-2×5)
12--10
=22
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×5) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 22. If translated (2,2) co-ordinates then we can see in the grid on the next page that the TTn is 12.
So if I take away 22-12 then I get 10.
22-(22+6)
22-10
=12
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+6) = TTn
This formula is going to work for all 6×6 Grid T-shape translations when both vectors are same and positive.
90º Anti-Clockwise Rotated T-shape 5×5 Grid size Investigation
Tn – 18
T-total – 18+17+16+11+21
=83
Tn – 19
T-total – 19+18+17+12+22
=88
Algebra
T-total = (Tn - 1) + (Tn - 2) + (Tn - 7) + (Tn + 3) + Tn
5Tn - 7
Table
The difference between the T-totals is 5
Now I am going to check whether my formula is correct
T18 5 × 18 = 90 – 7 = 83
Relationship between the grid size, T-number and T-total
T18 5 × 18 = 90 - 7 = 83
Grid Size (g) = 5
So the formula is 5Tn - 7
Relationship between the grid size, T-number, T-total and Translation
Investigation of negative vectors
The vectors I have chosen for this is (-2,-2)
Tn (-2,-2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 10. If translated (-2,-2) co-ordinates then the TTn is 18.
So if I take away 10-18 then I get -8. I took 2 factors of -8 and put them in an equation.
10-(-2×4)
10--8
=18
If I replace the numbers with Algebra then I can find out the equation
Tn-(V×4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and negative.
Investigation of Positive Vectors
The vectors I have chosen for this is (2,2)
Tn (2,2) = TTn (Translated Tn)
To find out TTn I am going to take a T-shape randomly and see whether there is any relationship between the Tn and TTn.
I have chosen the T-shape which has the Tn of 18. If translated (2,2) co-ordinates then the TTn is 10.
So if I take away 18-10 then I get 8.
18-(22+4)
18-4
=16
If I replace the numbers with Algebra then I can find out the equation
Tn-(V2+4) = TTn
This formula is going to work for all 5×5 Grid T-shape translations when both vectors are same and positive.
- By this investigation I found out that the relationship between the T-number, T-total, Grid Size and Translation varies.
- I found the formula for the relationship between T-number and T-total by using algebra in the T-shape and put it in an equation.
- After solving the equation I found the formulae.
- I then used a table to represent my investigation.
- I have also used the re-arranging method to find out the formulae.
- Taking the 9×9 Grid Size Investigation I have shown below how I found out the formulae using re-arranging method.
- Y/X
Y = mx + c
Y = 5x + 63
10/2 = 5x = Tn
Y = 5Tn +63
- After that I investigated on the relationship between Tn, T-total and Grid Size and found the formula by representing the T-shape with Algebra.
- Then I transformed the T-shape to both positive vectors and negative vectors for each grid size and every T-shapes.
- I have learned from this investigation that there is endless possibilities of investigating the T-shapes by varying the Grid size and the type of transformation.
